Interquartile Range (IQR) Statistics Example 2

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

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 boundaries for outliers using the 1.5×IQR1.5 \times IQR rule.

Solution

  1. 1
    Step 1: 11 values, Q2Q_2 = 6th value = 75. Lower half {55,60,65,70,72}: Q1Q_1 = 65. Upper half {78,80,85,90,95}: Q3Q_3 = 85.
  2. 2
    Step 2: IQR=85−65=20IQR = 85 - 65 = 20.
  3. 3
    Step 3: Lower fence: Q1−1.5×IQR=65−30=35Q_1 - 1.5 \times IQR = 65 - 30 = 35. Upper fence: Q3+1.5×IQR=85+30=115Q_3 + 1.5 \times IQR = 85 + 30 = 115. Any value below 35 or above 115 is an outlier. All values fall within [35, 115], so there are no outliers.

Answer

IQR=20IQR = 20. Outlier boundaries: below 35 or above 115. No outliers in this data set.
The 1.5×IQR1.5 \times IQR rule is a standard method for identifying outliers. Values more than 1.5 IQRs below Q1Q_1 or above Q3Q_3 are considered outliers. This method uses quartiles rather than the mean, making it resistant to the influence of extreme values.

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 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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