Quartiles Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Quartiles.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept 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.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Quartiles split sorted data into four equal quarters. Q1 is the 25th percentile, Q2 is the median (50th percentile), and Q3 is the 75th percentile.

Common stuck point: Different textbooks use slightly different methods for computing Q1 and Q3 — always check which method is being used to avoid calculation discrepancies.

Worked Examples

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.

Solution

  1. 1
    Step 1: The data is already sorted. There are 9 values, so Q_2 (the median) is the 5th value: Q_2 = 12.
  2. 2
    Step 2: The lower half is {3, 5, 7, 8}. Q_1 is the median of this half: Q_1 = \frac{5 + 7}{2} = 6.
  3. 3
    Step 3: The upper half is {14, 16, 18, 21}. Q_3 is the median of this half: Q_3 = \frac{16 + 18}{2} = 17.

Answer

Q_1 = 6, Q_2 = 12, Q_3 = 17.
Quartiles divide sorted data into four equal parts. Q_1 is the median of the lower half, Q_2 is the overall median, and Q_3 is the median of the upper half. Together they describe the spread and centre of the data.

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.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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 2

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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Related Concepts

Median

Background Knowledge

These ideas may be useful before you work through the harder examples.

median introordering numbers