Question
In a study of two groups, the following results were obtained :
|
Group |
Group |
|
A |
B |
| Sample Size |
$$20$$ |
$$25$$ |
| Sample mean |
$$22$$ |
$$23$$ |
| Sample standard deviation |
$$10$$ |
$$12$$ |
Which of the following statements is correct ?
A.
Group A is less variable than Group B because Group A’s standard deviation is smaller.
B.
Group A is less variable than Group B because Group A’s sample size is smaller.
C.
Group A is less variable than Group B because Group A’s sample mean is smaller.
D.
Group A is less variable than group B because Group A’s coefficient of variation is smaller.
Answer :
Group A is less variable than group B because Group A’s coefficient of variation is smaller.
Solution :
$$\eqalign{
& {\text{For Group A :}} \cr
& {\text{Coefficient of variation}} \cr
& C{V_A} = \frac{{{\text{S}}{\text{.D}}{\text{.}}}}{{{\text{Mean}}}} = \frac{{10}}{{22}} = 0.4545 \cr
& {\text{For Group B :}} \cr
& C{V_B} = \frac{{12}}{{23}} = 0.522 \cr
& \Rightarrow {\text{Group A is less variable}}{\text{.}} \cr} $$