Interquartile Range Math Example 2

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Example 2

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Data set A: {1,2,3,4,5,6,7,8,9,100}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 100\} and Data set B: {1,2,3,4,5,6,7,8,9,10}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}. Compare the range and IQR for both sets and explain why IQR is preferred as a measure of spread.

Solution

  1. 1
    Range A = 100−1=99100 - 1 = 99; Range B = 10−1=910 - 1 = 9
  2. 2
    For set A: Q1=2+32=2.5Q_1 = \frac{2+3}{2}=2.5, Q3=7+82=7.5Q_3=\frac{7+8}{2}=7.5; IQRA=5IQR_A = 5
  3. 3
    For set B: Q1=2.5Q_1 = 2.5, Q3=7.5Q_3 = 7.5; IQRB=5IQR_B = 5
  4. 4
    Conclusion: The ranges differ dramatically (99 vs 9) due to one outlier (100), but IQRs are identical (5 vs 5), showing the middle 50% is equally spread

Answer

Range A=99, Range B=9; but IQRA=IQRB=5IQR_A = IQR_B = 5. IQR is resistant to the outlier 100.
The IQR is a resistant measure of spread — one extreme outlier changes the range drastically but leaves the IQR unchanged. This is why IQR is preferred over range when data may contain outliers.

About Interquartile Range

The interquartile range (IQR) is Q3−Q1Q3 - Q1 — the spread of the middle 50% of the data, resistant to outliers.

Learn more about Interquartile Range →

More Interquartile Range Examples

Example 1 easy

Calculate the IQR for: [formula] and explain what it measures.

Example 3 easy

A box plot shows [formula] and [formula]. Calculate the IQR and the lower and upper fences for outli

Example 4 hard

A data set has [formula], median [formula], [formula]. A new value of 120 is added. Without recalcul

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QuartilesBox Plot