Interquartile Range (IQR) Calculator
IQR = Q3 − Q1 — the middle 50% spread, robust to outliers.
Result
IQR (Q3 − Q1)
11.7500
Outlier fence: -5.13 … 41.88.
- Q1 (25th)12.5000
- Q2 (50th, median)16.5000
- Q3 (75th)24.2500
- IQR11.7500
- Outliers (1.5×IQR rule)None
Step-by-step
- Sort and compute Q1 (25th), Q2 (median), Q3 (75th) using linear interpolation.
- IQR = Q3 − Q1 = 24.2500 − 12.5000 = 11.7500.
- Tukey outlier fences: [Q1 − 1.5·IQR, Q3 + 1.5·IQR] = [-5.13, 41.88].
How to use this calculator
- Enter your data.
- Read IQR and Q1/Q3.
- Inspect the outlier fence.
About this calculator
IQR — interquartile range — captures the middle 50% of the data. Robust to outliers because it ignores the top and bottom quarters. Often used with the Tukey 1.5×IQR rule to flag potential outliers.
Frequently asked
IQR ignores the top and bottom 25% of the data, so a single extreme value can't pull it. SD weighs every value, so outliers move it a lot.
Related calculators
Percentile Calculator
Find the value at the kth percentile in a dataset (linear interpolation).
Median Calculator
Find the middle value (or average of two middle values) of a list of numbers.
Standard Deviation Calculator
Compute sample (n−1) and population (n) standard deviation from a list of numbers.
Mean (Average) Calculator
Compute the arithmetic mean of a list of numbers.
Variance Calculator
Sample (n−1) and population (n) variance — the square of standard deviation.
Z-Score Calculator
z = (x − μ) / σ — how many standard deviations a value is above or below the mean.