Time: 20 minutes. This quiz is open book, open notes.
1. A batch A has the summary statistics listed below. The values in batch B are obtained by subtracting each value in A from 20. (For example, if 7 is in A, then 20-7 = 13 is in B.) Compute the corresponding summary statistics for B. In cases where it is not possible to deduce the value, or if the value is not defined, then please so indicate.
| Statistic | A | B | C |
| Count | 77 | ||
| Median | 3.2 | ||
| H-spread | 1.9 | ||
| 95th percentile | 12.3 | ||
| Variance | 11.0 | ||
| Third order statistic (X[3]) | 0.8 | ||
| Geometric mean | 2.7 | ||
| 10% Trimmed mean | 3.5 |
Would you expect A to be positively skewed, negatively skewed, or have approximately zero skewness? What about B?
Extra credit: answer the same questions for a batch C that is formed from the squares of all values in A.
2. Draw a histogram of the following batch of bis (2-ethyl hexyl) phthalate measurements in groundwater (micrograms per liter). Choose bins in a way that helps portray the "shape" of the data.
0.24, 0.58, 0.77, 1.30, 3.23, 3.91, 7.71, 11.57, 13.51, 19.75, 24.57, 26.64, 37.85, 55.00, 60.05, 89.76
(The values have been sorted for you.) Label the histogram appropriately so that it can be read on its own. Use relative frequency on the y-axis.
3. A batch has 11 values. The five largest values are 33.0, 24.6, 17.0, 16.0, and 15.3 Compute the 80th percentile of this batch. Use Weibull plotting positions (the percentile at rank I is I/(N+1): text, page 96). Round the answer to one decimal place precision (the same as the data).
Scoring: The passing score is 96. Incorrect "extra credit" answers will be deducted from your score; correct extra credit answers will add to your score provided you answer all the other questions.
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