A land-grant university located in the Midwest has an entering freshman class of 1 522 students. A random sample of 150, or approximately 10%, of the entering first-year students’ cumulative grade points were recorded. Academic standards require each student to have a first-year grade average of 1.5 or better to return for the sophomore year and 3.5 or better to be eligible for the Dean’s list. The grade point averages (GPA) below have been partially grouped.
(a) Determine the mean grade point average and standard deviation for the sample.
(b) Group the data into equal classes and construct a frequency distribution table.
(c) Draw a histogram of the distribution.
GPA | # Students | GPA | # Students | GPA | # Students | GPA | # Students |
0 | 0 | 1 | 3 | 2 | 7 | 3 | 5 |
0.1 | 0 | 1.1 | 2 | 2.1 | 7 | 3.1 | 2 |
0.2 | 1 | 1.2 | 3 | 2.2 | 10 | 3.2 | 1 |
0.3 | 0 | 1.3 | 2 | 2.3 | 8 | 3.3 | 3 |
0.4 | 1 | 1.4 | 4 | 2.4 | 12 | 3.4 | 2 |
0.5 | 1 | 1.5 | 4 | 2.5 | 14 | 3.5 | 4 |
0.6 | 0 | 1.6 | 3 | 2.6 | 6 | 3.6 | 2 |
0.7 | 2 | 1.7 | 5 | 2.7 | 7 | 3.7 | 1 |
0.8 | 1 | 1.8 | 6 | 2.8 | 5 | 3.8 | 0 |
0.9 | 2 | 1.9 | 6 | 2.9 | 6 | 3.9 | 1 |
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| 4 | 1 |
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