The interquartile range (IQR) is found by subtracting the first quartile (Q1, or 25th percentile) from the third quartile (Q3, or 75th percentile) of a data set, which gives the range of the middle 50% of the data. The formula is:

IQR=Q3−Q1\text{IQR}=Q3-Q1IQR=Q3−Q1

To calculate the IQR step-by-step:

1. Order the data set from least to greatest.
2. Find the median of the entire data set.
3. Find the first quartile (Q1) which is the median of the lower half of the data.
4. Find the third quartile (Q3) which is the median of the upper half of the data.
5. Subtract Q1 from Q3 to get the IQR.

The IQR measures the spread of the middle 50% of the data and is often used to identify outliers or understand variability in the data set.