Question

Calculate Mean and standard deviation for the following distribution

X	$5$	$15$	$25$	$35$	$45$
f	$5$	$8$	$15$	$16$	$6$

Answer 1

Table of calculation
Score X	Frequency f	fX	Deviation $(D=X-\overline{X})$	Square of Deviation $D^2$	f.D2
$5$	$5$	$25$	$–22$	$484$	$2420$
$15$	$8$	$120$	$-12$	$144$	$1152$
$25$	$15$	$375$	$–2$	$4$	$60$
$35$	$16$	$560$	$8$	$64$	$1024$
$45$	$6$	$270$	$18$	$324$	$1944$
	$\sum f=50$	$\sum fx=1350$			$\sum f{D}^2=6600$

Sum of the frequencies $=N=\sum f=50$

(i) Mean $=\overline{X}=\frac{\sum fx}{N}=\frac{1350}{50}=27$

(ii) Standard deviation, S.D $=\sigma =\sqrt{\frac{\sum f{D}^2}{N}}=\sqrt{\frac{6600}{50}}=\sqrt{132}=11.49$