Interquartile Range (IQR) Calculator
Calculate the interquartile range (IQR) along with Q1, Q3, and the median of your data.
Enter your data set. Invalid values will be ignored.
Interquartile Range (IQR)
First Quartile (Q1)
Median (Q2)
Third Quartile (Q3)
Count (n)
Calculation Steps
What the Interquartile Range Measures
The interquartile range (IQR) describes the spread of the middle 50% of a data set. It is the difference between the third quartile (Q3) and the first quartile (Q1). Because it ignores the lowest and highest 25% of values, the IQR is a robust measure of dispersion that is not affected by extreme outliers.
Tukey's Method for Quartiles
This calculator uses Tukey's method. First, sort the data in ascending order and find the median. Then split the data into a lower half and an upper half. When the number of values is odd, the median itself is excluded from both halves. Q1 is the median of the lower half and Q3 is the median of the upper half.
- Q1: median of the lower half of the data
- Q3: median of the upper half of the data
- IQR: Q3 − Q1
Why Use the IQR
The IQR is commonly used to identify outliers and to build box plots. Values that fall more than 1.5 × IQR below Q1 or above Q3 are often flagged as potential outliers. Because it relies on quartiles rather than the mean, the IQR gives a reliable picture of variability even when the data is skewed.