Skip to content
Statistics

Interquartile Range (IQR) Calculator

Calculate the interquartile range of up to 8 numbers and check for outliers using the standard 1.5×IQR fence rule.

Only the first this-many values below are included.

Your results

Interquartile range (IQR)13
Q1 (25th percentile)50.75
Q3 (75th percentile)63.75
Outlier fences (1.5×IQR rule)31.25 to 83.25

No values fall outside the 1.5×IQR outlier fences.

Calculation breakdown

IQR
IQR = Q3 − Q1
Outlier fences
lower = Q1 − 1.5×IQR, upper = Q3 + 1.5×IQR

Worked example

For the values 41, 47, 52, 55, 58, 63, 66 and 70, Q1 is about 51 and Q3 about 64.75, giving an IQR of roughly 13.75, a measure of the spread of the middle 50% of the data.

Assumptions

  • The IQR describes the spread of the middle 50% of the data and is less affected by outliers than the range.
  • The 1.5×IQR outlier rule is a common convention, not a strict statistical law.

How this calculator works

Enter up to 8 numeric values to find Q1, Q3 and the interquartile range (Q3 minus Q1), a robust measure of spread. The calculator also flags any values that fall outside the standard 1.5×IQR outlier fences.

Frequently asked questions

Why use IQR instead of the full range?

IQR only measures the middle 50% of the data, so it is far less affected by a single very high or low outlier than the full range.

What is the 1.5×IQR rule?

It's a common convention that flags any value more than 1.5 times the IQR below Q1 or above Q3 as a potential outlier.

Is the 1.5×IQR rule always correct?

No, it's a useful default but not a strict law — some genuinely valid data points will fall outside the fences, especially in skewed datasets.

Related calculators

← Back to all calculators