Practice Quartiles in Statistics

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

Quick Recap

Quartiles are values that divide ordered data into four equal parts: Q_1 (25th percentile) marks the boundary below which 25% of data falls, Q_2 (the median, 50th percentile) splits the data in half, and Q_3 (75th percentile) marks the boundary below which 75% falls.

If you line up 100 people by height and divide into 4 equal groups, quartiles mark the dividing points. Q_1 is where the shortest 25% ends, Q_2 is the middle, Q_3 is where the tallest 25% begins.

Example 1

easy
Find the quartiles (Q_1, Q_2, Q_3) of the data set: 3, 5, 7, 8, 12, 14, 16, 18, 21.

Example 2

medium
Find the quartiles of this data set with an even number of values: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65.

Example 3

medium
The ages of 15 members of a sports club are: 18, 19, 20, 21, 22, 23, 24, 25, 27, 30, 32, 35, 40, 45, 50. Find Q_1, Q_2, and Q_3, and determine how many members are between Q_1 and Q_3.

Example 4

hard
Two data sets have the same median (Q_2 = 50). Data set A: Q_1 = 45, Q_3 = 55. Data set B: Q_1 = 20, Q_3 = 80. Compare the distributions and explain what the quartiles reveal about each data set.
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