What is the interquartile range?

Understanding the Interquartile Range

The interquartile range (IQR) is a measure of statistical dispersion and can be calculated using the formula:

$IQR=Q3–Q1$

Where:

• $IQR$ represents the interquartile range,
• $Q3$ is the third quartile, and
• $Q1$ is the first quartile.

Advantages and Examples of the Interquartile Range

One significant advantage of using the interquartile range over other measures of dispersion, like the range, is its insensitivity to outliers. To illustrate this, consider the following data set:

$2,3,3,4,5,6,6,7,8,8,8,9$

The statistical summary for this data set is:

• Minimum: 2
• First quartile (Q1): 3.5
• Median: 6
• Third quartile (Q3): 8
• Maximum: 9

From this data set, we derive an interquartile range of 4.5 (8-3.5), a range of 7 (9-2), and a standard deviation of 2.34.

Now, if we replace the highest value of 9 with an extreme outlier of 100, the standard deviation skyrockets to 27.37 and the range jumps to 98. However, the interquartile range remains unchanged, demonstrating its resilience to outliers.

Bibliography

• Caja Poma, R. Probability and Statistics: A theoretical and practical approach. 2018, Kindle. Spain: Ruddy Poma Box.
• AIDEP. Statistics and probabilities. 1971. Spain: Editorial Reverté.
• Devore, J. Probability and Statistics for Engineering and Science. 2016. Spain: Cengage Learning.