Practice Box Plot in Math

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

Worksheet PDF Free Answer-key PDF Family

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%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 7070, Q3 9090; B left-skewed with median near Q3, Q1 5050, Q3 8585. Which has higher typical scores and lower spread?

Example 4

medium
Data 1,3,4,6,8,9,121,3,4,6,8,9,12. 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%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}\{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=15, Q3 =25=25. Compute the lower and upper fences (1.5×1.5\timesIQR).

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 33, Q1 1010, median 1414, Q3 2020, max 4848. 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 44, Q1 99, median 1414, Q3 1919, max 2424. What is the range?

Example 15

medium
Two box plots compare exam scores for two classes. Class A: median=72, Q1=65Q_1=65, Q3=80Q_3=80. Class B: median=78, Q1=70Q_1=70, Q3=85Q_3=85. Compare center and spread for both classes.

Example 16

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

Example 17

hard
Box plot A has Q1 =20=20, Q3 =30=30. Plot B has Q1 =10=10, Q3 =40=40. Both medians equal 2525. Which is more variable?

Example 18

easy
A box plot shows: minimum=10, Q1=25Q_1=25, median=40, Q3=55Q_3=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 2020 to 3535. Find Q1, Q3, and IQR.
← Back to Box Plot Worked Examples Formula Explained