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Interested in student athletes study habits, Abby conducts a survey of baseball and track and field athletes asking them how many hours a week they spend studying. Her data is below. Construct outlier boxplots for each group and compare and contrast the two groups.
| Baseball | 3 | 4 | 5 | 5 | 7 | 7 | 8 | 9 | 10 | 11 | |||||
| Track and Field | 0 | 4 | 6 | 9 | 9 | 10 | 11 | 11 | 12 | 13 | 14 | 14 | 15 | 15 | 17 |
Baseball 10(3, 5, 7, 9, 11) IQR = 4 with step 6 Lower Fence = -1 and Upper Fence = 15 Lower Adjacent Value = 3 Upper Adjacent Value = 11 Track and Field 15(0, 9, 11, 14, 17) IQR = 5 with step 7.5 Lower Fence = 1.5 and Upper Fence = 21.5 Lower Adjacent Value = 4 Upper Adjacent Value = 17 There is one outlier at the low end, zero. The hours of study time for the baseball players is symmetric with a median of 7 and IQR of 4 hours. The track and field student athletes have a skewed left distribution with a median of 11, IQR of 5 hours and one outlier at the low end of the distribution. The shapes of the distribution have different shapes with no overlap of the IQRs. The track and field student athletes have a higher typical value then the baseball student athletes, their medians differ by 4 hours. The spread of the middle half of the data for the two groups are similar, the track and field student athletes IQR is one hour longer than the baseball student athletes. These two groups differ in how much time they spend studying each week with a third of the track and field athletes studying more than any of the baseball players.
Three students were applying to the same graduate school. They came from schools with different grading systems. Which student had the best G.P.A. when compared to his school? Explain how you determined your answer.
| Student | G.P.A. | School Ave. G.P.A. | School Standard Deviation |
|---|---|---|---|
| Thuy | 2.7 | 3.2 | 0.8 |
| Vichet | 8.7 | 7.5 | 2.0 |
| Kamala | 8.6 | 8.0 | 0.4 |
Kamala
Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, each asked adult consumers the number of fiction paperbacks they had purchased the previous month. The results are below.
| # of books | Freq. | Rel. Freq. |
|---|---|---|
| 0 | 10 | |
| 1 | 12 | |
| 2 | 16 | |
| 3 | 12 | |
| 4 | 8 | |
| 5 | 6 | |
| 6 | 2 | |
| 8 | 2 |
| # of books | Freq. | Rel. Freq. |
|---|---|---|
| 0 | 18 | |
| 1 | 24 | |
| 2 | 24 | |
| 3 | 22 | |
| 4 | 15 | |
| 5 | 10 | |
| 7 | 5 | |
| 9 | 1 |
| # of books | Freq. | Rel. Freq. |
|---|---|---|
| 0-1 | 20 | |
| 2-3 | 35 | |
| 4-5 | 12 | |
| 6-7 | 2 | |
| 8-9 | 1 |
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