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Question

If the mean of the following frequency distibution is 24, find the value of p.
Class0101020203030404050Frequency34p32


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Solution

The given data is shown as follows:

Class Frequency (fi) Class mark (xi) (fixi)
0 - 10 3 5 15
10 - 20 4 15 60
20 - 30 p 25 25p
30 - 40 3 35 105
40 - 50 2 45 90
Total fi=12+p fixi=270+25p

The mean of given data is given by

¯x=fixifi

⇒ 24 = 270+25p12+p
⇒ 24(12 + p) = 270 + 25p
⇒288 + 24p = 270 + 25p
⇒ 25p - 24p = 288 - 270
⇒ p = 18

Hence, the value of p is 18.


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