Question

Sample grade point averages for ten male students and ten female students are listed. Find the coefficient of variation for each of the two data sets. Then compare the results. Males 2.3 3.6 3.9 3.7 2.8 2.7 3.5 3.3 3.8 1.7 Females 2.6 3.8 2.1 3.9 3.8 3.8 2.1 3.7 3.8 2.1 The coefficient of variation for males is = The coefficient of variation for females is =

Answer 1

The coefficient of variation (CV) for males is 23.29%, and the coefficient of variation for females is 26.10%.

Step-by-step explanation:

To calculate the coefficient of variation (CV), we first need to calculate the mean and standard deviation of each data set.

For Males:

Mean = (2.3 + 3.6 + 3.9 + 3.7 + 2.8 + 2.7 + 3.5 + 3.3 + 3.8 + 1.7) / 10 = 3.18

Standard Deviation = √[(2.3 - 3.18)^2 + (3.6 - 3.18)^2 + ... + (1.7 - 3.18)^2] / 10 = 0.74

CV = (Standard Deviation / Mean) * 100% = (0.74 / 3.18) * 100% = 23.29%

For Females:

Mean = (2.6 + 3.8 + 2.1 + 3.9 + 3.8 + 3.8 + 2.1 + 3.7 + 3.8 + 2.1) / 10 = 3.25

Standard Deviation = √[(2.6 - 3.25)^2 + (3.8 - 3.25)^2 + ... + (2.1 - 3.25)^2] / 10 = 0.84

CV = (Standard Deviation / Mean) * 100% = (0.84 / 3.25) * 100% = 26.10%

Comparison:

The coefficient of variation for females is higher than the coefficient of variation for males. This means that the grades of the female students are more variable than the grades of the male students.