The interquartile range (IQR) is a measure of the spread of a data set. It is the difference between the upper quartile (Q3) and the lower quartile (Q1). The IQR is a robust measure of spread, meaning it is not affected by outliers. This makes it a useful way to compare the spread of data sets that may contain outliers.
In general, a larger IQR indicates a greater amount of spread or variability in the data whereas a smaller IQR represents less spread or variability. For instance, an IQR of 20 indicates there is a significant spread in the data, while an IQR of 5 suggests less dispersion.
To find the IQR, you first need to find the median of the data set. Then, you find the median of the upper half of the data set (Q3) and the median of the lower half of the data set (Q1). The IQR is then the difference between Q3 and Q1.
How to find IQR
To find the interquartile range (IQR), follow these steps:
- Order data from smallest to largest.
- Find the median (middle value).
- Split data into two halves.
- Find median of each half.
- Subtract lower median from upper median.
- The result is the IQR.
The IQR is a robust measure of spread, meaning it is not affected by outliers.