Wiki Page, Math 13 - Perez Sandbox : Module 6 - Interquartile Range and Boxplots (3 of 3)

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2026-01-17T21:15:51-08:00

Comparing Distributions with Side-by-Side Boxplots

On this page we again use boxplots to compare two distributions. This time we focus on

how to use boxplots to determine if two distributions are similar or substantially different.

how to write a comparison using the five-number summary to compare and contrast the shape, center and spread of the distributions.

EXAMPLE Using boxplots to compare distributions

This movie compares and contrasts distributions using boxplots. (7:17)

Now we will work on writing a paragraph that compares distributions based on boxplots. This is similar to the work we did with dotplots and histograms. In our paragraph we will develop a central thesis and support it with observations from the boxplots, instead of just listing observations.

EXAMPLE Comparing ages for Best Actor/Actress Oscar winners

Here we examine the age distributions of ages for Best Actor/Actress Oscar winners for the years 1929-2019.

Best actress/actor age summary

Column | n | Min | Q1 | Median | Q3 | Max
Actress age | 92 | 21 | 28.5 | 33 | 41 | 80
Actor ages | 92 | 29 | 37.5 | 42 | 49 | 76

We start our analysis by making observations about shape, center and spread. We focus on comparing the two distributions, instead of just making a list of disconnected observations.

Shape: For both men and women, the distribution of ages is skewed to the right because the upper half of the data has more variability than the lower half. This is due to older actresses and actors who are outliers. In both cases, the shape suggests that fewer older actresses and actors win the Oscar for best acting.

Center: Actresses tend to win the Oscar at a younger age than do actors. The median age for actresses (33) is lower than for the actors (42), and quite a bit lower because it is also less than Q1 for actors (37.5).

Spread: The actresses have more variability in their overall ages (range = 59) compared to the actors (range = 47). But the variability in the middle half each distribution is similar: the actresses’ ages (IQR = 12.5) than in the actors’ ages (IQR = 11.5).

Intervals of ages for the middle half of each distribution overlap. Typical ages for actors range from 37.5 to 49 years, compared to 28.5 to 41 years for actresses. This overlap is largely due to the 3rd quartile for actresses overlapping the 2nd quartile for actors.

The 1st quartile mark for actresses is almost equal to the minimum age for actors, which means that about 25% of the winning actresses were younger than the youngest winner actor.

Outliers: We see that we have outliers in both distributions. There is only one high outlier in the actors’ distribution, compared with six high outliers in the actresses’ distribution.

Now let’s pull these observations together into a paragraph that compares the two distributions and supports a central thesis. Our paragraph demonstrates a good use of course concepts and vocabulary, which makes it less appropriate for a general audience who may not be trained in statistics.

We are going to argue that actresses tend to win the Oscar for best acting at younger ages than actors.

Our paragraph:

In general, actresses win the Best Actress Oscar at a younger age than actors. The median age for actresses is 33, lower than median (42) and lower than the first quartile mark (37.5) for actors. There is some overlap in middle half of each distribution which can be interpreted as representing typical winning ages. Typical actors win this Oscar between the ages of 37.5 and 49, compared to typical actresses who are between the ages of 28.5 and 41. For both sexes, the typical winning ages are similarly consistent as seen by a comparison of the IQRs (Actresses IQR = 12.5; Actor IQR = 11.5.) Despite this overlap and the similar spread in the middle half of the distributions, it is important to note that about 25% of the winning actresses are younger than the youngest winning actor. Though winning actresses are arguably younger than winning actors, both distributions have older winners that are outliers. These older winners are unusual and skew the distribution of ages to the right.

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