Question

Find the mean deviation about mean for the following data.

Class interval	$10-19$	$20-29$	$30-39$	$40-49$	$50-59$	$60-69$	$70-79$
Frequency	$6$	$4$	$10$	$9$	$11$	$8$	$2$

Answer 1

Class Interval	Frequency
10-19 20-29 30-39 40-49 50-59 60-69 70-79	6 4 10 9 11 8 2

Change the class interval into continuous data.

Class Interval	Frequency	Mid point $x_i$	${|x}_i-M|$	$f_i(x_i-M)$
9.5-19.5 19.5-29.5 29.5-39.5 39.5-49.5 49.5-59.5 59.5-69.5 69.5-79.5	6 4 10 9 11 8 2	14.5 24.5 34.5 44.5 54.5 64.5 74.5	37.9 39.9 33.9 34.9 32.9 35.9 30.1	226.8 159.6 339 314.1 361.9 287.2 60.2
	$\sum f=50$			$\sum f_i(x_i-M)=1748.8$

$\overline{x}=\frac{2195}{50}=43.9$

Therefore, Mean deviation about Mean, $\frac{\sum f_i(x_i-M)}{\sum f}=\frac{1748.8}{50}=\mathrm{34.976.}$