Interquartile Range (IQR) Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Interquartile Range (IQR).

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

Concept Recap

The range of the middle 50% of data, calculated as Q_3 - Q_1. It measures spread while ignoring extreme values.

IQR focuses on where most of the data lives, ignoring the extremes. If regular range is how far the outliers stretched, IQR is how wide the main crowd is. More resistant to outliers than range.

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: The IQR measures the spread of the middle 50% of the data by subtracting Q1 from Q3. It ignores the top and bottom 25%, making it resistant to outliers.

Common stuck point: Students sometimes compute IQR as max minus min (that is the range). IQR specifically uses Q3 − Q1, not the overall extremes.

Worked Examples

Example 1

easy
Given the data set: 4, 7, 9, 12, 15, 18, 22, 25, 30, find the interquartile range (IQR).

Solution

  1. 1
    Step 1: Sort the data (already sorted). Find Q_2: 9 values, median is the 5th value = 15.
  2. 2
    Step 2: Lower half {4, 7, 9, 12}: Q_1 = \frac{7+9}{2} = 8. Upper half {18, 22, 25, 30}: Q_3 = \frac{22+25}{2} = 23.5.
  3. 3
    Step 3: IQR = Q_3 - Q_1 = 23.5 - 8 = 15.5.

Answer

IQR = 15.5.
The interquartile range (IQR) measures the spread of the middle 50% of the data. It is calculated as Q_3 - Q_1. Unlike the range, the IQR is not affected by extreme values (outliers), making it a robust measure of spread.

Example 2

medium
Test scores: 55, 60, 65, 70, 72, 75, 78, 80, 85, 90, 95. Find the IQR and use it to determine the boundaries for outliers using the 1.5 \times IQR rule.

Practice Problems

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

Example 1

medium
Two classes took the same test. Class A: Q_1 = 60, Q_3 = 80. Class B: Q_1 = 70, Q_3 = 90. Which class has greater consistency in scores? Explain using the IQR.

Example 2

hard
Daily temperatures (°C) for two weeks: 15, 16, 14, 18, 20, 22, 19, 35, 17, 16, 18, 21, 20, 19. Find the IQR and use the 1.5 \times IQR rule to identify any outliers. Then recalculate the mean with and without the outlier(s).
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Related Concepts

Outlier Detection

Background Knowledge

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

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