Question

The following table gives the distribution of total household expenditure (in Rs) of 200 manual workers in a city: Expenditure (Rs) 100 – 150 150 - 200 200 - 250 250 - 300 300 - 350 350 - 400 400 - 450 450 - 500 No of workers 24 40 33 28 30 22 16 7 Find mean, mode and median of the above data. Also compare and interpret the three measures of central tendency

Answer 1

Given :  household expenditure (in Rs) of 200 manual workers in a city: Expenditure (Rs) 100 – 150 150 - 200 200 - 250 250 - 300 300 - 350 350 - 400 400 - 450 450 - 500

No of workers 24 40 33 28 30 22 16 7

To Find :  mean, mode and median

Solution:

Class            Mean   A= (Mean-275)50     f          cf          A*f

100 – 150      125             -3                       24       24         -72

150 - 200     175             -2                       40       64         -80

200 - 250    225             -1                       33       97         -33

250 - 300     275             0                       28       125         0

300 - 350     325             1                       30       155        30

350 - 400     375             2                       22       177        44

400 - 450     425             3                       16        193        48

450 - 500     475             4                       7        200       28

                                                                 200                   -35            

Mean = 275  + (50 ) * (-35)/200

= 275 - 8.75

= 266.25

Median =  250  + 50 *   ( 100 - 97)/28

= 250 + 5.36

= 255.36

Mode = 150 + 50 x (40 - 24)/(40 - 24 + 40 - 33)

= 150 + 50 x 16 / 23

= 150 + 34.78

= 184.78

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