Textbook reference: Understanding Statistics in the Behavioral Sciences.

Use any of these formulas:

• cumfp= P/100* N
• P = XL + (i/fi) * (cumfp - cumfl)
• PR = [cumfl+ (fi/i)(X - XL)]/N * 100
• P = XL + (i/fi) * [(P/100* N] - cumfl)

Question 15, page 72:

A small eastern college uses the grading system of

0-4.0, with 4.0 being the highest possible grade. The

scores shown here are the grade point averages of the

students currently enrolled as psychology majors at

the college.

2.7 1.9 1.0 3.3 1.3 1.8 2.6 3.7

3.1 2.2 3.0 3.4 3.1 2.2 1.9 3.1

3.4 3.0 3.5 3.0 2.4 3.0 3.4 2.4

2.4 3.2 3.3 2.7 3.5 3.2 3.1 3.3

2.1 1.5 2.7 2.4 3.4 3.3 3.0 3.8

1.4 2.6 2.9 2.1 2.6 1.5 2.8 2.3

3.3 3.1 1.6 2.8 2.3 2.8 3.2 2.8

2.8 3.8 1.4 1.9 3.3 2.9 2.0 3.2

a. Construct a frequency distribution of grouped

scores with approximately 10 intervals.

b. Construct a histogram of the frequency distribu-

tion constructed in part a.

c. Is the distribution skewed or symmetrical? If

skewed, is it skewed positively or negatively?

d. Construct a stem and leaf diagram with the last

digit being a leaf and the first digit a stem. Repeat

stem values five times.

e. Which diagram do you like better, the histogram

of part b or the stem and leaf diagram of part d?Explain

Question 17, page 72:

Sarah's grade point average is 3.1. Based on the frequency distribution of grouped scores constructed in Problem 15, part a, what is the percentile rank of Sarah's grade point average?

Question 18, page 72:

The policy of the school in Problem 15 is that to

graduate with a major in psychology, a student must

have a grade point average of 2.5 or higher.

a. Based on the ungrouped scores shown in Problem

15, what percentage of current psychology majors

needs to raise its grades?

b. Based on the frequency distribution of grouped

scores, what percentage needs to raise its grades?

c. Explain the difference between the answers to a and b parts.

Thank you.