Question

Calculate the Mean and Standard Deviation for the following distribution:

Class-interval	Frequency
$0-4$	$2$
$5-9$	$3$
$10-14$	$10$
$15-19$	$3$
$20-24$	$2$

Answer 1

C.I	$f$	$x$	$fx$	$x-\overline{x}=D$	$D^2$	$f{D}^2$
$0-4$	$2$	$2$	$4$	$-10$	$100$	$200$
$5-9$	$3$	$7$	$21$	$-5$	$25$	$75$
$10-14$	$10$	$12$	$120$	$0$	$0$	$0$
$15-19$	$3$	$17$	$51$	$5$	$25$	$75$
$20-24$	$2$	$22$	$44$	$10$	$100$	$200$

$N=20$
$\sum fx=240$
$\sum f{d}^2=550$
$\overline{X}=\frac{240}{20}=12$
Standard Deviation $\sigma =\sqrt{\frac{\sum f{d}^2}{N}}=\sqrt{\frac{550}{20}}=\sqrt{27.5}$
$=5.24$