How is the Interquartile Range (IQR) calculated?

The Interquartile Range (IQR) is a measure of statistical dispersion that indicates the range within which the central 50% of the data points lie. It is calculated by taking the difference between the third quartile (Q3) and the first quartile (Q1).

Q1, also known as the first quartile, is the value below which 25% of the data fall, while Q3, or the third quartile, is the value below which 75% of the data fall. By subtracting Q1 from Q3, you effectively measure the spread of the middle half of the data, allowing you to assess variability without being affected by outliers or extreme values.

For instance, if Q1 is 10 and Q3 is 20, the IQR would be 20 - 10, which equals 10. This tells us that half of the data lies within a span of 10 units, from the first quartile to the third quartile. Understanding how to calculate the IQR is essential in descriptive statistics, as it provides insight into the data's distribution.