Interquartile range

Description

The interquartile range (IQR) measures the spread of the middle 50% of a dataset. It is less affected by extreme values (outliers) than the range.

$$\text{IQR} = Q3 - Q1$$

where $Q1$ is the lower quartile (25th percentile) and $Q3$ is the upper quartile (75th percentile).

Finding quartiles for small datasets:

• Order the data
• $Q2$ (median): middle value
• $Q1$: median of the lower half
• $Q3$: median of the upper half

Example: Data: 3, 5, 7, 8, 10, 12, 15 $Q1 = 5$, $Q2 = 8$, $Q3 = 12$, so $\text{IQR} = 12 - 5 = 7$

A smaller IQR means the data is more consistent. Compare IQRs when comparing two distributions.

Common error: including the median in both halves when calculating Q1 and Q3 for an odd-numbered dataset — exclude the median from each half.

Links

Median Boxplots Cumulative frequency