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Reading Distributions In-Class Exercises

The goal of this exercise is to gain experience reading charts that show distributions, including boxplots, histograms, and eCDFs.

Instructions: Gather into groups of 2-3 students and work together to answer the following questions. We will discuss the answers in class.

Exercise

Part A - Boxplots

(Questions and chart from What’s Going On in This Graph? | Jan. 9, 2018)

Examine the boxplots in the figure below.

https://static01.nyt.com/images/2018/01/03/learning/careerearningsgraphLN/careerearningsgraphLN-superJumbo.png

For a refresher on how to read the boxplots, see the "Stat Nuggets" section (near the bottom) at https://www.nytimes.com/2018/01/04/learning/whats-going-on-in-this-graph-jan-9-2018.html

Answer the following questions:

  1. What is the significance of a longer or shorter boxplot?

  2. What is the significance of the darker blue segments of the boxplots? And, the lighter blue segments?

  3. Compare the medians of the different majors and also compare the other percentiles — 10%, 25%, 75%, and 90%. Which majors tend to have the least career earnings and most career earnings? Do career earnings vary more above or below the median? What does this imply?

  4. The length of each segment of the boxplot shows the variability of the earnings within that segment. Which majors have the greatest variability in earnings? The least variability?

Refer to Chapter 9.15 - Exercises from Introduction to Data Science questions 3-6 for the remaining questions in Part A.

  1. Q3: Which continent has the country with the biggest population size?

  2. Q4: What continent has the largest median population size?

  3. Q5: What is median population size for Africa to the nearest million?

  4. Q6: What proportion of countries in Europe have populations below 14 million?

Part B - Histograms and eCDFs

Refer to Chapter 9.7 - Exercises from Introduction to Data Science.

  1. Q1: To the closest 5%, what proportion of the states are in the North Central region?

  2. Q3: Based on the plot, what percentage of males are shorter than 75 inches?

  3. Q4: To the closest inch, what height m has the property that 1/2 of the male students are taller than m and 1/2 are shorter?

  4. Q5: Knowing that there are 51 states (counting DC) and based on this plot, how many states have murder rates larger than 10 per 100,000 people?

  5. Q6: Based on the eCDF above, which of the following statements are true:

  6. Q7: Based on this plot, how many males are between 63.5 and 65.5?

  7. Q8: About what percentage are shorter than 60 inches?

  8. Q9: Based on the density plot below, about what proportion of US states have populations larger than 10 million?