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 - 4000No. of shops818272120188

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

Solution

## The correct option is B Rs.$$2167$$Consider the following table, to calculate median: $$c_i$$ $$f_i$$ $$cf$$ 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=120Median $$=l +\dfrac {(\dfrac{N}{2}-cf)}{ f_m}\times c$$Here, Class Interval $$c=500$$$$N=\Sigma f_i=120$$   $$\dfrac {N}{2}=60$$$$\Rightarrow$$ Median class $$=2000-2500$$$$\Rightarrow$$Frequency of median class$$f_m=21$$Lower boundary of median class $$l=2000$$previous cumulative frequency of median class $$cf=53$$$$\therefore$$ Median $$=2000 +\dfrac {(\dfrac{120}{2}-53)}{ 21}\times 500$$$$\therefore$$ Median $$=2000 +\dfrac {(7)}{ 21}\times 500$$$$\therefore$$ Median $$=2166.67 \Rightarrow 2167$$ Hence. option $$C$$ is correct.Mathematics

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