Interquartile Range (IQR) Calculator
Calculate the interquartile range of a data set. The IQR measures the spread of the middle 50% of values.
Enter a data set to calculate the IQR.
IQR Formula
IQR = Q3 − Q1
The interquartile range is the difference between the third quartile (75th percentile) and the first quartile (25th percentile). It represents the range of the middle 50% of data.
How to Calculate IQR
- Sort the data in ascending order.
- Find Q1 (the median of the lower half).
- Find Q3 (the median of the upper half).
- Subtract: IQR = Q3 − Q1.
Example: Data: 2, 4, 6, 8, 10, 12, 14
Q1 = 4, Q3 = 12
IQR = 12 − 4 = 8
Q1 = 4, Q3 = 12
IQR = 12 − 4 = 8
Why Use IQR?
- Resistant to outliers (unlike range or standard deviation).
- Describes variability of the central portion of data.
- Used in box plots and outlier detection (1.5×IQR rule).
FAQ
What is the 1.5 IQR rule for outliers?
Any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is considered a potential outlier. Values beyond 3×IQR from the quartiles are considered extreme outliers.
Is IQR better than standard deviation?
IQR is more robust against outliers and skewed distributions. Standard deviation considers all values. Use IQR for skewed data and standard deviation for normally distributed data.
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Last updated: 2026-08-08