The following scores represent a sample of final examination grades for a statistics course
23 60 98 32 57 74 52 70 82 69 74 63 80 62 80 77 81 95 41 65 92 85 85 61 36 79 55 76 52 10 64 75 78 25 80 48 83 64 88 82 81 67 41 71 67 54 34 72 74 43 60 78 84 89 76 84 17 90 15 79
a) Provide a frequency polygon with report quality (i.e. including all necessary information (e.g. titles), preferably using Excel) of these data along with a table summarizing the grouped data.
b) Provide a report-quality empirical distribution function of the data.
c) Compute the 20th percentile of the sample and explain what it means.
d) Calculate the mean, variance, and coefficient of variation of the grades.
(a) The frequency table is:
lower | upper | midpoint | width | frequency | |
10 | < | 20 | 15 | 10 | 3 |
20 | < | 30 | 25 | 10 | 2 |
30 | < | 40 | 35 | 10 | 3 |
40 | < | 50 | 45 | 10 | 4 |
50 | < | 60 | 55 | 10 | 5 |
60 | < | 70 | 65 | 10 | 11 |
70 | < | 80 | 75 | 10 | 14 |
80 | < | 90 | 85 | 10 | 14 |
90 | < | 100 | 95 | 10 | 4 |
60 |
The frequency polygon is:
(b) The empirical distribution is:
(c)
20th percentile | 51.2 |
20% of the values are less than 51.2.
(d)
mean | 65.48 |
coefficient of variation (CV) | 32.27% |
sample variance | 446.63 |
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