Interquartile Range (IQR) Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

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 Q2Q_2: 9 values, median is the 5th value = 15.
  2. 2
    Step 2: Lower half {4, 7, 9, 12}: Q1=7+92=8Q_1 = \frac{7+9}{2} = 8. Upper half {18, 22, 25, 30}: Q3=22+252=23.5Q_3 = \frac{22+25}{2} = 23.5.
  3. 3
    Step 3: IQR=Q3−Q1=23.5−8=15.5IQR = Q_3 - Q_1 = 23.5 - 8 = 15.5.

Answer

IQR=15.5IQR = 15.5.
The interquartile range (IQR) measures the spread of the middle 50% of the data. It is calculated as Q3−Q1Q_3 - Q_1. Unlike the range, the IQR is not affected by extreme values (outliers), making it a robust measure of spread.

About Interquartile Range (IQR)

The interquartile range (IQR) is the range of the middle 50% of data, calculated as Q3−Q1Q_3 - Q_1. It measures spread while ignoring the top and bottom 25% of values, making it resistant to outliers.

Learn more about Interquartile Range (IQR) →

More Interquartile Range (IQR) Examples

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 bo

Example 3 medium

Two classes took the same test. Class A: [formula], [formula]. Class B: [formula], [formula]. Which

Example 4 hard

Daily temperatures (°C) for two weeks: 15, 16, 14, 18, 20, 22, 19, 35, 17, 16, 18, 21, 20, 19. Find

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