Asked by Shadow
What is IQR?
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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.
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.
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