IQR Calculator (Interquartile Range)

Enter your dataset and get your IQR in seconds… plus other numbers and and step-by-step calculation breakdowns included.

Enter Your Dataset:

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Interquartile Range (IQR)

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Five-Number Summary

Minimum

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Q1 (25th Percentile)

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Q2 (Median)

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Q3 (75th Percentile)

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Maximum

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Box Plot Visualization

Min Q1 Med Q3 Max

Quartile Breakdown

Lower 25%

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Min to Q1

2nd Quartile

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Q1 to Median

3rd Quartile

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Median to Q3

Upper 25%

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Q3 to Max

Outlier Detection (1.5×IQR Rule)

Lower Fence

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Q1 − 1.5×IQR

Upper Fence

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Q3 + 1.5×IQR

Outlier Count

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Outside fences

Lower Outliers (below —)

None

Upper Outliers (above —)

None

Extreme Outliers (3×IQR Rule)

Extreme Lower

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Q1 − 3×IQR

Extreme Upper

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Q3 + 3×IQR

Extreme Count

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Beyond 3×IQR

Related Statistics

Mean

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Average

Std Dev (s)

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Sample

Range

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Max − Min

Midhinge

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(Q1+Q3)/2

Semi-IQR

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IQR / 2

Quartile Deviation

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(Q3−Q1)/2

Coeff. of QD

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(Q3−Q1)/(Q3+Q1)

Key Percentiles

P10 —

P20 —

P25 (Q1) —

P30 —

P40 —

P50 (Med) —

P60 —

P70 —

P75 (Q3) —

P80 —

P90 —

P95 —

Dataset Overview

Count (n)

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Sum (Σx)

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Non-Outlier Count

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Sorted Data (ascending)

Calculation Steps

Sort the data

Find the median (Q2)

Find Q1 (median of lower half)

Find Q3 (median of upper half)

Calculate IQR = Q3 − Q1

Quartiles calculated using Tukey's hinges method (exclusive median). The IQR represents the middle 50% of your data.

What Is the Interquartile Range (IQR)?

The interquartile range (IQR) measures the spread of the middle 50% of your data. Unlike the total range, which can be heavily skewed by extreme values, the IQR focuses exclusively on the central portion of your dataset—making it one of the most reliable measures of statistical dispersion.

The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1):

IQR = Q3 − Q1

Where Q1 represents the 25th percentile (the median of the lower half) and Q3 represents the 75th percentile (the median of the upper half). The resulting value tells you the range within which the middle half of your observations fall.

How to Calculate IQR Step by Step

1. Order Your Data

Arrange all values from smallest to largest. This is essential for identifying the correct positions of each quartile.

2. Find the Median (Q2)

Locate the middle value of your dataset. For an odd number of values, this is the center value. For an even number, average the two center values.

3. Determine Q1 and Q3

Q1 is the median of all values below Q2. Q3 is the median of all values above Q2. Exclude the median itself when your dataset has an odd count.

4. Subtract Q1 from Q3

The difference gives you the IQR—a single number representing the spread of your data’s middle half.

Using IQR to Detect Outliers

The IQR provides a robust method for identifying outliers through the “1.5×IQR rule.” Any data point is considered a potential outlier if it falls:

Below the lower fence: Q1 − 1.5 × IQR
Above the upper fence: Q3 + 1.5 × IQR

Values beyond 3×IQR from the quartiles are typically classified as extreme outliers and often warrant closer investigation or removal from analysis.

When to Use IQR Over Standard Deviation

The IQR offers distinct advantages in specific scenarios:

Skewed distributions: When data isn’t symmetrical, IQR provides a more accurate picture of typical spread than standard deviation.
Datasets with outliers: Because IQR ignores the top and bottom 25%, extreme values don’t distort the measurement.
Ordinal data: When exact intervals between values aren’t meaningful, IQR remains interpretable.

Standard deviation remains preferable for normally distributed data where you need to make probabilistic inferences or when working with statistical models that assume normality.

IQR in Box Plots

The IQR forms the foundation of box plot visualizations. The “box” spans from Q1 to Q3, with its height representing the IQR. The median appears as a line within the box, while whiskers extend to the smallest and largest non-outlier values. This visual representation makes comparing distributions across groups intuitive and immediate.