IQR Calculator (Interquartile Range)
Calculate the interquartile range — the spread of the middle 50% of a data set.
Calculate the interquartile range — the spread of the middle 50% of a data set.
How IQR Calculator (Interquartile Range) Works
The data is sorted, then split into quarters. The interquartile range is the distance between the first quartile (Q1, the value 25% of the way through) and the third quartile (Q3, 75% of the way through) — this middle-50% spread isn't affected by extreme values the way the full range is.
Who Uses IQR Calculator (Interquartile Range) and Why
- Describing the typical spread of the middle portion of a data set without letting a few extreme values dominate the picture.
- Computing the underlying value needed to set outlier fences using the standard 1.5×IQR rule.
- Comparing the spread of two skewed data sets where the mean and standard deviation alone could be misleading.
Mistakes to Avoid
- Confusing IQR with the full range (max − min) — IQR only reflects the middle 50% of the data, which is exactly why it's resistant to a few extreme outliers, unlike the full range.
- Assuming a small IQR by itself means "no outliers" — IQR just measures middle-50% spread; you still need the separate 1.5×IQR fence calculation to actually flag outliers.
- Computing IQR on unsorted or improperly formatted data — quartile positions depend entirely on the data being correctly sorted first.
Tips for Best Results
- Pair the IQR with the median (rather than the mean and standard deviation) when describing a skewed data set — both are far less sensitive to extreme values.
- If you actually need to flag specific outlier values rather than just measure spread, use the Outlier Calculator on this site, which applies the 1.5×IQR rule directly.
Fixing Common Problems
My IQR value differs slightly from what a spreadsheet program calculated. — Different tools use different interpolation methods when a quartile falls between two data points. This calculator uses linear interpolation, a common convention, but spreadsheet software sometimes defaults to a different method, producing small differences.
Terms Explained
Interquartile range (IQR): The distance between the first quartile (Q1) and third quartile (Q3), representing the spread of the middle 50% of a data set.
Fence: A boundary set at 1.5 times the IQR beyond Q1 or Q3, used to flag statistical outliers.