Question

Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.

a.The salaries of all persons employed by a large university

b.The grades on an easy test

c.The grades on a difficult test

d.The amounts of time students in your class studied last week

e.The ages of automobiles on a used-car lot

f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)

Short answer

a) Rightward Skewness

b) Leftward Skewness

c) Rightward Skewness

d) Rightward Skewness

e) Leftward Skewness

f) Leftward Skewness

Step-by-step solution

Determining the skewness of the data set in (a)

The salaries of everybody employed at a large university will be skewed to the right because while the majority of the people would have an average salary, there might be some outliers who would have higher salaries.

Determining the skewness of the data set in (b)

The grades on an easy test will have a leftward skewed distribution because most of them would perform well on the test, but there might be only a few who would not score well.

Determining the skewness of the data set in (c)

The grades on a difficult test will be skewed to the right because, as it is a difficult test, only a few would do well while the majority would have performed poorly.

Determining the skewness of the data set in (d)

The number of time students in your class studied last week would be skewed to the right because the majority of students would study moderately, whilst there would be some that would dedicate extra time to study

Determining the skewness of the data set in (e)

The ages of automobiles on a used-car lot would be skewed to the left because there would mostly be a wide range of new vehicles, with only a few that have been used for a very long time.

Determining the skewness of the data set in (f)

The amount of time spent on a difficult examination is skewed to the left because most of the students would take the whole 50 minutes time to complete the test; some of them might be able to do it in less time.