Question

A study in the Journal of Leisure Research investigated the relationship between academic performance and leisure activities. Each in a sample of 159 high school students was asked to state how many leisure activities they participated in weekly. From the list, activities that involved reading, writing, or arithmetic were labeled "academic leisure activities." Some of the results are listed below:

	Mean	Standard Deviation
GPA	2.96	0.71
Number of leisure activities	12.38	5.07
Number of academic leisure activities	2.77	1.97

1. Knowing that GPA is a value between 0 and 4, discuss the potential skewness of the variable, GPA.
2. Knowing that the number of activities cannot be negative, discuss the potential skewness and compare the two variables, Number of leisure activities and Number of academic leisure activities.

Answer 1

a. The mean GPA for the values 0 to 4 is (0+1+2+3+4)/5 = 2 but the mean we have is 2.96 which is greater than 2 hence the variable GPA is positively skewed.

b. Since the number of activities cannot be negative the skewness in the activities variables is will be negative because all the data will lie on the right-hand side. The variable Number of leisure activities will be less skewed as compared to the variable Number of academic leisure activities because the standard deviation of the latter is high as compared to the first in terms of the within variation, these values are not compared with each other.

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