Interquartile Range
Calculator
Results
- Interquartile range (IQR)
- 50
- Lower outlier fence
- -50
- Upper outlier fence
- 150
Statistical results
| Interquartile range (IQR) | 50 |
| Lower outlier fence | -50 |
| Upper outlier fence | 150 |
formula-map diagram
- Interquartile range (IQR)
- 50
- Lower outlier fence
- -50
- Upper outlier fence
- 150
Statistical relationship
Formula
IQR = Q3 − Q1, fences = Q1 − 1.5·IQR and Q3 + 1.5·IQR= 50
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What is the interquartile range and what does it measure?+
The interquartile range (IQR) is the spread of the middle 50% of a data set, calculated as the third quartile (Q3) minus the first quartile (Q1). It measures variability while ignoring the most extreme values at both ends.
Why use IQR instead of standard deviation or range?+
IQR is much less sensitive to outliers than standard deviation or the full range, since it's based on the middle half of ordered data and ignores the extremes entirely. This makes it a more robust measure of spread for skewed data or data with outliers.
How is IQR used to detect outliers?+
A common rule flags any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as a potential outlier. This 1.5×IQR fence is the basis for the whiskers on a standard box plot.
What does a small IQR versus a large IQR tell you?+
A small IQR means the middle half of your data is tightly clustered together, indicating low variability in the typical case. A large IQR means the middle 50% is spread out, even if you ignore the extreme outliers entirely.
Are quartiles calculated the same way in every tool?+
No, there are several accepted methods for calculating quartile positions (different interpolation methods), and different software or calculators can give slightly different Q1 and Q3 values for the same data set. The IQR differences are usually small, but they can matter for edge cases or very small data sets.