Due: Friday Sep 26, 2025 at 10pm

Numerical Summaries

Question 1 – Conceptual Questions (1 pt each)

  • Part A How does outlier classification differ between boxplots and histograms?

  • Part B What does it mean to say a statistic is robust?

  • Part C Why do we use median and IQR (instead of mean and standard deviation) for the center and spread when we have skews, outliers, or both?

  • Part D If a distribution is right-skewed with no outliers, which of these will be larger: the median or the mean?

Question 2 (4 pts)

This question is 5.10-Question #22 from the textbook and has been reproduced here.

The first histogram below shows the distribution of the yearly incomes of 40 patrons at a college coffee shop. Suppose two new people walk into the coffee shop: one making $225,000 and the other $250,000. The second histogram shows the new income distribution. Summary statistics are also provided, rounded to the nearest whole number.

  1. Would the mean or the median best represent what we might think of as a typical income for the 42 patrons at this coffee shop? What does this say about the robustness of the two measures?

  2. Describe the distribution of incomes for the coffee shop’s 42 patrons using the bottom histogram (‘After’). You may assume the value for Q3 is $68,000 (this may or may not be necessary).

Question 3 (IMS book)

From the IMS Textbook, do the following exercises (you do not need to read anything from the textbook to answer these):

  • Chapter 4.8: Questions 2, 7, 8, 9
  • Ch 5.10: Questions 10, 14