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:
- Order the data set from least to greatest.
- Find the median of the entire data set.
- Find the first quartile (Q1) which is the median of the lower half of the data.
- Find the third quartile (Q3) which is the median of the upper half of the data.
- 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.
