Find the missing frequency (p) for the following distribution who… - Vidyadip

Question

Find the missing frequency (p) for the following distribution whose mean is 7.68.

x	3	5	7	9	11	13
f	6	8	15	P	8	4

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Answer

x	f	fx
3	6	18
5	8	40
7	15	105
9	P	9P
11	8	88
13	4	52
	N = P + 41	$\sum\text{fx}=9\text{P}+303$

Given
$\Rightarrow\text{Mean}=7.68$
$\Rightarrow\frac{\sum\text{fx}}{\text{N}}=68$
$\Rightarrow\frac{9\text{P}+303}{\text{P}+41}=7.68$
$\Rightarrow9\text{P}+303=\text{P}(7.68)+314.88$
$\Rightarrow9\text{P}-7.68\text{P}=314.88-303$
$\Rightarrow1.32\text{P}=11.88$
$\Rightarrow\text{P}=\frac{11.88}{1.32}$
$\Rightarrow\text{P}=9.$

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