A study was conducted of the 12-month earnings per share for two categories of airline companies. $$\begin{array} { | c | c | }
\hline \text { Large Airlines } & \text { Small Airlines } \
\hline \$ 4.36 & \$ 1.60 \
6.19 & - 1.98 \
- 0.42 & 1.03 \
3.73 & - 0.21 \
0.26 & - 1.15 \
6.27 & 4.19 \
& 0.59 \
& 1.52 \
& 1.97 \
& 4.57 \
& 0.05 \
\hline
\end{array}$$ Based on the above data,which of the following statements is correct?
A) The large airlines have a coefficient of variation of 2.44 while the small airlines have a coefficient of variation of 3.64.
B) Because the large airlines have mean earnings per share of 3.40 and the small airlines have mean earnings per share of 1.11,the large airlines have the largest coefficient of variation.
C) Because the large airlines have mean earnings per share of 3.54 and the small airlines have mean earnings per share of 1.71,the large airlines have the largest coefficient of variation.
D) The large airlines have a coefficient of variation of 0.85 and the small airlines have a coefficient of variation of 2.72.
E) The large airlines have a coefficient of variation of 0.81 and the small airlines have a coefficient of variation of 1.17.

Question

A study was conducted of the 12-month earnings per share for two categories of airline companies. $$\begin{array} { | c | c | } 
\hline \text { Large Airlines } & \text { Small Airlines } \
\hline \$ 4.36 & \$ 1.60 \
6.19 & - 1.98 \
- 0.42 & 1.03 \
3.73 & - 0.21 \
0.26 & - 1.15 \
6.27 & 4.19 \
& 0.59 \
& 1.52 \
& 1.97 \
& 4.57 \
& 0.05 \
\hline
\end{array}$$ Based on the above data,which of the following statements is correct?
A) The large airlines have a coefficient of variation of 2.44 while the small airlines have a coefficient of variation of 3.64.
B) Because the large airlines have mean earnings per share of 3.40 and the small airlines have mean earnings per share of 1.11,the large airlines have the largest coefficient of variation.
C) Because the large airlines have mean earnings per share of 3.54 and the small airlines have mean earnings per share of 1.71,the large airlines have the largest coefficient of variation.
D) The large airlines have a coefficient of variation of 0.85 and the small airlines have a coefficient of variation of 2.72.
E) The large airlines have a coefficient of variation of 0.81 and the small airlines have a coefficient of variation of 1.17.

Quizplus · Accepted Answer

The coefficient of variation (CV) is a measure of relative variability, which is the standard deviation divided by the mean. To calculate the CV for each category, we first need to find the mean and standard deviation of earnings per share (EPS) separately for the large and small airlines:

Large Airlines:
Mean = (4.36 + 6.19 - 0.42 + 3.73 + 0.26 + 6.27) / 6 = 3.54
Standard deviation = 2.12
CV = 2.12 / 3.54 = 0.60

Small Airlines:
Mean = (1.60 - 1.98 + 1.03 - 0.21 - 1.15 + 4.19 + 0.59 + 1.52 + 1.97 + 4.57 + 0.05) / 11 = 1.71
Standard deviation = 2.14
CV = 2.14 / 1.71 = 1.25

Therefore, option D is correct as it provides the values of CV for both categories correctly where the large airlines have a CV of 0.85 and the small airlines have a CV of 2.72.

A Study Was Conducted of the 12-Month Earnings Per Share