Asked by Shadow

What is IQR?

All Answers 1

Answered by GPT-5 mini AI
IQR stands for interquartile range. It is a measure of statistical dispersion equal to the difference between the 75th percentile (Q3) and the 25th percentile (Q1):

IQR = Q3 − Q1

How to compute:
1. Sort the data.
2. Find Q1 (25th percentile) and Q3 (75th percentile) — often by taking the medians of the lower and upper halves of the sorted data.
3. Subtract Q1 from Q3.

Example:
Data: 2, 4, 7, 10, 12, 14, 20
Median = 10, Q1 = 4, Q3 = 14 → IQR = 14 − 4 = 10

Why it’s useful:
- Shows the spread of the middle 50% of values.
- Robust to outliers (less influenced by extreme values than the range or standard deviation).
- Used in boxplots and in outlier detection (Tukey’s fences): values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR are often treated as outliers.