Question

Find the mean deviations about the mean for the following data:

Marks obtained	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Number of students	$2$	$3$	$8$	$14$	$8$	$3$	$2$

Answer 1

$CI$	$f_i$	$Mid-value$ $x_i$	$f_i{x}_i$	$|x_i-\overline{x}|$	$f_i|x_i-\overline{x}|$
$10-20$	$2$	$15$	$30$	$30$	$60$
$20-30$	$3$	$25$	$75$	$20$	$60$
$30-40$	$8$	$35$	$280$	$10$	$80$
$40-50$	$14$	$45$	$630$	$0$	$0$
$50-60$	$8$	$55$	$440$	$10$	$80$
$60-70$	$3$	$65$	$195$	$20$	$60$
$70-80$	$2$	$75$	$150$	$30$	$60$
	$\sum f_i=40$		$\sum f_i{x}_i=$ $1800$		$\sum f_i|x_i-\overline{x}|=$ $400$

$\Rightarrow$ $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{1800}{40}=45$

$\Rightarrow$ Mean deviation about mean $=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}=\frac{400}{40}=10$