(a) The mean of the following frequency distribution is 25. Find the value of f.

Class	$\displaystyle x$	$\displaystyle f$	$\displaystyle f x$
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 5$	$\displaystyle 5$	$\displaystyle 25$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle 15$	$\displaystyle 18$	$\displaystyle 270$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 25$	$\displaystyle 15$	$\displaystyle 375$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 35$	$\displaystyle f$	$\displaystyle 35 f$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle 45$	$\displaystyle 6$	$\displaystyle 270$
		$\displaystyle 44+f$	$\displaystyle 940+35 f$

\[\begin{array}{c} \bar{x}=25=\frac{940+35 f}{44+f} \\ \Rightarrow f=16 \end{array} \]Or

Class	$\displaystyle x$	$\displaystyle f$	$\displaystyle d=x-12 \cdot 5$	$\displaystyle f d$
$\displaystyle 0$-$\displaystyle 5$	$\displaystyle 2 \cdot 5$	$\displaystyle 8$	-$\displaystyle 10$	-$\displaystyle 80$
$\displaystyle 5$-$\displaystyle 10$	$\displaystyle 7 \cdot 5$	$\displaystyle 7$	-$\displaystyle 5$	-$\displaystyle 35$
$\displaystyle 10$-$\displaystyle 15$	$\displaystyle 12 \cdot 5$	$\displaystyle 10$	$\displaystyle 0$	$\displaystyle 0$
$\displaystyle 15$-$\displaystyle 20$	$\displaystyle 17 \cdot 5$	$\displaystyle 13$	$\displaystyle 5$	$\displaystyle 65$
$\displaystyle 20$-$\displaystyle 25$	$\displaystyle 22 \cdot 5$	$\displaystyle 12$	$\displaystyle 10$	$\displaystyle 120$
		$\displaystyle 50$		$\displaystyle 70$

\[\begin{array}{c} \bar{x}=12 \cdot 5+\frac{70}{50} \\ =13 \cdot 9 \end{array} \]