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Question

If the mean of the following distribution is 54, find the value of p:
Class : 0−20 20−40 40−60 60−80 80−100
Frequency : 7 p 10 9 13

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Solution

Consider the table given below:
Class Interval Frequency(fi) Class Mark(xi) fi xi
0–20 7 10 70
20–40 p 30 30p
40–60 10 50 500
60–80 9 70 630
80–100 13 90 1170
fi=39+p fixi=2370+30p

It given that the mean of the distribution is 54.

Mean=fixifi2370+30p39+p=542370+30p=2106+54p54p-30p=2370-2106

24p=264p=26424=11

Hence, the value of p is 11.

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