A.1.14.3 Origins of Outliers

The number of property crime (such as theft) reports is collected for 50 colleges in California. Some summary statistics are given: 15 17 27 31 33 39 39 45 46 48 49 51 52 59 72 72 75 77 77 83 86 88 91 99 103 112 136 139 145 145 175 193 198 213 230 256 258 260 288 289 337 344 418 424 442 464 555 593 699 768 Summary Statistics: Mean: 191.1 reports Min: 15 reports Q1: 52 reports Median: 107.5 reports Q3: 260 reports Max: 768 reports Are any of the values outliers? Explain or show your reasoning. If there are any outliers, why do you think they might exist? Should they be included in an analysis of the data?

Situation #1: A number cube has sides labelled 1–6. After rolling 15 times, Tyler records his data: 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 20

Situation #2: The dot plot represents the distribution of the number of siblings reported by a group of 20 people.

Situation #3: In a science class, 12 groups of students are synthesizing biodiesel. At the end of the experiment, each group recorded the mass in grams of the biodiesel they synthesized. The masses of biodiesel are: 0, 1.245, 1.292, 1.375, 1.383, 1.412, 1.435, 1.471, 1.482, 1.501, 1.532