Question

Mrs. Leahy and Mr. Johnson decide to compare the heights of students in their classes. Mrs. Leahy's class has a mean height of 67 inches, with a standard deviation of 2.13 inches. Mr. Johnson’s class had an average height of 165 cm with a standard deviation of 5 cm. Use the coefficient of variation to compare the two classes.

a) Mrs. Leahy's class has a higher coefficient of variation.
b) Mr. Johnson’s class has a higher coefficient of variation.
c) Both classes have the same coefficient of variation.
d) Coefficient of variation is not a suitable measure for this comparison.

Answer 1

To compare the coefficient of variation between Mrs. Leahy’s class and Mr. Johnson’s class, calculate the CV for each class by using the formula CV = (standard deviation / mean) x 100.

Step-by-step explanation:

To compare the coefficient of variation between Mrs. Leahy’s class and Mr. Johnson’s class, we need to use the formula: CV = (standard deviation / mean) x 100.

For Mrs. Leahy’s class:
Mean height = 67 inches
Standard deviation = 2.13 inches
CV = (2.13 / 67) x 100 = 3.18%

For Mr. Johnson’s class:
Mean height = 165 cm
Standard deviation = 5 cm
First, we need to convert the mean and standard deviation into inches:
Mean height = 165 cm x 0.3937 inches/cm = 64.96 inches
Standard deviation = 5 cm x 0.3937 inches/cm = 1.97 inches
CV = (1.97 / 64.96) x 100 = 3.03%

Based on the calculations, Mrs. Leahy’s class has a higher coefficient of variation (3.18%) compared to Mr. Johnson’s class (3.03%). Therefore, option a) Mrs. Leahy's class has a higher coefficient of variation is the correct answer.