Question

Calculate mean deviation about mean for the given data.

Score $\left(x\right)$	$6$	$20$	$8$	$18$	$16$	$12$	$14$	$10$
Frequency $\left(f\right)$	$2$	$7$	$11$	$27$	$18$	$13$	$17$	$5$

• A. $3.117$
• B. $3.217$
• C. $4.212$
• D. $6.21$

Answer 1

The correct option is A $3.117$

x (1)	f (2)	$f\times x$ (3) = (2) \times (1)	$|x-\overline{x}|$ = $|x-14.38|$ (4)	$f\times |x-14.38|$ (5) = (2) \times (4)
6	2	12	8.58	17.16
20	7	140	5.42	37.94
8	11	88	6.58	72.38
18	27	486	3.42	92.34
16	18	288	1.42	25.56
12	13	156	2.58	33.54
14	17	238	0.58	9.86
10	5	50	4.58	22.9
-	-	----	--	----
	n = 100	$\sum \left[f\times x\right]=1458$		$\sum \left[f\times |x-\overline{x}|\right]=311.68$

Mean $\overline{x}$ = $\frac{\sum f.x}{N}$

$=$ $\frac{1458}{100}$

Mean deviation of mean $=$ $\frac{\sum f.|x-\overline{x}|}{N}$

$=$ $\frac{311.68}{100}$

$=3.117$