In [1]:
import pandas as pd
import numpy as np
import missingno as msno
import datetime as dt
from stringcase import snakecase


#with np.printoptions(threshold=np.inf):
In [2]:
# create a new class which makes it possible to format text in colour or bold etc.

class color:
   PURPLE = '\033[95m'
   CYAN = '\033[96m'
   DARKCYAN = '\033[36m'
   BLUE = '\033[94m'
   GREEN = '\033[92m'
   YELLOW = '\033[93m'
   RED = '\033[91m'
   BOLD = '\033[1m'
   UNDERLINE = '\033[4m'
   END = '\033[0m'
    
In [3]:
autos = pd.read_csv("autos.csv",encoding='Latin-1')

Analyzing Used Car Listings on eBay Kleinanzeigen

This is an analysis of used car listings on eBay Kleinanzeigen, a classifieds section of the German eBay website.

During this analysis data will be cleaned and explored.\ After cleaning and exploration the top ten car brands will be analysed in more detail (mean price and mean mileage).\ Lastly the effect of mileage on price will be investigated.

The dataset was originally scraped and uploaded to Kaggle.\ The version of the dataset that is used for this analysis is a sample of 50,000 data points that was prepared by Dataquest including simulating a less-cleaned version of the data.

Short exploration

In [4]:
autos.head(5)
Out[4]:
dateCrawled name seller offerType price abtest vehicleType yearOfRegistration gearbox powerPS model odometer monthOfRegistration fuelType brand notRepairedDamage dateCreated nrOfPictures postalCode lastSeen
0 2016-03-26 17:47:46 Peugeot_807_160_NAVTECH_ON_BOARD privat Angebot $5,000 control bus 2004 manuell 158 andere 150,000km 3 lpg peugeot nein 2016-03-26 00:00:00 0 79588 2016-04-06 06:45:54
1 2016-04-04 13:38:56 BMW_740i_4_4_Liter_HAMANN_UMBAU_Mega_Optik privat Angebot $8,500 control limousine 1997 automatik 286 7er 150,000km 6 benzin bmw nein 2016-04-04 00:00:00 0 71034 2016-04-06 14:45:08
2 2016-03-26 18:57:24 Volkswagen_Golf_1.6_United privat Angebot $8,990 test limousine 2009 manuell 102 golf 70,000km 7 benzin volkswagen nein 2016-03-26 00:00:00 0 35394 2016-04-06 20:15:37
3 2016-03-12 16:58:10 Smart_smart_fortwo_coupe_softouch/F1/Klima/Pan... privat Angebot $4,350 control kleinwagen 2007 automatik 71 fortwo 70,000km 6 benzin smart nein 2016-03-12 00:00:00 0 33729 2016-03-15 03:16:28
4 2016-04-01 14:38:50 Ford_Focus_1_6_Benzin_TÜV_neu_ist_sehr_gepfleg... privat Angebot $1,350 test kombi 2003 manuell 0 focus 150,000km 7 benzin ford nein 2016-04-01 00:00:00 0 39218 2016-04-01 14:38:50
In [5]:
autos.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 50000 entries, 0 to 49999
Data columns (total 20 columns):
 #   Column               Non-Null Count  Dtype 
---  ------               --------------  ----- 
 0   dateCrawled          50000 non-null  object
 1   name                 50000 non-null  object
 2   seller               50000 non-null  object
 3   offerType            50000 non-null  object
 4   price                50000 non-null  object
 5   abtest               50000 non-null  object
 6   vehicleType          44905 non-null  object
 7   yearOfRegistration   50000 non-null  int64 
 8   gearbox              47320 non-null  object
 9   powerPS              50000 non-null  int64 
 10  model                47242 non-null  object
 11  odometer             50000 non-null  object
 12  monthOfRegistration  50000 non-null  int64 
 13  fuelType             45518 non-null  object
 14  brand                50000 non-null  object
 15  notRepairedDamage    40171 non-null  object
 16  dateCreated          50000 non-null  object
 17  nrOfPictures         50000 non-null  int64 
 18  postalCode           50000 non-null  int64 
 19  lastSeen             50000 non-null  object
dtypes: int64(5), object(15)
memory usage: 7.6+ MB

Dataframe of 50,000 rows and 20 columns.

Column description can be seen below:

Column Description
dateCrawled When this ad was first crawled, all field-values are taken from this date
name Name of the car
seller Whether the seller is private or a dealer
offerType The type of listing
price The price on the ad to sell the car
abtest Whether the listing is included in an A/B test
vehicleType The vehicle Type
yearOfRegistration The year in which the car was first registered
gearbox The transmission type
powerPS The power of the car in PS
model The car model name
odometer How many kilometers the car has driven
monthOfRegistration The month in which the car was first registered
fuelType What type of fuel the car uses
brand The brand of the car
notRepairedDamage If the car has a damage which is not yet repaired
dateCreated The date on which the eBay listing was created
nrOfPictures The number of pictures in the ad
postalCode The postal code for the location of the vehicle
lastSeenOnline When the crawler saw this ad last online

The following columns seem to contain numeric data but are currently stored as object data:

  • price
  • odometer

Cleaning of data

There are five columns that have null values:

  • vehicleType
  • gearbox
  • model
  • fuelType
  • notRepairedDamage

None of these columns have more than 20% null values.

In [6]:
msno.bar(autos)
Out[6]:
<AxesSubplot:>

The column names use camelcase instead of Python's preferred snakecase.\ In below chunk of code column names will be converted from camelcase to snakecase.\ Furthermore, some of the column names will be renamed based on the data dictionary to be more descriptive.

In [7]:
#turning camelcase columns into snakecase columns
snakecase_col = []    
    
for col in autos.columns:
    col = snakecase(col)
    snakecase_col.append(col)
    
autos.columns = snakecase_col

#renaming some columns by using a for loop with old and new values
rename_columns = [
    ['year_of_registration','registration_year'],
    ['month_of_registration','registration_month'],
    ['not_repaired_damage','unrepaired_damage'],
    ['date_created','ad_created'],
    ['power_p_s','power_PS']
]

for old_col, new_col in rename_columns:
    autos.rename({old_col: new_col},axis=1,inplace=True)
In [8]:
autos.describe(include='all')
Out[8]:
date_crawled name seller offer_type price abtest vehicle_type registration_year gearbox power_PS model odometer registration_month fuel_type brand unrepaired_damage ad_created nr_of_pictures postal_code last_seen
count 50000 50000 50000 50000 50000 50000 44905 50000.000000 47320 50000.000000 47242 50000 50000.000000 45518 50000 40171 50000 50000.0 50000.000000 50000
unique 48213 38754 2 2 2357 2 8 NaN 2 NaN 245 13 NaN 7 40 2 76 NaN NaN 39481
top 2016-03-16 21:50:53 Ford_Fiesta privat Angebot $0 test limousine NaN manuell NaN golf 150,000km NaN benzin volkswagen nein 2016-04-03 00:00:00 NaN NaN 2016-04-07 06:17:27
freq 3 78 49999 49999 1421 25756 12859 NaN 36993 NaN 4024 32424 NaN 30107 10687 35232 1946 NaN NaN 8
mean NaN NaN NaN NaN NaN NaN NaN 2005.073280 NaN 116.355920 NaN NaN 5.723360 NaN NaN NaN NaN 0.0 50813.627300 NaN
std NaN NaN NaN NaN NaN NaN NaN 105.712813 NaN 209.216627 NaN NaN 3.711984 NaN NaN NaN NaN 0.0 25779.747957 NaN
min NaN NaN NaN NaN NaN NaN NaN 1000.000000 NaN 0.000000 NaN NaN 0.000000 NaN NaN NaN NaN 0.0 1067.000000 NaN
25% NaN NaN NaN NaN NaN NaN NaN 1999.000000 NaN 70.000000 NaN NaN 3.000000 NaN NaN NaN NaN 0.0 30451.000000 NaN
50% NaN NaN NaN NaN NaN NaN NaN 2003.000000 NaN 105.000000 NaN NaN 6.000000 NaN NaN NaN NaN 0.0 49577.000000 NaN
75% NaN NaN NaN NaN NaN NaN NaN 2008.000000 NaN 150.000000 NaN NaN 9.000000 NaN NaN NaN NaN 0.0 71540.000000 NaN
max NaN NaN NaN NaN NaN NaN NaN 9999.000000 NaN 17700.000000 NaN NaN 12.000000 NaN NaN NaN NaN 0.0 99998.000000 NaN

What can be seen is that columns "seller" and "offer_type" consist of almost all the same values.\ Therefore, these columns are deemed unuseful for further analysis and will be dropped from the dataframe.

In [9]:
#remove columns that provide unuseful data
autos.drop(['seller','offer_type'],axis=1,inplace=True)

Exploration of price and odometer_km

As mentioned before, there are two columns which contain numeric data that need to be reformatted.\ This will be done below. Afterwards they will be investigated for the presence of outliers.

In [10]:
#price
autos['price'] = (autos['price']
                  .str.replace("$","")
                  .str.replace(",","")
                  .astype(float)
                  #.apply('{:,}'.format) # I thought to use this to format a 1000 separator, 
                                         # but this changes the float into an object at the same time. 
                                         # Someone knows how to prevent this?
                 )


#odometer
autos['odometer'] = (autos['odometer'].
                     str.replace("km","").
                     str.replace(",","").
                     astype(int)
                    )

autos.rename({'odometer': 'odometer_km'},axis=1,inplace=True)
<ipython-input-10-1092ff9012d8>:2: FutureWarning: The default value of regex will change from True to False in a future version. In addition, single character regular expressions will*not* be treated as literal strings when regex=True.
  autos['price'] = (autos['price']

The columns 'price' and 'odometer_km' have now succesfully been transformed to integer values.\ They will now be further analysed in order to check for outliers that might need to be removed.

In [11]:
def explore_series(dataframe, column, value_counts=False): #define a function to give detailed info about a column
    
    # length of .unique()
    template = (color.BOLD + "Number of unique values in column " 
                + color.RED + column + color.END 
                + color.BOLD + " is " 
                + color.RED + "{:,} " + color.END)
    print(template.format(len(dataframe[column].unique())))
    print('\n')
    
    # .describe()
    print(color.BOLD + "Descriptive statistics of column " 
          + color.RED + column + color.END)
    print(dataframe[column].describe())
    print('\n')
    
    # .value_counts (put into a dataframe to calculate cumulative percentages as well)
    if value_counts:
        print(color.BOLD + "Unique values with their respective counts:" + color.END)
        with pd.option_context('display.max_rows', None, 'display.max_columns', None): 
            df = dataframe[column].value_counts().sort_index(ascending=True).to_frame()
            df.columns = ['count']                #rename column to 'count'
            df.index.name = column                #rename index to column thats being explored
            df['cum_sum'] = df['count'].cumsum()  #calculating cumulative sum
            df['cum_perc'] = round(100*df.cum_sum/df['count'].sum(),2)  #calculating cumulative perc.
            print(df)
In [12]:
explore_series(autos,"price", value_counts=True)
Number of unique values in column price is 2,357 


Descriptive statistics of column price
count    5.000000e+04
mean     9.840044e+03
std      4.811044e+05
min      0.000000e+00
25%      1.100000e+03
50%      2.950000e+03
75%      7.200000e+03
max      1.000000e+08
Name: price, dtype: float64


Unique values with their respective counts:
            count  cum_sum  cum_perc
price                               
0.0          1421     1421      2.84
1.0           156     1577      3.15
2.0             3     1580      3.16
3.0             1     1581      3.16
5.0             2     1583      3.17
8.0             1     1584      3.17
9.0             1     1585      3.17
10.0            7     1592      3.18
11.0            2     1594      3.19
12.0            3     1597      3.19
13.0            2     1599      3.20
14.0            1     1600      3.20
15.0            2     1602      3.20
17.0            3     1605      3.21
18.0            1     1606      3.21
20.0            4     1610      3.22
25.0            5     1615      3.23
29.0            1     1616      3.23
30.0            7     1623      3.25
35.0            1     1624      3.25
40.0            6     1630      3.26
45.0            4     1634      3.27
47.0            1     1635      3.27
49.0            4     1639      3.28
50.0           49     1688      3.38
55.0            2     1690      3.38
59.0            1     1691      3.38
60.0            9     1700      3.40
65.0            5     1705      3.41
66.0            1     1706      3.41
70.0           10     1716      3.43
75.0            5     1721      3.44
79.0            1     1722      3.44
80.0           15     1737      3.47
89.0            1     1738      3.48
90.0            5     1743      3.49
99.0           19     1762      3.52
100.0         134     1896      3.79
110.0           3     1899      3.80
111.0           2     1901      3.80
115.0           2     1903      3.81
117.0           1     1904      3.81
120.0          39     1943      3.89
122.0           1     1944      3.89
125.0           8     1952      3.90
129.0           1     1953      3.91
130.0          15     1968      3.94
135.0           1     1969      3.94
139.0           1     1970      3.94
140.0           9     1979      3.96
145.0           2     1981      3.96
149.0           7     1988      3.98
150.0         224     2212      4.42
156.0           2     2214      4.43
160.0           8     2222      4.44
170.0           7     2229      4.46
173.0           1     2230      4.46
175.0          12     2242      4.48
179.0           1     2243      4.49
180.0          35     2278      4.56
185.0           1     2279      4.56
188.0           1     2280      4.56
190.0          16     2296      4.59
193.0           1     2297      4.59
195.0           2     2299      4.60
198.0           1     2300      4.60
199.0          41     2341      4.68
200.0         266     2607      5.21
205.0           1     2608      5.22
210.0           1     2609      5.22
215.0           2     2611      5.22
217.0           1     2612      5.22
219.0           1     2613      5.23
220.0          33     2646      5.29
222.0          12     2658      5.32
225.0           8     2666      5.33
230.0          12     2678      5.36
235.0           2     2680      5.36
238.0           1     2681      5.36
240.0           3     2684      5.37
248.0           1     2685      5.37
249.0          13     2698      5.40
250.0         291     2989      5.98
251.0           1     2990      5.98
255.0           1     2991      5.98
260.0           5     2996      5.99
269.0           1     2997      5.99
270.0           6     3003      6.01
275.0           7     3010      6.02
277.0           1     3011      6.02
280.0          30     3041      6.08
285.0           1     3042      6.08
290.0          19     3061      6.12
295.0           1     3062      6.12
299.0          56     3118      6.24
300.0         384     3502      7.00
310.0           1     3503      7.01
320.0          12     3515      7.03
325.0           5     3520      7.04
329.0           2     3522      7.04
330.0           8     3530      7.06
333.0          17     3547      7.09
340.0          11     3558      7.12
349.0          15     3573      7.15
350.0         335     3908      7.82
356.0           1     3909      7.82
359.0           1     3910      7.82
360.0           8     3918      7.84
369.0           1     3919      7.84
370.0          21     3940      7.88
375.0           7     3947      7.89
378.0           1     3948      7.90
379.0           1     3949      7.90
380.0          29     3978      7.96
385.0           1     3979      7.96
388.0           1     3980      7.96
390.0          26     4006      8.01
395.0           2     4008      8.02
399.0          71     4079      8.16
400.0         321     4400      8.80
410.0           1     4401      8.80
414.0           1     4402      8.80
420.0           9     4411      8.82
425.0           4     4415      8.83
430.0          13     4428      8.86
435.0           1     4429      8.86
440.0           1     4430      8.86
444.0           8     4438      8.88
449.0          12     4450      8.90
450.0         265     4715      9.43
459.0           1     4716      9.43
460.0           5     4721      9.44
470.0           7     4728      9.46
475.0           4     4732      9.46
480.0          25     4757      9.51
485.0           2     4759      9.52
490.0          34     4793      9.59
495.0           4     4797      9.59
499.0          92     4889      9.78
500.0         781     5670     11.34
501.0           1     5671     11.34
510.0           2     5673     11.35
517.0           1     5674     11.35
520.0           8     5682     11.36
525.0           4     5686     11.37
530.0           8     5694     11.39
540.0           2     5696     11.39
549.0          13     5709     11.42
550.0         356     6065     12.13
554.0           1     6066     12.13
555.0          33     6099     12.20
560.0           4     6103     12.21
566.0           1     6104     12.21
570.0           7     6111     12.22
575.0           5     6116     12.23
578.0           1     6117     12.23
579.0           1     6118     12.24
580.0          20     6138     12.28
590.0          52     6190     12.38
595.0           2     6192     12.38
598.0           2     6194     12.39
599.0         122     6316     12.63
600.0         531     6847     13.69
606.0           1     6848     13.70
620.0           7     6855     13.71
625.0           5     6860     13.72
628.0           1     6861     13.72
630.0           3     6864     13.73
640.0           3     6867     13.73
644.0           1     6868     13.74
648.0           1     6869     13.74
649.0          14     6883     13.77
650.0         419     7302     14.60
655.0           1     7303     14.61
660.0           5     7308     14.62
666.0          14     7322     14.64
669.0           2     7324     14.65
670.0           6     7330     14.66
675.0           5     7335     14.67
679.0           1     7336     14.67
680.0          30     7366     14.73
686.0           1     7367     14.73
689.0           2     7369     14.74
690.0          68     7437     14.87
695.0           3     7440     14.88
699.0         127     7567     15.13
700.0         395     7962     15.92
710.0           1     7963     15.93
719.0           1     7964     15.93
720.0           7     7971     15.94
725.0           2     7973     15.95
729.0           1     7974     15.95
730.0           5     7979     15.96
740.0           3     7982     15.96
744.0           1     7983     15.97
745.0           2     7985     15.97
749.0          23     8008     16.02
750.0         433     8441     16.88
755.0           1     8442     16.88
760.0           8     8450     16.90
770.0           6     8456     16.91
777.0          20     8476     16.95
780.0          19     8495     16.99
785.0           1     8496     16.99
789.0           1     8497     16.99
790.0          45     8542     17.08
795.0           2     8544     17.09
799.0         120     8664     17.33
800.0         498     9162     18.32
810.0           3     9165     18.33
820.0           6     9171     18.34
825.0           4     9175     18.35
829.0           1     9176     18.35
830.0           6     9182     18.36
834.0           1     9183     18.37
839.0           1     9184     18.37
840.0           5     9189     18.38
846.0           1     9190     18.38
849.0          13     9203     18.41
850.0         410     9613     19.23
855.0           3     9616     19.23
860.0           1     9617     19.23
870.0          12     9629     19.26
875.0           3     9632     19.26
879.0           1     9633     19.27
880.0          14     9647     19.29
885.0           1     9648     19.30
887.0           1     9649     19.30
888.0          29     9678     19.36
889.0           1     9679     19.36
890.0          66     9745     19.49
895.0           3     9748     19.50
898.0           1     9749     19.50
899.0         129     9878     19.76
900.0         420    10298     20.60
910.0           1    10299     20.60
919.0           1    10300     20.60
920.0           1    10301     20.60
925.0           1    10302     20.60
930.0           4    10306     20.61
940.0           2    10308     20.62
945.0           2    10310     20.62
949.0          11    10321     20.64
950.0         379    10700     21.40
951.0           1    10701     21.40
958.0           1    10702     21.40
960.0           1    10703     21.41
965.0           2    10705     21.41
970.0           7    10712     21.42
975.0           2    10714     21.43
980.0          48    10762     21.52
985.0           4    10766     21.53
989.0           2    10768     21.54
990.0         147    10915     21.83
995.0           5    10920     21.84
996.0           1    10921     21.84
998.0           5    10926     21.85
999.0         434    11360     22.72
1000.0        639    11999     24.00
1039.0          1    12000     24.00
1040.0          1    12001     24.00
1049.0          6    12007     24.01
1050.0         95    12102     24.20
1059.0          1    12103     24.21
1070.0          1    12104     24.21
1080.0          6    12110     24.22
1090.0          4    12114     24.23
1095.0          3    12117     24.23
1098.0          1    12118     24.24
1099.0         44    12162     24.32
1100.0        376    12538     25.08
1111.0         39    12577     25.15
1112.0          1    12578     25.16
1119.0          1    12579     25.16
1120.0          2    12581     25.16
1149.0         10    12591     25.18
1150.0        226    12817     25.63
1169.0          1    12818     25.64
1170.0          1    12819     25.64
1180.0          4    12823     25.65
1189.0          1    12824     25.65
1190.0         37    12861     25.72
1195.0          1    12862     25.72
1199.0        126    12988     25.98
1200.0        639    13627     27.25
1201.0          2    13629     27.26
1209.0          1    13630     27.26
1212.0          2    13632     27.26
1221.0          1    13633     27.27
1222.0          3    13636     27.27
1234.0          3    13639     27.28
1240.0          2    13641     27.28
1247.0          1    13642     27.28
1249.0          4    13646     27.29
1250.0        335    13981     27.96
1265.0          1    13982     27.96
1270.0          4    13986     27.97
1275.0          1    13987     27.97
1280.0         12    13999     28.00
1285.0          3    14002     28.00
1290.0         38    14040     28.08
1295.0          1    14041     28.08
1299.0        135    14176     28.35
1300.0        371    14547     29.09
1310.0          1    14548     29.10
1325.0          1    14549     29.10
1330.0          1    14550     29.10
1333.0          3    14553     29.11
1340.0          2    14555     29.11
1345.0          2    14557     29.11
1349.0          5    14562     29.12
1350.0        276    14838     29.68
1355.0          1    14839     29.68
1370.0          3    14842     29.68
1375.0          3    14845     29.69
1379.0          1    14846     29.69
1380.0         10    14856     29.71
1385.0          1    14857     29.71
1390.0         67    14924     29.85
1395.0          5    14929     29.86
1398.0          2    14931     29.86
1399.0         95    15026     30.05
1400.0        292    15318     30.64
1414.0          1    15319     30.64
1420.0          1    15320     30.64
1425.0          2    15322     30.64
1430.0          3    15325     30.65
1432.0          1    15326     30.65
1440.0          2    15328     30.66
1444.0          4    15332     30.66
1448.0          2    15334     30.67
1449.0          8    15342     30.68
1450.0        252    15594     31.19
1466.0          1    15595     31.19
1470.0          2    15597     31.19
1475.0          2    15599     31.20
1480.0          8    15607     31.21
1485.0          1    15608     31.22
1490.0         88    15696     31.39
1494.0          1    15697     31.39
1495.0          3    15700     31.40
1497.0          1    15701     31.40
1498.0          1    15702     31.40
1499.0        157    15859     31.72
1500.0        734    16593     33.19
1520.0          2    16595     33.19
1525.0          2    16597     33.19
1530.0          2    16599     33.20
1545.0          1    16600     33.20
1549.0          5    16605     33.21
1550.0        150    16755     33.51
1555.0          7    16762     33.52
1560.0          1    16763     33.53
1570.0          2    16765     33.53
1575.0          2    16767     33.53
1579.0          1    16768     33.54
1580.0          5    16773     33.55
1590.0         43    16816     33.63
1595.0          3    16819     33.64
1599.0         92    16911     33.82
1600.0        327    17238     34.48
1630.0          2    17240     34.48
1640.0          1    17241     34.48
1642.0          1    17242     34.48
1645.0          1    17243     34.49
1649.0          8    17251     34.50
1650.0        238    17489     34.98
1659.0          1    17490     34.98
1660.0          2    17492     34.98
1666.0          3    17495     34.99
1670.0          2    17497     34.99
1675.0          2    17499     35.00
1680.0          8    17507     35.01
1689.0          1    17508     35.02
1690.0         43    17551     35.10
1695.0          2    17553     35.11
1698.0          1    17554     35.11
1699.0         85    17639     35.28
1700.0        268    17907     35.81
1730.0          1    17908     35.82
1749.0          5    17913     35.83
1750.0        238    18151     36.30
1755.0          1    18152     36.30
1759.0          1    18153     36.31
1760.0          1    18154     36.31
1765.0          1    18155     36.31
1770.0          1    18156     36.31
1775.0          1    18157     36.31
1777.0          4    18161     36.32
1780.0          1    18162     36.32
1790.0         42    18204     36.41
1795.0          1    18205     36.41
1797.0          1    18206     36.41
1798.0          1    18207     36.41
1799.0         73    18280     36.56
1800.0        355    18635     37.27
1820.0          1    18636     37.27
1840.0          4    18640     37.28
1845.0          1    18641     37.28
1849.0          5    18646     37.29
1850.0        216    18862     37.72
1856.0          1    18863     37.73
1860.0          1    18864     37.73
1870.0          1    18865     37.73
1875.0          2    18867     37.73
1880.0          6    18873     37.75
1888.0          3    18876     37.75
1890.0         38    18914     37.83
1895.0          1    18915     37.83
1899.0         53    18968     37.94
1900.0        239    19207     38.41
1906.0          1    19208     38.42
1925.0          1    19209     38.42
1930.0          1    19210     38.42
1933.0          1    19211     38.42
1935.0          1    19212     38.42
1945.0          2    19214     38.43
1949.0          1    19215     38.43
1950.0        208    19423     38.85
1955.0          1    19424     38.85
1960.0          1    19425     38.85
1970.0          2    19427     38.85
1975.0          1    19428     38.86
1980.0         15    19443     38.89
1981.0          1    19444     38.89
1984.0          1    19445     38.89
1985.0          1    19446     38.89
1990.0        117    19563     39.13
1995.0          4    19567     39.13
1996.0          1    19568     39.14
1998.0          4    19572     39.14
1999.0        322    19894     39.79
2000.0        460    20354     40.71
2001.0          1    20355     40.71
2004.0          1    20356     40.71
2033.0          1    20357     40.71
2035.0          1    20358     40.72
2050.0         27    20385     40.77
2070.0          1    20386     40.77
2090.0          2    20388     40.78
2095.0          1    20389     40.78
2099.0         21    20410     40.82
2100.0        208    20618     41.24
2111.0          2    20620     41.24
2128.0          1    20621     41.24
2134.0          1    20622     41.24
2140.0          1    20623     41.25
2149.0          2    20625     41.25
2150.0         95    20720     41.44
2175.0          1    20721     41.44
2180.0          1    20722     41.44
2190.0         29    20751     41.50
2195.0          1    20752     41.50
2199.0         52    20804     41.61
2200.0        382    21186     42.37
2210.0          6    21192     42.38
2222.0         27    21219     42.44
2225.0          1    21220     42.44
2241.0          1    21221     42.44
2245.0          1    21222     42.44
2249.0          2    21224     42.45
2250.0        147    21371     42.74
2265.0          2    21373     42.75
2270.0          1    21374     42.75
2280.0          6    21380     42.76
2288.0          1    21381     42.76
2290.0         29    21410     42.82
2295.0          2    21412     42.82
2299.0         38    21450     42.90
2300.0        290    21740     43.48
2321.0          2    21742     43.48
2333.0          5    21747     43.49
2340.0          3    21750     43.50
2349.0          2    21752     43.50
2350.0        127    21879     43.76
2359.0          1    21880     43.76
2380.0          2    21882     43.76
2390.0         31    21913     43.83
2398.0          2    21915     43.83
2399.0         55    21970     43.94
2400.0        193    22163     44.33
2410.0          1    22164     44.33
2430.0          1    22165     44.33
2444.0          5    22170     44.34
2449.0          5    22175     44.35
2450.0        120    22295     44.59
2455.0          1    22296     44.59
2459.0          1    22297     44.59
2460.0          1    22298     44.60
2470.0          2    22300     44.60
2479.0          1    22301     44.60
2480.0          9    22310     44.62
2490.0         66    22376     44.75
2495.0          1    22377     44.75
2496.0          1    22378     44.76
2498.0          1    22379     44.76
2499.0        136    22515     45.03
2500.0        643    23158     46.32
2549.0          1    23159     46.32
2550.0         64    23223     46.45
2555.0          5    23228     46.46
2569.0          1    23229     46.46
2570.0          1    23230     46.46
2580.0          2    23232     46.46
2589.0          1    23233     46.47
2590.0         19    23252     46.50
2598.0          1    23253     46.51
2599.0         50    23303     46.61
2600.0        241    23544     47.09
2649.0          3    23547     47.09
2650.0        125    23672     47.34
2651.0          1    23673     47.35
2655.0          1    23674     47.35
2660.0          2    23676     47.35
2666.0          3    23679     47.36
2670.0          1    23680     47.36
2671.0          1    23681     47.36
2680.0          2    23683     47.37
2690.0         22    23705     47.41
2695.0          1    23706     47.41
2699.0         33    23739     47.48
2700.0        221    23960     47.92
2725.0          1    23961     47.92
2749.0          8    23969     47.94
2750.0        169    24138     48.28
2775.0          2    24140     48.28
2777.0          3    24143     48.29
2780.0          3    24146     48.29
2785.0          1    24147     48.29
2789.0          1    24148     48.30
2790.0         29    24177     48.35
2798.0          1    24178     48.36
2799.0         53    24231     48.46
2800.0        291    24522     49.04
2849.0          1    24523     49.05
2850.0        131    24654     49.31
2860.0          3    24657     49.31
2870.0          1    24658     49.32
2874.0          1    24659     49.32
2880.0          1    24660     49.32
2888.0          4    24664     49.33
2890.0         26    24690     49.38
2895.0          1    24691     49.38
2899.0         30    24721     49.44
2900.0        256    24977     49.95
2910.0          1    24978     49.96
2920.0          1    24979     49.96
2944.0          1    24980     49.96
2949.0          4    24984     49.97
2950.0        173    25157     50.31
2980.0          7    25164     50.33
2985.0          1    25165     50.33
2986.0          1    25166     50.33
2989.0          1    25167     50.33
2990.0        134    25301     50.60
2993.0          1    25302     50.60
2995.0          5    25307     50.61
2997.0          1    25308     50.62
2998.0          4    25312     50.62
2999.0        242    25554     51.11
3000.0        365    25919     51.84
3001.0          2    25921     51.84
3010.0          1    25922     51.84
3012.0          1    25923     51.85
3020.0          1    25924     51.85
3049.0          1    25925     51.85
3050.0          9    25934     51.87
3055.0          1    25935     51.87
3060.0          2    25937     51.87
3075.0          1    25938     51.88
3080.0          1    25939     51.88
3099.0         11    25950     51.90
3100.0        133    26083     52.17
3111.0          2    26085     52.17
3119.0          1    26086     52.17
3120.0          1    26087     52.17
3122.0          1    26088     52.18
3125.0          1    26089     52.18
3129.0          1    26090     52.18
3149.0          3    26093     52.19
3150.0         64    26157     52.31
3178.0          1    26158     52.32
3180.0          2    26160     52.32
3190.0         12    26172     52.34
3195.0          1    26173     52.35
3199.0         37    26210     52.42
3200.0        261    26471     52.94
3210.0          1    26472     52.94
3211.0          1    26473     52.95
3220.0          1    26474     52.95
3222.0          2    26476     52.95
3230.0          2    26478     52.96
3240.0          2    26480     52.96
3249.0          3    26483     52.97
3250.0        109    26592     53.18
3260.0          1    26593     53.19
3266.0          1    26594     53.19
3279.0          1    26595     53.19
3280.0          3    26598     53.20
3285.0          1    26599     53.20
3290.0         21    26620     53.24
3295.0          1    26621     53.24
3299.0         35    26656     53.31
3300.0        197    26853     53.71
3318.0          1    26854     53.71
3330.0          3    26857     53.71
3333.0         39    26896     53.79
3349.0          1    26897     53.79
3350.0         61    26958     53.92
3360.0          1    26959     53.92
3380.0          4    26963     53.93
3390.0         18    26981     53.96
3395.0          1    26982     53.96
3399.0         24    27006     54.01
3400.0        137    27143     54.29
3410.0          1    27144     54.29
3420.0          1    27145     54.29
3425.0          1    27146     54.29
3444.0          2    27148     54.30
3449.0          1    27149     54.30
3450.0         82    27231     54.46
3455.0          1    27232     54.46
3456.0          2    27234     54.47
3470.0          2    27236     54.47
3475.0          1    27237     54.47
3480.0          5    27242     54.48
3485.0          1    27243     54.49
3490.0         46    27289     54.58
3495.0          6    27295     54.59
3498.0          2    27297     54.59
3499.0         80    27377     54.75
3500.0        498    27875     55.75
3501.0          1    27876     55.75
3540.0          1    27877     55.75
3549.0          3    27880     55.76
3550.0         46    27926     55.85
3555.0          4    27930     55.86
3560.0          1    27931     55.86
3580.0          1    27932     55.86
3589.0          1    27933     55.87
3590.0         13    27946     55.89
3599.0         22    27968     55.94
3600.0        127    28095     56.19
3620.0          1    28096     56.19
3633.0          1    28097     56.19
3650.0         83    28180     56.36
3660.0          1    28181     56.36
3666.0          6    28187     56.37
3670.0          3    28190     56.38
3680.0          2    28192     56.38
3690.0         28    28220     56.44
3699.0         35    28255     56.51
3700.0        155    28410     56.82
3710.0          1    28411     56.82
3725.0          1    28412     56.82
3749.0          2    28414     56.83
3750.0        112    28526     57.05
3760.0          1    28527     57.05
3774.0          1    28528     57.06
3777.0          3    28531     57.06
3780.0          1    28532     57.06
3790.0         24    28556     57.11
3795.0          1    28557     57.11
3799.0         41    28598     57.20
3800.0        264    28862     57.72
3849.0          1    28863     57.73
3850.0         78    28941     57.88
3876.0          1    28942     57.88
3879.0          1    28943     57.89
3880.0          2    28945     57.89
3888.0          4    28949     57.90
3890.0         18    28967     57.93
3895.0          2    28969     57.94
3899.0         31    29000     58.00
3900.0        238    29238     58.48
3940.0          2    29240     58.48
3945.0          1    29241     58.48
3949.0          1    29242     58.48
3950.0        135    29377     58.75
3952.0          1    29378     58.76
3955.0          2    29380     58.76
3957.0          1    29381     58.76
3965.0          1    29382     58.76
3969.0          1    29383     58.77
3970.0          1    29384     58.77
3975.0          1    29385     58.77
3980.0          7    29392     58.78
3989.0          1    29393     58.79
3990.0        103    29496     58.99
3993.0          1    29497     58.99
3995.0          3    29500     59.00
3996.0          1    29501     59.00
3998.0          4    29505     59.01
3999.0        212    29717     59.43
4000.0        246    29963     59.93
4004.0          1    29964     59.93
4005.0          1    29965     59.93
4050.0          3    29968     59.94
4090.0          3    29971     59.94
4099.0          8    29979     59.96
4100.0         86    30065     60.13
4111.0          1    30066     60.13
4123.0          1    30067     60.13
4125.0          1    30068     60.14
4149.0          1    30069     60.14
4150.0         42    30111     60.22
4159.0          1    30112     60.22
4180.0          1    30113     60.23
4190.0         14    30127     60.25
4199.0         32    30159     60.32
4200.0        226    30385     60.77
4201.0          1    30386     60.77
4210.0          1    30387     60.77
4220.0          1    30388     60.78
4222.0          1    30389     60.78
4239.0          1    30390     60.78
4249.0          4    30394     60.79
4250.0         92    30486     60.97
4270.0          1    30487     60.97
4275.0          1    30488     60.98
4279.0          1    30489     60.98
4280.0          1    30490     60.98
4286.0          1    30491     60.98
4290.0         14    30505     61.01
4295.0          1    30506     61.01
4299.0         26    30532     61.06
4300.0        132    30664     61.33
4320.0          1    30665     61.33
4333.0          1    30666     61.33
4335.0          1    30667     61.33
4349.0          1    30668     61.34
4350.0         45    30713     61.43
4390.0         19    30732     61.46
4398.0          1    30733     61.47
4399.0         26    30759     61.52
4400.0         88    30847     61.69
4440.0          1    30848     61.70
4444.0         23    30871     61.74
4450.0         35    30906     61.81
4470.0          2    30908     61.82
4475.0          1    30909     61.82
4480.0          2    30911     61.82
4485.0          1    30912     61.82
4490.0         38    30950     61.90
4495.0          1    30951     61.90
4497.0          2    30953     61.91
4498.0          2    30955     61.91
4499.0         58    31013     62.03
4500.0        394    31407     62.81
4510.0          1    31408     62.82
4525.0          1    31409     62.82
4545.0          1    31410     62.82
4549.0          1    31411     62.82
4550.0         28    31439     62.88
4555.0          2    31441     62.88
4567.0          1    31442     62.88
4580.0          2    31444     62.89
4590.0         16    31460     62.92
4598.0          1    31461     62.92
4599.0         14    31475     62.95
4600.0         82    31557     63.11
4649.0          1    31558     63.12
4650.0         61    31619     63.24
4655.0          1    31620     63.24
4666.0          2    31622     63.24
4680.0          2    31624     63.25
4690.0         13    31637     63.27
4699.0         22    31659     63.32
4700.0         99    31758     63.52
4740.0          1    31759     63.52
4750.0         66    31825     63.65
4755.0          1    31826     63.65
4770.0          1    31827     63.65
4777.0          1    31828     63.66
4780.0          1    31829     63.66
4790.0         14    31843     63.69
4799.0         15    31858     63.72
4800.0        186    32044     64.09
4830.0          2    32046     64.09
4840.0          1    32047     64.09
4850.0         59    32106     64.21
4855.0          1    32107     64.21
4860.0          1    32108     64.22
4877.0          1    32109     64.22
4888.0          2    32111     64.22
4890.0          7    32118     64.24
4895.0          1    32119     64.24
4899.0         19    32138     64.28
4900.0        188    32326     64.65
4949.0          3    32329     64.66
4950.0        126    32455     64.91
4955.0          1    32456     64.91
4980.0         10    32466     64.93
4985.0          2    32468     64.94
4990.0         99    32567     65.13
4994.0          1    32568     65.14
4995.0          7    32575     65.15
4998.0          4    32579     65.16
4999.0        174    32753     65.51
5000.0        239    32992     65.98
5012.0          1    32993     65.99
5015.0          1    32994     65.99
5049.0          1    32995     65.99
5050.0          3    32998     66.00
5099.0          4    33002     66.00
5100.0         51    33053     66.11
5120.0          1    33054     66.11
5150.0         18    33072     66.14
5180.0          1    33073     66.15
5185.0          1    33074     66.15
5190.0          4    33078     66.16
5195.0          1    33079     66.16
5198.0          1    33080     66.16
5199.0         19    33099     66.20
5200.0        156    33255     66.51
5222.0          3    33258     66.52
5248.0          1    33259     66.52
5249.0          2    33261     66.52
5250.0         56    33317     66.63
5255.0          1    33318     66.64
5290.0         15    33333     66.67
5298.0          1    33334     66.67
5299.0         15    33349     66.70
5300.0         86    33435     66.87
5333.0          3    33438     66.88
5350.0         32    33470     66.94
5380.0          2    33472     66.94
5390.0         10    33482     66.96
5399.0         15    33497     66.99
5400.0         74    33571     67.14
5444.0          1    33572     67.14
5450.0         37    33609     67.22
5454.0          1    33610     67.22
5475.0          1    33611     67.22
5485.0          1    33612     67.22
5489.0          1    33613     67.23
5490.0         46    33659     67.32
5495.0          1    33660     67.32
5499.0         48    33708     67.42
5500.0        340    34048     68.10
5540.0          1    34049     68.10
5550.0         18    34067     68.13
5555.0         31    34098     68.20
5590.0          5    34103     68.21
5599.0          5    34108     68.22
5600.0         91    34199     68.40
5634.0          1    34200     68.40
5650.0         29    34229     68.46
5666.0          2    34231     68.46
5685.0          1    34232     68.46
5689.0          1    34233     68.47
5690.0          9    34242     68.48
5695.0          2    34244     68.49
5699.0         11    34255     68.51
5700.0         67    34322     68.64
5740.0          1    34323     68.65
5749.0          1    34324     68.65
5750.0         41    34365     68.73
5790.0          8    34373     68.75
5799.0         18    34391     68.78
5800.0        123    34514     69.03
5849.0          1    34515     69.03
5850.0         40    34555     69.11
5855.0          1    34556     69.11
5870.0          2    34558     69.12
5879.0          1    34559     69.12
5880.0          2    34561     69.12
5888.0          2    34563     69.13
5890.0         13    34576     69.15
5895.0          1    34577     69.15
5899.0         11    34588     69.18
5900.0        209    34797     69.59
5913.0          1    34798     69.60
5924.0          1    34799     69.60
5949.0          1    34800     69.60
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29380.0         1    49106     98.21
29400.0         1    49107     98.21
29445.0         1    49108     98.22
29450.0         1    49109     98.22
29490.0         3    49112     98.22
29499.0         2    49114     98.23
29500.0        20    49134     98.27
29550.0         1    49135     98.27
29600.0         1    49136     98.27
29699.0         1    49137     98.27
29700.0         2    49139     98.28
29750.0         2    49141     98.28
29777.0         1    49142     98.28
29800.0         4    49146     98.29
29850.0         2    49148     98.30
29890.0         1    49149     98.30
29900.0        15    49164     98.33
29950.0         5    49169     98.34
29970.0         1    49170     98.34
29980.0         1    49171     98.34
29989.0         1    49172     98.34
29990.0         9    49181     98.36
29999.0        15    49196     98.39
30000.0        10    49206     98.41
30200.0         1    49207     98.41
30400.0         1    49208     98.42
30499.0         2    49210     98.42
30500.0         7    49217     98.43
30570.0         1    49218     98.44
30650.0         1    49219     98.44
30700.0         2    49221     98.44
30800.0         1    49222     98.44
30888.0         1    49223     98.45
30899.0         1    49224     98.45
30900.0         5    49229     98.46
30933.0         1    49230     98.46
30950.0         1    49231     98.46
30987.0         1    49232     98.46
30990.0         2    49234     98.47
30999.0         2    49236     98.47
31000.0         8    49244     98.49
31111.0         1    49245     98.49
31199.0         2    49247     98.49
31200.0         1    49248     98.50
31313.0         1    49249     98.50
31400.0         1    49250     98.50
31450.0         1    49251     98.50
31490.0         3    49254     98.51
31499.0         2    49256     98.51
31500.0        13    49269     98.54
31600.0         1    49270     98.54
31799.0         2    49272     98.54
31800.0         5    49277     98.55
31900.0        12    49289     98.58
31950.0         2    49291     98.58
31990.0         4    49295     98.59
31999.0         8    49303     98.61
32000.0        10    49313     98.63
32150.0         1    49314     98.63
32222.0         2    49316     98.63
32400.0         2    49318     98.64
32490.0         1    49319     98.64
32500.0        16    49335     98.67
32700.0         2    49337     98.67
32800.0         1    49338     98.68
32900.0         7    49345     98.69
32949.0         1    49346     98.69
32950.0         2    49348     98.70
32990.0         3    49351     98.70
32999.0         4    49355     98.71
33000.0         9    49364     98.73
33200.0         1    49365     98.73
33300.0         1    49366     98.73
33449.0         1    49367     98.73
33490.0         2    49369     98.74
33499.0         1    49370     98.74
33500.0         8    49378     98.76
33600.0         1    49379     98.76
33650.0         1    49380     98.76
33700.0         2    49382     98.76
33750.0         1    49383     98.77
33777.0         1    49384     98.77
33800.0         3    49387     98.77
33850.0         1    49388     98.78
33900.0        10    49398     98.80
33950.0         2    49400     98.80
33980.0         1    49401     98.80
33990.0         3    49404     98.81
33999.0         3    49407     98.81
34000.0         8    49415     98.83
34150.0         1    49416     98.83
34490.0         1    49417     98.83
34499.0         2    49419     98.84
34500.0        15    49434     98.87
34550.0         1    49435     98.87
34650.0         1    49436     98.87
34750.0         1    49437     98.87
34800.0         4    49441     98.88
34850.0         1    49442     98.88
34890.0         1    49443     98.89
34900.0        12    49455     98.91
34940.0         1    49456     98.91
34950.0         2    49458     98.92
34980.0         1    49459     98.92
34990.0         3    49462     98.92
34996.0         1    49463     98.93
34999.0         4    49467     98.93
35000.0        10    49477     98.95
35222.0         1    49478     98.96
35370.0         1    49479     98.96
35450.0         1    49480     98.96
35460.0         1    49481     98.96
35499.0         2    49483     98.97
35500.0         3    49486     98.97
35555.0         1    49487     98.97
35700.0         1    49488     98.98
35790.0         2    49490     98.98
35800.0         1    49491     98.98
35890.0         2    49493     98.99
35900.0         9    49502     99.00
35911.0         1    49503     99.01
35950.0         1    49504     99.01
35980.0         1    49505     99.01
35990.0         1    49506     99.01
35999.0         2    49508     99.02
36000.0        12    49520     99.04
36500.0         4    49524     99.05
36675.0         1    49525     99.05
36800.0         1    49526     99.05
36850.0         1    49527     99.05
36900.0         4    49531     99.06
36999.0         2    49533     99.07
37000.0         4    49537     99.07
37300.0         1    49538     99.08
37400.0         1    49539     99.08
37450.0         1    49540     99.08
37480.0         1    49541     99.08
37499.0         1    49542     99.08
37500.0         4    49546     99.09
37700.0         1    49547     99.09
37750.0         1    49548     99.10
37800.0         4    49552     99.10
37850.0         2    49554     99.11
37900.0         9    49563     99.13
37950.0         1    49564     99.13
37999.0         3    49567     99.13
38000.0         4    49571     99.14
38200.0         1    49572     99.14
38400.0         1    49573     99.15
38450.0         1    49574     99.15
38500.0         8    49582     99.16
38700.0         1    49583     99.17
38760.0         1    49584     99.17
38800.0         2    49586     99.17
38850.0         1    49587     99.17
38900.0         8    49595     99.19
38950.0         1    49596     99.19
38990.0         2    49598     99.20
38999.0         2    49600     99.20
39000.0         3    49603     99.21
39300.0         2    49605     99.21
39500.0         9    49614     99.23
39700.0         1    49615     99.23
39800.0         1    49616     99.23
39890.0         1    49617     99.23
39900.0        12    49629     99.26
39911.0         1    49630     99.26
39979.0         1    49631     99.26
39990.0         1    49632     99.26
39999.0         6    49638     99.28
40000.0         3    49641     99.28
40400.0         1    49642     99.28
40499.0         1    49643     99.29
40500.0         2    49645     99.29
40800.0         1    49646     99.29
40850.0         1    49647     99.29
40900.0         3    49650     99.30
40990.0         1    49651     99.30
40999.0         2    49653     99.31
41000.0         3    49656     99.31
41500.0         6    49662     99.32
41800.0         1    49663     99.33
41850.0         1    49664     99.33
41900.0         6    49670     99.34
41999.0         1    49671     99.34
42000.0         3    49674     99.35
42222.0         1    49675     99.35
42500.0         3    49678     99.36
42750.0         1    49679     99.36
42760.0         1    49680     99.36
42800.0         1    49681     99.36
42900.0         7    49688     99.38
42990.0         2    49690     99.38
42996.0         2    49692     99.38
42999.0         1    49693     99.39
43000.0         2    49695     99.39
43461.0         1    49696     99.39
43500.0         2    49698     99.40
43900.0         5    49703     99.41
44000.0         4    49707     99.41
44200.0         2    49709     99.42
44444.0         1    49710     99.42
44497.0         1    49711     99.42
44499.0         2    49713     99.43
44500.0         1    49714     99.43
44777.0         1    49715     99.43
44900.0         5    49720     99.44
44990.0         1    49721     99.44
44996.0         1    49722     99.44
45000.0         5    49727     99.45
45500.0         4    49731     99.46
45800.0         1    49732     99.46
45900.0         3    49735     99.47
45949.0         1    49736     99.47
45950.0         1    49737     99.47
46000.0         2    49739     99.48
46200.0         1    49740     99.48
46500.0         1    49741     99.48
46800.0         1    49742     99.48
46900.0         3    49745     99.49
46911.0         1    49746     99.49
46990.0         1    49747     99.49
46999.0         1    49748     99.50
47000.0         4    49752     99.50
47499.0         1    49753     99.51
47500.0         3    49756     99.51
47800.0         1    49757     99.51
47900.0         3    49760     99.52
47950.0         1    49761     99.52
47997.0         1    49762     99.52
48000.0         4    49766     99.53
48300.0         1    49767     99.53
48490.0         1    49768     99.54
48500.0         4    49772     99.54
48600.0         1    49773     99.55
48700.0         2    49775     99.55
48850.0         1    49776     99.55
48888.0         1    49777     99.55
48900.0         3    49780     99.56
48999.0         2    49782     99.56
49000.0         3    49785     99.57
49500.0         4    49789     99.58
49900.0         5    49794     99.59
49999.0         4    49798     99.60
50000.0         2    49800     99.60
50500.0         2    49802     99.60
50900.0         1    49803     99.61
51000.0         1    49804     99.61
51500.0         1    49805     99.61
51900.0         2    49807     99.61
51990.0         1    49808     99.62
51999.0         1    49809     99.62
52000.0         1    49810     99.62
52500.0         3    49813     99.63
52900.0         5    49818     99.64
52911.0         1    49819     99.64
53000.0         4    49823     99.65
53500.0         2    49825     99.65
53900.0         2    49827     99.65
54500.0         2    49829     99.66
54990.0         1    49830     99.66
55000.0         5    49835     99.67
55500.0         1    49836     99.67
55555.0         1    49837     99.67
55800.0         1    49838     99.68
55900.0         1    49839     99.68
55996.0         1    49840     99.68
55999.0         1    49841     99.68
56000.0         4    49845     99.69
56500.0         2    49847     99.69
56800.0         1    49848     99.70
56900.0         1    49849     99.70
57800.0         1    49850     99.70
58500.0         2    49852     99.70
58700.0         1    49853     99.71
58900.0         1    49854     99.71
59000.0         3    49857     99.71
59500.0         3    49860     99.72
59850.0         1    49861     99.72
60000.0         3    49864     99.73
61500.0         1    49865     99.73
61900.0         1    49866     99.73
61950.0         1    49867     99.73
61999.0         1    49868     99.74
62000.0         2    49870     99.74
62900.0         2    49872     99.74
63000.0         1    49873     99.75
63499.0         1    49874     99.75
63999.0         2    49876     99.75
64280.0         1    49877     99.75
64500.0         2    49879     99.76
64600.0         1    49880     99.76
64900.0         3    49883     99.77
64990.0         1    49884     99.77
64999.0         1    49885     99.77
65000.0         1    49886     99.77
65699.0         1    49887     99.77
65700.0         1    49888     99.78
65990.0         1    49889     99.78
66500.0         1    49890     99.78
66964.0         1    49891     99.78
67000.0         1    49892     99.78
67911.0         1    49893     99.79
68000.0         1    49894     99.79
68300.0         1    49895     99.79
68500.0         1    49896     99.79
68750.0         1    49897     99.79
68900.0         1    49898     99.80
69500.0         1    49899     99.80
69900.0         1    49900     99.80
69993.0         1    49901     99.80
69997.0         1    49902     99.80
69999.0         1    49903     99.81
70000.0         1    49904     99.81
70850.0         1    49905     99.81
71000.0         1    49906     99.81
72500.0         1    49907     99.81
72600.0         1    49908     99.82
72900.0         1    49909     99.82
73500.0         1    49910     99.82
73900.0         1    49911     99.82
73996.0         1    49912     99.82
74900.0         3    49915     99.83
74999.0         2    49917     99.83
75000.0         1    49918     99.84
75900.0         1    49919     99.84
75997.0         1    49920     99.84
76997.0         1    49921     99.84
78911.0         1    49922     99.84
79500.0         1    49923     99.85
79933.0         1    49924     99.85
79980.0         1    49925     99.85
79999.0         1    49926     99.85
80000.0         3    49929     99.86
82987.0         1    49930     99.86
83000.0         1    49931     99.86
84000.0         1    49932     99.86
84997.0         1    49933     99.87
85000.0         1    49934     99.87
86500.0         1    49935     99.87
88900.0         1    49936     99.87
89000.0         1    49937     99.87
89900.0         1    49938     99.88
93000.0         2    49940     99.88
93911.0         1    49941     99.88
94999.0         1    49942     99.88
98500.0         1    49943     99.89
99000.0         2    49945     99.89
99900.0         2    49947     99.89
104900.0        1    49948     99.90
105000.0        2    49950     99.90
109999.0        1    49951     99.90
114400.0        1    49952     99.90
115000.0        1    49953     99.91
115991.0        1    49954     99.91
116000.0        1    49955     99.91
119500.0        1    49956     99.91
119900.0        1    49957     99.91
120000.0        2    49959     99.92
128000.0        1    49960     99.92
129000.0        1    49961     99.92
130000.0        1    49962     99.92
135000.0        1    49963     99.93
137999.0        1    49964     99.93
139997.0        1    49965     99.93
145000.0        1    49966     99.93
151990.0        1    49967     99.93
155000.0        1    49968     99.94
163500.0        1    49969     99.94
163991.0        1    49970     99.94
169000.0        1    49971     99.94
169999.0        1    49972     99.94
175000.0        1    49973     99.95
180000.0        1    49974     99.95
190000.0        1    49975     99.95
194000.0        1    49976     99.95
197000.0        1    49977     99.95
198000.0        1    49978     99.96
220000.0        1    49979     99.96
250000.0        1    49980     99.96
259000.0        1    49981     99.96
265000.0        1    49982     99.96
295000.0        1    49983     99.97
299000.0        1    49984     99.97
345000.0        1    49985     99.97
350000.0        1    49986     99.97
999990.0        1    49987     99.97
999999.0        2    49989     99.98
1234566.0       1    49990     99.98
1300000.0       1    49991     99.98
3890000.0       1    49992     99.98
10000000.0      1    49993     99.99
11111111.0      2    49995     99.99
12345678.0      3    49998    100.00
27322222.0      1    49999    100.00
99999999.0      1    50000    100.00

A mean of nearly ten thousand euro's for used cars of all types seems realistic.\ The mean is only a fraction of the standard deviation (which is 481,000 euro's).\ This suggests that there are outliers in the dataset.

The lowest price is zero, which has 1421 occurences in the dataset.\ Price represents the starting value of an action. Since it is only the starting price it does not mean that a car will be sold for that price.\ Therefore anything below 500 euro's (which seems like a realistic lower bound for used car prices) is not removed from the dataset.

There are also outliers at the top. When investigating the unique values with their respective counts the starting price increases slowly until 350,000.\ Onwards the price increases rapidly. Occurences with a starting price higher than 350,000 will be investigated further.

In [ ]:
 
In [13]:
price_above_350000 = autos[autos['price']>350000]

template = (color.BOLD + "There are " 
            + color.RED + "{}" + color.END 
            + color.BOLD + " instances with a starting price of 350,000 or higher" + color.END)

print(template.format(len(price_above_350000)))
    
price_above_350000
There are 14 instances with a starting price of 350,000 or higher
Out[13]:
date_crawled name price abtest vehicle_type registration_year gearbox power_PS model odometer_km registration_month fuel_type brand unrepaired_damage ad_created nr_of_pictures postal_code last_seen
514 2016-03-17 09:53:08 Ford_Focus_Turnier_1.6_16V_Style 999999.0 test kombi 2009 manuell 101 focus 125000 4 benzin ford nein 2016-03-17 00:00:00 0 12205 2016-04-06 07:17:35
2897 2016-03-12 21:50:57 Escort_MK_1_Hundeknochen_zum_umbauen_auf_RS_2000 11111111.0 test limousine 1973 manuell 48 escort 50000 3 benzin ford nein 2016-03-12 00:00:00 0 94469 2016-03-12 22:45:27
7814 2016-04-04 11:53:31 Ferrari_F40 1300000.0 control coupe 1992 NaN 0 NaN 50000 12 NaN sonstige_autos nein 2016-04-04 00:00:00 0 60598 2016-04-05 11:34:11
11137 2016-03-29 23:52:57 suche_maserati_3200_gt_Zustand_unwichtig_laufe... 10000000.0 control coupe 1960 manuell 368 NaN 100000 1 benzin sonstige_autos nein 2016-03-29 00:00:00 0 73033 2016-04-06 21:18:11
22947 2016-03-22 12:54:19 Bmw_530d_zum_ausschlachten 1234566.0 control kombi 1999 automatik 190 NaN 150000 2 diesel bmw NaN 2016-03-22 00:00:00 0 17454 2016-04-02 03:17:32
24384 2016-03-21 13:57:51 Schlachte_Golf_3_gt_tdi 11111111.0 test NaN 1995 NaN 0 NaN 150000 0 NaN volkswagen NaN 2016-03-21 00:00:00 0 18519 2016-03-21 14:40:18
27371 2016-03-09 15:45:47 Fiat_Punto 12345678.0 control NaN 2017 NaN 95 punto 150000 0 NaN fiat NaN 2016-03-09 00:00:00 0 96110 2016-03-09 15:45:47
37585 2016-03-29 11:38:54 Volkswagen_Jetta_GT 999990.0 test limousine 1985 manuell 111 jetta 150000 12 benzin volkswagen ja 2016-03-29 00:00:00 0 50997 2016-03-29 11:38:54
39377 2016-03-08 23:53:51 Tausche_volvo_v40_gegen_van 12345678.0 control NaN 2018 manuell 95 v40 150000 6 NaN volvo nein 2016-03-08 00:00:00 0 14542 2016-04-06 23:17:31
39705 2016-03-22 14:58:27 Tausch_gegen_gleichwertiges 99999999.0 control limousine 1999 automatik 224 s_klasse 150000 9 benzin mercedes_benz NaN 2016-03-22 00:00:00 0 73525 2016-04-06 05:15:30
42221 2016-03-08 20:39:05 Leasinguebernahme 27322222.0 control limousine 2014 manuell 163 c4 40000 2 diesel citroen NaN 2016-03-08 00:00:00 0 76532 2016-03-08 20:39:05
43049 2016-03-21 19:53:52 2_VW_Busse_T3 999999.0 test bus 1981 manuell 70 transporter 150000 1 benzin volkswagen NaN 2016-03-21 00:00:00 0 99880 2016-03-28 17:18:28
47598 2016-03-31 18:56:54 Opel_Vectra_B_1_6i_16V_Facelift_Tuning_Showcar... 12345678.0 control limousine 2001 manuell 101 vectra 150000 3 benzin opel nein 2016-03-31 00:00:00 0 4356 2016-03-31 18:56:54
47634 2016-04-04 21:25:21 Ferrari_FXX 3890000.0 test coupe 2006 NaN 799 NaN 5000 7 NaN sonstige_autos nein 2016-04-04 00:00:00 0 60313 2016-04-05 12:07:37

There are 14 occurences with a price higher than 350,000.\ Since most of these cars are normal family cars (with brands like Ford, BMW, Fiat, Volkswagen) these prices are unrealistic.\ The 14 instances will be removed from the dataset.

In [14]:
autos = autos[autos['price']<=350000]
explore_series(autos,'price')
Number of unique values in column price is 2,347 


Descriptive statistics of column price
count     49986.000000
mean       5721.525167
std        8983.617820
min           0.000000
25%        1100.000000
50%        2950.000000
75%        7200.000000
max      350000.000000
Name: price, dtype: float64


After removal there are 49,986 instances left in the dataset.\ Removing the outliers at the top has had its impact on the mean starting price.\ This has decreased from 9,840 to 5,721.\ The standard deviation has decreased drastically as it is now less than 9,000.

The "odometer_km" will be explored next.

In [15]:
explore_series(autos, 'odometer_km', value_counts=True)
Number of unique values in column odometer_km is 13 


Descriptive statistics of column odometer_km
count     49986.000000
mean     125736.506222
std       40038.133399
min        5000.000000
25%      125000.000000
50%      150000.000000
75%      150000.000000
max      150000.000000
Name: odometer_km, dtype: float64


Unique values with their respective counts:
             count  cum_sum  cum_perc
odometer_km                          
5000           966      966      1.93
10000          264     1230      2.46
20000          784     2014      4.03
30000          789     2803      5.61
40000          818     3621      7.24
50000         1025     4646      9.29
60000         1164     5810     11.62
70000         1230     7040     14.08
80000         1436     8476     16.96
90000         1757    10233     20.47
100000        2168    12401     24.81
125000        5169    17570     35.15
150000       32416    49986    100.00

There are only 13 different values of mileages in the dataset. This suggests that people have to use a preset of values when creating an auction on eBay.

The lowest value is 5,000 and the highest is 150,000 which are both plausible values for mileage on a used car.\ Therefore there will be no correction on outliers for this column.

The mean is more than 120,000 km which suggests that most cars sold through eBay are likely to be a couple years old.\ 65% of the dataset has a mileage of 150,000 (or more).

This concludes the exploration of the columns "price" and "odometer_km".

Exploration of date columns

There are five columns containing date information.

Column Description
date_crawled When this ad was first crawled, all field-values are taken from this date
registration_year The year in which the car was first registered
registration_month The month in which the car was first registered
ad_created The date on which the eBay listing was created
last_seen When the crawler saw this ad last online

In order to explore the date columns more easily date_crawled, ad_created and last_seen have to be reformatted into a date type.\ Once this has been done all columns will be explored shortly.

In [16]:
#creating a function to reformat the columns with string format into date format.
def formatDate(dataset,column):
    newformat = []
    for element in dataset[column]:
        element = dt.datetime.strptime(element, "%Y-%m-%d %H:%M:%S")
        element = element.date()
        newformat.append(element)
    dataset[column] = newformat
                   
formatDate(autos,'date_crawled')
formatDate(autos,'ad_created')
formatDate(autos,'last_seen')

date_crawled

In [17]:
explore_series(autos,'date_crawled', value_counts=True)
Number of unique values in column date_crawled is 34 


Descriptive statistics of column date_crawled
count          49986
unique            34
top       2016-04-03
freq            1934
Name: date_crawled, dtype: object


Unique values with their respective counts:
              count  cum_sum  cum_perc
date_crawled                          
2016-03-05     1269     1269      2.54
2016-03-06      697     1966      3.93
2016-03-07     1798     3764      7.53
2016-03-08     1663     5427     10.86
2016-03-09     1660     7087     14.18
2016-03-10     1606     8693     17.39
2016-03-11     1624    10317     20.64
2016-03-12     1838    12155     24.32
2016-03-13      778    12933     25.87
2016-03-14     1831    14764     29.54
2016-03-15     1699    16463     32.94
2016-03-16     1475    17938     35.89
2016-03-17     1575    19513     39.04
2016-03-18      653    20166     40.34
2016-03-19     1745    21911     43.83
2016-03-20     1891    23802     47.62
2016-03-21     1874    25676     51.37
2016-03-22     1645    27321     54.66
2016-03-23     1619    28940     57.90
2016-03-24     1455    30395     60.81
2016-03-25     1587    31982     63.98
2016-03-26     1624    33606     67.23
2016-03-27     1552    35158     70.34
2016-03-28     1742    36900     73.82
2016-03-29     1707    38607     77.24
2016-03-30     1681    40288     80.60
2016-03-31     1595    41883     83.79
2016-04-01     1690    43573     87.17
2016-04-02     1770    45343     90.71
2016-04-03     1934    47277     94.58
2016-04-04     1824    49101     98.23
2016-04-05      655    49756     99.54
2016-04-06      159    49915     99.86
2016-04-07       71    49986    100.00

Looking at the data above it seems like the period over which the data has been crawled covers roughly one month (March-April 2016).\ The distribution is more or less uniform.

ad_created

In [18]:
explore_series(autos, 'ad_created', value_counts=True)
Number of unique values in column ad_created is 76 


Descriptive statistics of column ad_created
count          49986
unique            76
top       2016-04-03
freq            1946
Name: ad_created, dtype: object


Unique values with their respective counts:
            count  cum_sum  cum_perc
ad_created                          
2015-06-11      1        1      0.00
2015-08-10      1        2      0.00
2015-09-09      1        3      0.01
2015-11-10      1        4      0.01
2015-12-05      1        5      0.01
2015-12-30      1        6      0.01
2016-01-03      1        7      0.01
2016-01-07      1        8      0.02
2016-01-10      2       10      0.02
2016-01-13      1       11      0.02
2016-01-14      1       12      0.02
2016-01-16      1       13      0.03
2016-01-22      1       14      0.03
2016-01-27      3       17      0.03
2016-01-29      1       18      0.04
2016-02-01      1       19      0.04
2016-02-02      2       21      0.04
2016-02-05      2       23      0.05
2016-02-07      1       24      0.05
2016-02-08      1       25      0.05
2016-02-09      2       27      0.05
2016-02-11      1       28      0.06
2016-02-12      3       31      0.06
2016-02-14      2       33      0.07
2016-02-16      1       34      0.07
2016-02-17      1       35      0.07
2016-02-18      2       37      0.07
2016-02-19      3       40      0.08
2016-02-20      2       42      0.08
2016-02-21      3       45      0.09
2016-02-22      1       46      0.09
2016-02-23      4       50      0.10
2016-02-24      2       52      0.10
2016-02-25      3       55      0.11
2016-02-26      2       57      0.11
2016-02-27      6       63      0.13
2016-02-28     10       73      0.15
2016-02-29      8       81      0.16
2016-03-01      5       86      0.17
2016-03-02      5       91      0.18
2016-03-03     43      134      0.27
2016-03-04     72      206      0.41
2016-03-05   1152     1358      2.72
2016-03-06    756     2114      4.23
2016-03-07   1737     3851      7.70
2016-03-08   1665     5516     11.04
2016-03-09   1661     7177     14.36
2016-03-10   1593     8770     17.54
2016-03-11   1639    10409     20.82
2016-03-12   1830    12239     24.48
2016-03-13    846    13085     26.18
2016-03-14   1761    14846     29.70
2016-03-15   1687    16533     33.08
2016-03-16   1500    18033     36.08
2016-03-17   1559    19592     39.19
2016-03-18    686    20278     40.57
2016-03-19   1692    21970     43.95
2016-03-20   1893    23863     47.74
2016-03-21   1884    25747     51.51
2016-03-22   1638    27385     54.79
2016-03-23   1609    28994     58.00
2016-03-24   1454    30448     60.91
2016-03-25   1594    32042     64.10
2016-03-26   1628    33670     67.36
2016-03-27   1545    35215     70.45
2016-03-28   1748    36963     73.95
2016-03-29   1705    38668     77.36
2016-03-30   1672    40340     80.70
2016-03-31   1595    41935     83.89
2016-04-01   1690    43625     87.27
2016-04-02   1754    45379     90.78
2016-04-03   1946    47325     94.68
2016-04-04   1842    49167     98.36
2016-04-05    592    49759     99.55
2016-04-06    163    49922     99.87
2016-04-07     64    49986    100.00

The dates ads were created range from June 2015 until April of 2016.\ The majority (+- 97%) of ads in the dataset were created after the date on which data was crawled for the first time.\ This make sense as most auctions are only 'live' for a short period of time.

last_seen

In [19]:
explore_series(autos, 'last_seen', value_counts=True)
Number of unique values in column last_seen is 34 


Descriptive statistics of column last_seen
count          49986
unique            34
top       2016-04-06
freq           11046
Name: last_seen, dtype: object


Unique values with their respective counts:
            count  cum_sum  cum_perc
last_seen                           
2016-03-05     54       54      0.11
2016-03-06    221      275      0.55
2016-03-07    268      543      1.09
2016-03-08    379      922      1.84
2016-03-09    492     1414      2.83
2016-03-10    538     1952      3.91
2016-03-11    626     2578      5.16
2016-03-12   1190     3768      7.54
2016-03-13    449     4217      8.44
2016-03-14    640     4857      9.72
2016-03-15    794     5651     11.31
2016-03-16    822     6473     12.95
2016-03-17   1396     7869     15.74
2016-03-18    371     8240     16.48
2016-03-19    787     9027     18.06
2016-03-20   1035    10062     20.13
2016-03-21   1036    11098     22.20
2016-03-22   1079    12177     24.36
2016-03-23    929    13106     26.22
2016-03-24    978    14084     28.18
2016-03-25    960    15044     30.10
2016-03-26    848    15892     31.79
2016-03-27    801    16693     33.40
2016-03-28   1042    17735     35.48
2016-03-29   1116    18851     37.71
2016-03-30   1242    20093     40.20
2016-03-31   1191    21284     42.58
2016-04-01   1155    22439     44.89
2016-04-02   1244    23683     47.38
2016-04-03   1268    24951     49.92
2016-04-04   1231    26182     52.38
2016-04-05   6212    32394     64.81
2016-04-06  11046    43440     86.90
2016-04-07   6546    49986    100.00

The last three days contain a disproportionate amount of 'last seen' values.\ Given that these are 6-10x the values from the previous days, it's unlikely that there was a massive spike in sales.\ It's more likely that these values are to do with the crawling period ending and don't indicate car sales.

registration_year

In [20]:
explore_series(autos, 'registration_year', value_counts=True)
Number of unique values in column registration_year is 97 


Descriptive statistics of column registration_year
count    49986.000000
mean      2005.075721
std        105.727161
min       1000.000000
25%       1999.000000
50%       2003.000000
75%       2008.000000
max       9999.000000
Name: registration_year, dtype: float64


Unique values with their respective counts:
                   count  cum_sum  cum_perc
registration_year                          
1000                   1        1      0.00
1001                   1        2      0.00
1111                   1        3      0.01
1500                   1        4      0.01
1800                   2        6      0.01
1910                   9       15      0.03
1927                   1       16      0.03
1929                   1       17      0.03
1931                   1       18      0.04
1934                   2       20      0.04
1937                   4       24      0.05
1938                   1       25      0.05
1939                   1       26      0.05
1941                   2       28      0.06
1943                   1       29      0.06
1948                   1       30      0.06
1950                   3       33      0.07
1951                   2       35      0.07
1952                   1       36      0.07
1953                   1       37      0.07
1954                   2       39      0.08
1955                   2       41      0.08
1956                   5       46      0.09
1957                   2       48      0.10
1958                   4       52      0.10
1959                   7       59      0.12
1960                  33       92      0.18
1961                   6       98      0.20
1962                   4      102      0.20
1963                   9      111      0.22
1964                  12      123      0.25
1965                  17      140      0.28
1966                  22      162      0.32
1967                  27      189      0.38
1968                  26      215      0.43
1969                  19      234      0.47
1970                  45      279      0.56
1971                  27      306      0.61
1972                  35      341      0.68
1973                  25      366      0.73
1974                  24      390      0.78
1975                  19      409      0.82
1976                  27      436      0.87
1977                  22      458      0.92
1978                  47      505      1.01
1979                  35      540      1.08
1980                  97      637      1.27
1981                  30      667      1.33
1982                  43      710      1.42
1983                  53      763      1.53
1984                  53      816      1.63
1985                 104      920      1.84
1986                  76      996      1.99
1987                  75     1071      2.14
1988                 142     1213      2.43
1989                 181     1394      2.79
1990                 395     1789      3.58
1991                 356     2145      4.29
1992                 390     2535      5.07
1993                 445     2980      5.96
1994                 660     3640      7.28
1995                1312     4952      9.91
1996                1444     6396     12.80
1997                2028     8424     16.85
1998                2453    10877     21.76
1999                2998    13875     27.76
2000                3354    17229     34.47
2001                2702    19931     39.87
2002                2533    22464     44.94
2003                2727    25191     50.40
2004                2737    27928     55.87
2005                3015    30943     61.90
2006                2707    33650     67.32
2007                2304    35954     71.93
2008                2231    38185     76.39
2009                2097    40282     80.59
2010                1597    41879     83.78
2011                1634    43513     87.05
2012                1323    44836     89.70
2013                 806    45642     91.31
2014                 665    46307     92.64
2015                 399    46706     93.44
2016                1316    48022     96.07
2017                1452    49474     98.98
2018                 491    49965     99.96
2019                   3    49968     99.96
2800                   1    49969     99.97
4100                   1    49970     99.97
4500                   1    49971     99.97
4800                   1    49972     99.97
5000                   4    49976     99.98
5911                   1    49977     99.98
6200                   1    49978     99.98
8888                   1    49979     99.99
9000                   2    49981     99.99
9996                   1    49982     99.99
9999                   4    49986    100.00

Both the minimum as maximum value of registration year seems strange.

The lowest registration year is 1,000 which must be incorrect as cars only started appearing in the late 1800's.\ Due to this all occurences with a registration year before 1885 (first patented practical automobile) will be removed.

All registration years after 2016 must be incorrect as ads were created in 2015 & 2016.\ These will be removed from the dataset as well.

In [21]:
autos = autos[autos['registration_year'].between(1885,2016)]
In [22]:
explore_series(autos, 'registration_year')
Number of unique values in column registration_year is 78 


Descriptive statistics of column registration_year
count    48016.000000
mean      2002.806002
std          7.306212
min       1910.000000
25%       1999.000000
50%       2003.000000
75%       2008.000000
max       2016.000000
Name: registration_year, dtype: float64


There is still a large variety in registration years of the cars.\ The mean of 2002 with a small standard deviation indicate that most cars are approximately between 7 and 21 years old.

This concludes the exploration of date columns.

Exploration of variations between car brands

When working with data on cars, it's natural to explore variations across different car brands.\ Aggregation can be used to understand the brand column.

In [23]:
explore_series(autos, 'brand', value_counts=True)
Number of unique values in column brand is 40 


Descriptive statistics of column brand
count          48016
unique            40
top       volkswagen
freq           10185
Name: brand, dtype: object


Unique values with their respective counts:
                count  cum_sum  cum_perc
brand                                   
alfa_romeo        318      318      0.66
audi             4149     4467      9.30
bmw              5283     9750     20.31
chevrolet         274    10024     20.88
chrysler          176    10200     21.24
citroen           668    10868     22.63
dacia             123    10991     22.89
daewoo             72    11063     23.04
daihatsu          123    11186     23.30
fiat             1242    12428     25.88
ford             3350    15778     32.86
honda             377    16155     33.65
hyundai           473    16628     34.63
jaguar             76    16704     34.79
jeep              108    16812     35.01
kia               341    17153     35.72
lada               29    17182     35.78
lancia             52    17234     35.89
land_rover         98    17332     36.10
mazda             727    18059     37.61
mercedes_benz    4579    22638     47.15
mini              415    23053     48.01
mitsubishi        391    23444     48.83
nissan            725    24169     50.34
opel             5194    29363     61.15
peugeot          1418    30781     64.11
porsche           293    31074     64.72
renault          2274    33348     69.45
rover              65    33413     69.59
saab               77    33490     69.75
seat              873    34363     71.57
skoda             770    35133     73.17
smart             668    35801     74.56
sonstige_autos    523    36324     75.65
subaru            105    36429     75.87
suzuki            284    36713     76.46
toyota            599    37312     77.71
trabant            75    37387     77.86
volkswagen      10185    47572     99.08
volvo             444    48016    100.00

There is a large variety of car brands in the dataset and data is not uniformly distributed.\ For further analysis the dataset will be limited to the top 10 brands in terms of number of ads.

In [24]:
top_10_brands = (autos['brand']
                 .value_counts(normalize=True,dropna=False)
                 .head(10)
                 .index)

autos = autos[autos.brand.isin(top_10_brands)]
In [25]:
explore_series(autos, 'brand', value_counts=True)
Number of unique values in column brand is 10 


Descriptive statistics of column brand
count          38547
unique            10
top       volkswagen
freq           10185
Name: brand, dtype: object


Unique values with their respective counts:
               count  cum_sum  cum_perc
brand                                  
audi            4149     4149     10.76
bmw             5283     9432     24.47
fiat            1242    10674     27.69
ford            3350    14024     36.38
mercedes_benz   4579    18603     48.26
opel            5194    23797     61.74
peugeot         1418    25215     65.41
renault         2274    27489     71.31
seat             873    28362     73.58
volkswagen     10185    38547    100.00

There are still more then 38,000 entries left after limiting the dataset to the top 10 brands.\ All brands left are European, except for Ford. Out of those 10, 5 are German which can be explained by the dataset being from the German section of eBay.

Now that the dataset contains only the top 10 brands it might be interesting to check whether there are differences in mean price between those brands.

In [26]:
mean_price_per_brand = {}

for brand in top_10_brands:
    mean_price = autos.loc[autos['brand'] == brand,'price'].mean()
    mean_price_per_brand[brand] = int(round(mean_price,0))

mean_price_per_brand = pd.Series(mean_price_per_brand, name='mean_price')
In [27]:
mean_price_per_brand.sort_values(ascending=False)
Out[27]:
audi             9094
mercedes_benz    8485
bmw              8103
volkswagen       5231
seat             4296
ford             3652
peugeot          3039
opel             2877
fiat             2712
renault          2395
Name: mean_price, dtype: int64

Brands can be divided into three price categories:

  • Audi, Mercedes Benz and BMW being expensive (above €8,000)
  • Volkswagen and Seat being average priced (between €4,000 and €8,000)
  • Ford, Peugeut, Opel, Fiat, and Renault being cheap (below €4,000)

Normally a car will become less valuable when the mileage of the car becomes higher.\ It is interesting to see whether this principle can be found in the dataset.\ For that the mean mileage per brand needs to be calculated.

In [28]:
mean_mileage_per_brand = {}

for brand in top_10_brands:
    mean_mileage = autos.loc[autos['brand'] == brand,'odometer_km'].mean()
    mean_mileage_per_brand[brand] = int(round(mean_mileage,0))
    
mean_mileage_per_brand = pd.Series(mean_mileage_per_brand,name='mean_mileage')

mean_mileage_per_brand 
Out[28]:
volkswagen       128724
bmw              132431
opel             129223
mercedes_benz    130856
audi             129288
ford             124069
renault          128184
peugeot          127137
fiat             116554
seat             121564
Name: mean_mileage, dtype: int64
In [29]:
price_mileage_per_brand = pd.concat([mean_price_per_brand,mean_mileage_per_brand],axis=1)

price_mileage_per_brand
Out[29]:
mean_price mean_mileage
volkswagen 5231 128724
bmw 8103 132431
opel 2877 129223
mercedes_benz 8485 130856
audi 9094 129288
ford 3652 124069
renault 2395 128184
peugeot 3039 127137
fiat 2712 116554
seat 4296 121564

Above both mean price and mean mileage can be seen. It is however not possible to conclude whether higher mileage is affecting the price.\ This is due to the fact that within a brand there are a lot of other variables affecting price (such as car type, engine type, registration year etc).\ In order to confirm whether mileage affects the price a slice of the dataset is necessary where all those variables are kept the same as much as possible.

In [30]:
unique_brands = autos['brand'].unique()

brand_model = {}
brand_model_count = {}

for ub in unique_brands:
        temp = autos.loc[autos['brand']==ub,'model'].value_counts().index[0]
        temp2 = autos.loc[autos['brand']==ub,'model'].value_counts()[0]
        brand_model[ub] = temp
        brand_model_count[ub] = temp2
        
brand_model_series = pd.Series(brand_model,name = 'model')
brand_model_count_series = pd.Series(brand_model_count,name = 'count')

df = pd.concat([brand_model_series, brand_model_count_series], axis=1)
In [31]:
df.sort_values(by='count', ascending=False)
Out[31]:
model count
volkswagen golf 3815
bmw 3er 2688
opel corsa 1645
audi a4 1265
mercedes_benz c_klasse 1147
ford focus 776
renault twingo 636
peugeot 2_reihe 611
fiat punto 431
seat ibiza 335

Volkswagen Golf is the most occuring combination of brand and model.

In [32]:
#creating new dataset with only brand = volkswagen & model = golf
vw_golf = (autos.loc[(
    autos['brand']=='volkswagen')&
    (autos['model']=='golf')]
    )

vw_golf['registration_year'].value_counts().head(5)
Out[32]:
1998    277
1999    256
2000    243
1995    201
1997    175
Name: registration_year, dtype: int64

The top three registration years for Volkswagen Golf's in the dataset are 1998, 1999 and 2000.

In [33]:
#creating new data set only containing registration year 1998 - 2000
vw_golf_ry = (vw_golf[
    vw_golf['registration_year'].isin([1998,1999,2000])])

vw_golf_ry['fuel_type'].value_counts().head(5)
Out[33]:
benzin    585
diesel    117
lpg         5
cng         2
Name: fuel_type, dtype: int64

Benzine is by far the most occuring fuel type for Volkswagen Golf's with a registration year between 1998 and 2000.

In [34]:
#creating new data set only containing fuel type benzine
vw_golf_ry_benzine = (
    vw_golf_ry[
        vw_golf_ry['fuel_type']=='benzin'])

vw_golf_ry_benzine['gearbox'].value_counts().head(5)
Out[34]:
manuell      534
automatik     36
Name: gearbox, dtype: int64

Almost all cars left in the dataset have a manual transmission

In [35]:
#creating new data set only containing manual gearboxes
vw_golf_ry_benzine_manual = (
    vw_golf_ry_benzine[
        vw_golf_ry_benzine['gearbox']=='manuell'])

vw_golf_ry_benzine_manual['unrepaired_damage'].value_counts()
Out[35]:
nein    363
ja       65
Name: unrepaired_damage, dtype: int64

There are almost no cars with damage in the remaining dataset

In [36]:
#creating new data set only containing cars with no unrepaired damage
vw_golf_ry_benzine_manual_nd = (
    vw_golf_ry_benzine_manual[
        vw_golf_ry_benzine_manual['unrepaired_damage']=='nein'])

vw_golf_ry_benzine_manual_nd['power_PS'].value_counts().head(5)
Out[36]:
75     165
101     98
105     21
150     20
116     15
Name: power_PS, dtype: int64

The amount of horsepowers for cars in the remainig dataset is more granular.\ However, cars with 75 and 101 horsepower still cover almost 75% of the dataset.\ Since the amount of horsepower is not so different between 75 and 101 both will be kept for further analysis.

In [37]:
#creating new data set only containing cars with 75 or 101 horsepower
vw_golf_ry_benzine_manual_nd_ps = (
    vw_golf_ry_benzine_manual_nd[
        vw_golf_ry_benzine_manual_nd['power_PS'].isin([75,101])])
In [38]:
#checking how distribution of odometer_km is within the remaining dataset
vw_golf_ry_benzine_manual_nd_ps['odometer_km'].value_counts()
Out[38]:
150000    235
125000     13
90000       5
60000       3
100000      3
80000       1
30000       1
50000       1
5000        1
Name: odometer_km, dtype: int64

Conclusions

After filtering the dataset on several variables the distribution of odometer_km is skewered heavily towards 150,000.\ There are so few occurences left for other values of odometer_km that it is not possible anymore to make conclusions about the effect of mileage on price.

Furthermore, price in this dataset is the starting price of an auction and not the actual selling price.\ Some people might create an ad with an unrealistic starting price assuming that this will attract people and drive up the selling price.\ It would therefore be better to investigate this effect further with a dataset that contains the selling price instead of the starting price of an auction.

In [39]:
#just because I went through all the trouble already I will calculate anyway. xD

df = vw_golf_ry_benzine_manual_nd_ps

odometer_km_unique = vw_golf_ry_benzine_manual_nd_ps['odometer_km'].unique()

price_odo = {}

for odo in odometer_km_unique:
    temp = df.loc[df['odometer_km']==odo,'price'].mean()
    price_odo[odo] = round(temp,0)
    
price_odo = pd.Series(price_odo, name='price')

price_odo.sort_index()
Out[39]:
5000      1300.0
30000     1450.0
50000     3200.0
60000     3266.0
80000     2200.0
90000     2581.0
100000    2383.0
125000    1984.0
150000    1545.0
Name: price, dtype: float64