Practice Quartiles in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Values that divide ordered data into four equal parts: Q_1 (25th percentile), Q_2 (median, 50th), and Q_3 (75th percentile).
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
easyFind the quartiles (Q_1, Q_2, Q_3) of the data set: 3, 5, 7, 8, 12, 14, 16, 18, 21.
Example 2
mediumFind 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
mediumThe 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
hardTwo 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.