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If the mean of the following distribution 54, find the value o

Question

If the mean of the following distribution $54$ , 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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Scarlett Discussed

If the mean of the following distribution

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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Text solutionVerified

Computation Arithematic Mean

We have,
A= 50, N= 39 +p, h= 20,

\sum f_{i} u_{i} = 21 - p

and

\overline{X} = 54

∴ M e an = A + h (\frac{1}{N} \sum f_{i} u_{i})

\Rightarrow 54 = 50 + 20 \times (\frac{21 - p}{39 + p})

\Rightarrow 4 = 20 \times (\frac{21 - p}{39 + p})

\Rightarrow 1 = 5 (\frac{21 - p}{39 + p}) \Rightarrow 39 + p = 105 - 5 p \Rightarrow 6 p = 66 \Rightarrow p = 11

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Question Text	If the mean of the following distribution $54$ , find the value of $p$ :
Answer Type	Text solution:1
Upvotes	150