Question

Consider the following data

	Group I	Group II	Group III
Number of observations	50	60	90
Mean	113	120	115
Standard deviation	6	8	7

With respect to the consistencies of the above groups, the increasing order of them is

• A. I, III, II
• B. II, I, III
• C. III, II, I
• D. II, III, I

Answer 1

Answer: (D)

We have,

	Group I	Group II	Group III
n	50	60	90
mean	113	120	115
S. D	6	8	7

Coefficient of variation $( CV )=\frac{\sigma}{\bar{x}} \times 100$
for group I $ CV _{1} =\frac{\sigma_{1}}{\bar{x}_{1}} \times 100 \%=\frac{6}{113} \times 100 \% $
$ CV _{1} =5309 \% $
for group II
$CV _{2}=\frac{8}{120} \times 100 \%=6.66 \%$
for group III $CV _{3}=\frac{7}{115} \times 100=6.086 \%$
Now, if CV of the data is less then data is more consistent.
Since, $CV _{1}<\,CV _{3}<\, CV _{2}$
$\therefore $ Increasing order of consistencies II < III < I