Question

The coefficient of variation from the given data

class interval	0 -10	10- 20	20 -30	30- 40	40 -50
frequency	2	10	8	4	6

is

• A. 50
• B. 51.9
• C. 48
• D. 51.8

Answer 1

Answer: (C)

Class	mid value (x)	f	f x	d = x -M	$d^2$	$f{d}^2$
0 - 10	5	2	10	-20.7	428.49	856.98
10 - 20	15	10	150	-10.7	114.49	1144.9
20 - 30	25	8	200	-0.7	0.49	3.92
30 - 40	35	4	140	9.3	86.49	345.96
40 - 50	45	6	270	19.3	372.49	2234.94
			$\sum f=30$	$\sum fx=770$		$\sum f{d}^2=4586.7$

Now, M (A.M) = $\frac{\sum fx}{\sum f}=\frac{770}{30}=25.7$
Now, standard deviation (S.D)
$=\sqrt{\frac{\sum f{d}^2}{\sum f}}=\sqrt{\frac{4586.70}{30}}=12.36$
$\therefore$ Coeff of SD = $\frac{SD}{M}=\frac{12.36}{25.7}=0.480$
$\therefore$ Coeff of variation = Coeff of S.D $\times$ 100
= 0.480 $\times$ 100 = 48.