To find the interquartile range (IQR), follow these steps:

1. Order the data from least to greatest.
2. Find the median of the dataset, which divides the data into two halves.
3. Find the first quartile (Q1) , which is the median of the lower half of the data (values below the overall median).
4. Find the third quartile (Q3) , which is the median of the upper half of the data (values above the overall median).
5. Calculate the IQR by subtracting Q1 from Q3:

IQR=Q3−Q1\text{IQR}=Q3-Q1IQR=Q3−Q1

The IQR represents the range containing the middle 50% of the data and is useful for understanding data spread and identifying outliers

Example:

Given the dataset: 2, 5, 8, 9, 12, 18, 22

• Median = 9
• Lower half = 2, 5, 8 → Q1 = 5 (median of lower half)
• Upper half = 12, 18, 22 → Q3 = 18 (median of upper half)
• IQR = 18 - 5 = 13

So, the interquartile range is 13