If the mean of the following frequency distribution is $7.2$ find value of $k$ .
$\begin{matrix} x & 2 & 4 & 6 & 8 & 10 & 12 f & 4 & 7 & 10 & 16 & k & 3 \end{matrix}$

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Solution

$\begin{matrix} x & f & f x 2 & 4 & 8 4 & 7 & 28 6 & 10 & 60 8 & 16 & 128 10 & k & 10 k 12 & 3 & 36 Total & \sum f = 40 + k & \sum f x = 260 + 10 k \end{matrix}$
Given, Mean, $¯ ¯ ¯ x = 7.2$
Mean, $¯ ¯ ¯ x = \frac{\sum f x}{\sum f} = \frac{260 + 10 k}{40 + k} = 7.2$
$\Rightarrow 260 + 10 k = 7.2 (40 + k)$
$\Rightarrow 260 + 10 k = 288 + 7.2 k$

$\Rightarrow 2.8 k = 28$

$∴ k = 10.$

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