Question

The mean of the following data is 21, find the value of p.
Class:- 7.5-12.5, 12.5-17.5, 17.5-22.5 ,22.5-27.5 ,27.5-32.5 ,32.5-37.5
Frequency:- 6, 10 ,P ,10, 2 ,8.

Answer 1

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Answer 2

$\begin {tabular} {|c|c|c|c|} </p><p>\cline {1-4} class& frequency(f_{i} &class mark(x_{i}&\sum f_{i}x_{i} \\</p><p>\cline{1-4} 7.5-12.5&6&10&60 \\</p><p>\cline{1-4} 12.5-17.5&10&15&150 \\</p><p>\cline{1-4} 17.5-22.5&p&20&20p \\</p><p>\cline{1-4} 22.5-27.5&10&25&250 \\</p><p>\cline{1-4} 27.5-32.5&2&30&60 \\</p><p>\cline{1-4} 32.5-37.5&8&35&280\\</p><p>\cline{1-4} - & \sum f_{i}=36+8&-&\sum f_{i}x_{i} = 800+20p \\</p><p>\cline {1-4} </p><p>\end {tabular}$

$Mean = 21 \:(given)$

$\implies \frac{\sum \f_{i}x_{i}}{\sum f_{i}} = 21$

$\implies \frac{800+20p}{36+p} = 21$

$\implies 800 + 20p = 21(36+p)$

$\implies 800 + 20p = 756 + 21p$

$\implies 800 - 756 = 21p - 20p$

$\implies 44 = p$

Therefore.,

$\red { Value \:of \: p } \green {= 44}$

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