In a study of two groups, the following results were obtained:

Group A

Group B

Sample size

20

25

Sample mean

22

23

Sample standard deviation

10

12

Which of the following statements is correct?

Question

Question

This question was previously asked in

NDA (Held On: 18 Sept 2016) Maths Previous Year paper

Attempt Online

Group A is less variable than Group B because Group A's standard deviation is smaller.
Group A is less variable than Group B because Group A's sample size is smaller.
Group A is less variable than Group B because Group A's sample mean is smaller.
Group A is less variable than Group B because Group A's coefficient of variation is smaller.

Answer 1

Concept:

\({\rm{Coefficient\;of\;variation}} = \frac{{{\rm{standard\;deviation}}}}{{{\rm{mean}}}}\)

Calculation:

Coefficient of variation for Group A = 10/22 = 0.4545

Coefficient of variation for Group B = 12/23 = 0.522

Group A is less variable than Group B because Group A's coefficient of variation is smaller.