The mean of following frequency distribution is $14$ , find the value of $k$ .
$\begin{matrix} x f \end{matrix} \begin{matrix} 57 \end{matrix} \begin{matrix} 106 \end{matrix} \begin{matrix} 158 \end{matrix} \begin{matrix} 20 K \end{matrix} \begin{matrix} 255 \end{matrix}$

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Solution

Given that mean of following frequency distribution is $14$ .
x 5 10 15 20 25
f 7 6 8 k 5
we prepare to table
x f fx
5 7 35
10 6 60
15 8 120
20 k 20k
25 5 125
$\sum f = 26 + k$

$\sum f x = 340 + 20 k$

$∴$ we know mean $= \frac{\sum f x}{\sum f}$

$14 = \frac{340 + 20 k}{26 + k}$

$340 + 20 k = (26 + k) 14$

$340 + 20 k = 364 + 14 k$

$20 k - 14 k = 364 - 340$

$6 k = 24$

$k = 24 / 6$

$k = 4$

value of $k = 4$

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