Definition: The interquartile range, or IQR, is the difference between the third quartile and the first quartile, measuring the spread of the middle half of the data.
What is the IQR?
The IQR ignores the lowest quarter and highest quarter of the data, so it describes the middle 50 percent. IQR = Q3 – Q1.
How do you find it?
Order the data and find the median. Q1 is the median of the lower half, and Q3 is the median of the upper half. For 4, 6, 7, 10, 12, 15, 19, 24:
- Median: (10 + 12) / 2 = 11
- Lower half 4, 6, 7, 10 gives Q1 = (6 + 7) / 2 = 6.5
- Upper half 12, 15, 19, 24 gives Q3 = (15 + 19) / 2 = 17
So IQR = 17 – 6.5 = 10.5.
Why use it?
Outliers hardly affect it. Compare it with the range, which is 24 – 4 = 20 here and would balloon if 24 became 240.
What is the usual error?
Including the median in both halves when the count is odd. For an odd number of values, leave the median out when finding Q1 and Q3.
Example: If Q1 = 32 and Q3 = 51, the IQR is 19.