A visual display of the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
A box plot is like an X-ray of your data's skeleton. The box shows where the middle 50% of data lives. The line inside is the median. The whiskers stretch to the extremes. You instantly see the center, spread, and any unusual values.
Showing a random 20 of 50 problems.
Example 1
medium
Two box plots compare two classes. Class A: IQR 10. Class B: IQR 25. Which class has more consistent (less spread) middle scores?Which class has more consistent middle scores?
Example 2
hard
Dataset 1,2,3,4,5,6,7,8,9,100 (n=10). Is 100 an outlier by the 1.5⋅IQR rule?
Example 3
medium
A box plot's median sits much closer to Q1 than to Q3. What does this say about the data within the box?
Example 4
hard
Two box plots have the same five-number summary but one shows a tightly clustered histogram and one shows a uniform spread. What does this reveal about box plots?
Example 5
easy
A box plot has Q1 30 and Q3 60. What percent of the data lies between Q1 and Q3?
Example 6
easy
A box plot has min 10, Q1 12, median 18, Q3 24, max 30. About what percent of data is between 12 and 24?
Example 7
easy
A box plot has a very long right whisker and a short left whisker. What does this suggest about the data's shape?
Example 8
hard
A box plot has Q1 20, median 30, Q3 50, max 90. By the 1.5⋅IQR rule, is the max an outlier?
Example 9
hard
A box plot of 50 values has Q1 =30, Q3 =50. After adding 5 new values, all between 30 and 50, what happens to the IQR?
A box plot has min 10, Q1 20, median 35, Q3 40, max 80. Is the maximum likely an outlier by the 1.5*IQR rule?Is 80 an outlier? Upper fence = 40 + 1.5×20 = 70
Example 15
hard
A box plot has Q1 25, Q3 45, median 35. What is the IQR, and roughly what percent of values fall within ± IQR of the median?
Example 16
medium
A dataset 2, 4, 4, 6, 8, 8, 10, 12 (n=8) is shown as a box plot. Find Q1 and Q3.
Example 17
hard
Two box plots are compared. Plot A: median 40, IQR 20. Plot B: median 40, IQR 10. Which is more variable?
Example 18
medium
A box plot has Q1 10, Q3 50. A new data point is 90. Is it an outlier by the 1.5⋅IQR rule?
Example 19
medium
A box plot has min 0, Q1 10, median 15, Q3 25, max 50. Which whisker is longer?
Example 20
easy
Two box plots share the same axis. Box A's median is 30, box B's median is 50. Which dataset has the higher center?Which dataset has the higher center?