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Question

Below is given distribution of profit (in Rs.) per day of a shop in a certain town.
Calculate median profit of shops.

Profit (in Rs.)500 - 10001000 - 15001500 - 20002000 - 25002500 - 30003000 - 35003500 - 4000
No. of shops
818272120188

A
Rs. 1867
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B
Rs. 1967
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C
Rs.2167
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D
Rs.2567
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Solution

The correct option is B Rs.2167
Consider the following table, to calculate median:
ci fi cf
500-1000 8 8
1000-1500 18 8+18=26
1500-2000 27 26+27=53
2000-2500 21 53+21=74
2500-3000 20 74+20=94
3000-3500 18 94+18=112
3500-4000 8 112+8=120
Median =l+(N2cf)fm×c
Here,
Class Interval c=500
N=Σfi=120
N2=60
Median class =20002500
Frequency of median classfm=21
Lower boundary of median class l=2000
previous cumulative frequency of median class cf=53

Median =2000+(120253)21×500

Median =2000+(7)21×500

Median =2166.672167
Hence. option C is correct.

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