Practice Box Plot in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A box plot displays the five-number summary (minimum, Q1, median, Q3, maximum) of a data set using a box and whiskers.

A summary of spread and center in one picture. Box shows the middle 50%.

Showing a random 20 of 50 problems.

Example 1

easy
With min=2 and max=15, what is the range shown by a box plot?

Example 2

easy
For min=2, Q1=5, median=8, Q3=11, max=15, find the IQR.

Example 3

challenge
Two products have test-score box plots: A symmetric, Q1 70, Q3 90; B left-skewed with median near Q3, Q1 50, Q3 85. Which has higher typical scores and lower spread?

Example 4

medium
Data 1,3,4,6,8,9,12. Find Q1, median, and Q3.

Example 5

easy
In a box plot, the median line is exactly in the middle of the box. What does this suggest about the middle 50%?

Example 6

medium
A box plot shows median 50, Q1 40, Q3 80. Is it skewed, and which way?

Example 7

medium
Data {2,4,5,7,8,10,12,15}. Find the five-number summary.

Example 8

medium
Q1=10, Q3=22. A data value of 4 — is it an outlier (lower fence rule)?

Example 9

medium
In a box plot the median is much closer to Q3 than to Q1. Which way is the data skewed?

Example 10

medium
A box plot has Q1 =15, Q3 =25. Compute the lower and upper fences (1.5×IQR).

Example 11

challenge
Box plot A (median 30, IQR 4) vs B (median 30, IQR 20). Both symmetric. Compare standard deviations qualitatively.

Example 12

hard
A box plot has min 3, Q1 10, median 14, Q3 20, max 48. What does the long upper whisker plus a far max suggest?

Example 13

medium
Data: 4,8,8,12,16,20,24,28. Find Q1 and Q3 (8 values).

Example 14

easy
A box plot has min 4, Q1 9, median 14, Q3 19, max 24. What is the range?

Example 15

medium
Two box plots compare exam scores for two classes. Class A: median=72, Q1=65, Q3=80. Class B: median=78, Q1=70, Q3=85. Compare center and spread for both classes.

Example 16

easy
In a box plot, between which two summary values do the middle 50% of data lie?

Example 17

hard
Box plot A has Q1 =20, Q3 =30. Plot B has Q1 =10, Q3 =40. Both medians equal 25. Which is more variable?

Example 18

easy
A box plot shows: minimum=10, Q1=25, median=40, Q3=55, maximum=70. Calculate the IQR and determine the fence values for outlier detection.

Example 19

easy
In a box plot, the median line sits much closer to Q1 than Q3. What does this suggest?

Example 20

easy
The box of a box plot spans 20 to 35. Find Q1, Q3, and IQR.
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