What is the interquartile range (IQR)?

The interquartile range (IQR) is a measure of statistical dispersion and is defined as the difference between the third quartile (Q3) and the first quartile (Q1). It describes the spread of the middle 50% of the data.

How do you detect outliers with IQR?

Using Tukey's rule, values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are considered outliers.

Why use IQR instead of range?

The IQR is robust to extreme values, while the range depends only on the smallest and largest observations and can be distorted by outliers.

IQR Calculator – Interquartile Range, Q1, Median, Q3 & Outliers

2. Results

Q1 (25%)

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Median (Q2)

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Q3 (75%)

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IQR (Q3 − Q1)

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Count (n)

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Outlier fences (Tukey)

Lower fence: —

Upper fence: —

Any value < lower fence or > upper fence is a potential outlier.

Detected outliers

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What is the IQR?

The interquartile range (IQR) is a robust measure of variability. It tells you how spread out the middle 50% of your values are. Because it ignores the lowest 25% and highest 25% of data, it is much less sensitive to outliers than the full range.

How we computed your quartiles

This tool uses the classic “median-of-halves” method (Tukey style):

Sort the data.
Find the median (Q2).
If n is odd, exclude the median from both halves.
Q1 = median of the lower half, Q3 = median of the upper half.

IQR = Q3 − Q1
Lower fence = Q1 − 1.5 × IQR
Upper fence = Q3 + 1.5 × IQR

Why IQR is useful

It’s used in boxplots.
It’s a good default for outlier detection.
It’s robust and easy to explain.

Interquartile Range (IQR) Calculator

1. Enter your data