Interquartile Range (IQR) Statistics Example 3

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

Example 3

medium
Two classes took the same test. Class A: Q1=60Q_1 = 60, Q3=80Q_3 = 80. Class B: Q1=70Q_1 = 70, Q3=90Q_3 = 90. Which class has greater consistency in scores? Explain using the IQR.

Solution

  1. 1
    Step 1: Class A: IQR=80−60=20IQR = 80 - 60 = 20. Class B: IQR=90−70=20IQR = 90 - 70 = 20.
  2. 2
    Step 2: Both classes have the same IQR of 20, meaning the middle 50% of scores span the same width. Both classes show equal consistency, although Class B's scores are shifted 10 points higher.

Answer

Both classes have equal consistency (IQR = 20 each). Class B's scores are higher on average but the spread of the middle 50% is identical.
The IQR measures variability independently of the centre. Two distributions can have the same spread but different centres. Comparing IQRs tells us about relative consistency, while comparing medians or quartile positions tells us about relative performance levels.

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 1 easy

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

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 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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