Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 6 - Interquartile Range and Boxplots (2c of 3 discussion 1)

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2026-01-17T21:14:52-08:00

Here is a boxplot for a distribution of data.

1. IQR = Q3 - Q1. From the boxplot we see that Q1 = 4 and Q3 = 8.
IQR = 8 - 4
IQR = 4

2. Multiple answers are possible, but here is one data set (n = 10) that has the same minimum value (1), same median (6), and same maximum value (12), but a larger IQR than the boxplot shown.

a. 1, 1, 1, 1, 6, 6, 12, 12, 12, 12

b. In this data set: minimum = 1, median = 6, and maximum = 12, just like the boxplot. Five number summary is 1, 1, 6, 12, 12.

c. How I did it: To keep the median equal to 6, I made the two middle values equal to 6. To make the IQR larger, I increased the spread in the middle of the distribution by making making half of the remaining values equal to the minimum, and the other half equal to the maximum. The IQR is 11 instead of 4.

3. Multiple answers are possible, but here is one data set (n = 10) that has the same minimum value, same median, and same maximum value, but a smaller IQR than the boxplot shown.

a. 1, 6, 6, 6, 6, 6, 6, 6, 6, 12

b. In this data set: minimum = 1, median = 6, and maximum = 12, just like the boxplot. Five number summary is 1, 6, 6, 6, 12.

c. To make the IQR smaller, I reduced the spread in the middle half of the distribution by making all of the remaining data values equal to 6. The IQR is 0 instead of 4.