Interquartile Range Math Example 3

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Example 3

easy
A box plot shows Q1=30Q_1 = 30 and Q3=50Q_3 = 50. Calculate the IQR and the lower and upper fences for outlier detection.

Solution

  1. 1
    IQR=Q3−Q1=50−30=20IQR = Q_3 - Q_1 = 50 - 30 = 20
  2. 2
    Lower fence =30−1.5(20)=30−30=0= 30 - 1.5(20) = 30 - 30 = 0
  3. 3
    Upper fence =50+1.5(20)=50+30=80= 50 + 1.5(20) = 50 + 30 = 80

Answer

IQR = 20; fences at 0 and 80.
The 1.5×IQR rule creates symmetric fences around the box. Values outside these fences are potential outliers. The fences help standardize outlier detection across different data sets.

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 2 medium

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

Example 4 hard

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

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Related Concepts

QuartilesBox Plot