Interquartile Range Math Example 1

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

Example 1

easy
Calculate the IQR for: {15,22,28,35,42,50,58,65}\{15, 22, 28, 35, 42, 50, 58, 65\} and explain what it measures.

Solution

  1. 1
    Find Q1Q_1: lower half is {15,22,28,35}\{15, 22, 28, 35\}; Q1=22+282=25Q_1 = \frac{22+28}{2} = 25
  2. 2
    Find Q3Q_3: upper half is {42,50,58,65}\{42, 50, 58, 65\}; Q3=50+582=54Q_3 = \frac{50+58}{2} = 54
  3. 3
    Calculate IQR: IQR=Q3−Q1=54−25=29IQR = Q_3 - Q_1 = 54 - 25 = 29
  4. 4
    Interpretation: the middle 50% of values span a range of 29 units

Answer

IQR=29IQR = 29
The IQR measures the spread of the middle 50% of data. It is resistant to outliers (unlike the range) because it ignores the top and bottom 25% of values. A larger IQR indicates more variability in the central portion of the data.

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 2 medium

Data set A: [formula] and Data set B: [formula]. Compare the range and IQR for both sets and explain

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