What is the IQR Method?

The IQR Method (Interquartile Range Method) is a robust statistical technique used to measure the spread of data and detect outliers. Unlike the standard range (Max - Min), which is easily skewed by extreme values, the IQR method focuses on the middle 50% of your dataset.

It is calculated as the difference between the third quartile ($Q3$) and the first quartile ($Q1$):

IQR = Q3 - Q1

Why is IQR important?

The IQR is considered a robust statistic because it is resistant to outliers.

• Resistance to Skew: If you have one billionaire in a room of factory workers, the "Average" (Mean) income skyrockets, but the Median and IQR remain stable.
• Data Spread: A large IQR indicates the middle data points are spread far apart; a small IQR means they are clustered closely around the median.

Using IQR to Detect Outliers

The most common application of the IQR is the "1.5 x IQR Rule" for outlier detection, often attributed to John Tukey.

1. Calculate the IQR ($Q3 - Q1$).
2. Multiply the IQR by 1.5.
3. Lower Fence: $Q1 - (1.5 \times IQR)$
4. Upper Fence: $Q3 + (1.5 \times IQR)$

Any data point that falls below the Lower Fence or above the Upper Fence is considered a mild outlier. If you use a multiplier of 3.0 instead of 1.5, those points are considered extreme outliers.

PlotNerd's IQR Calculator makes it easy to detect outliers and measure data spread using the robust interquartile range method.