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Statistics · Descriptive statistics

Interquartile Range Calculator

Measure the spread of the middle half of a dataset and calculate standard outlier fences.

Statistics · Descriptive statistics

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Private in-browser calculation · explicit assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand the statistic

What the interquartile range calculator tells you

Measuring how observations vary. Spread describes how tightly or widely values lie around a reference. It complements a center: two datasets can share the same mean while behaving very differently.

Calculation rule

IQR = Q3 − Q1; fences = Q1 − 1.5×IQR and Q3 + 1.5×IQR.

The formula is applied only to the observations and options you enter. No population, distribution, or sampling process is inferred automatically.

How to read the answer

IQR is resistant to extreme values and is especially useful for skewed data.

Important: Fence exceedance is a screening rule, not proof that an observation is erroneous.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the interquartile range calculator works

IQR = Q3 − Q1; fences = Q1 − 1.5×IQR and Q3 + 1.5×IQR.

IQR is resistant to extreme values and is especially useful for skewed data.

Worked example

Interquartile Range example

If Q1=12 and Q3=20, IQR=8 and the fences are 0 and 32.

IQR = Q3 − Q1; fences = Q1 − 1.5×IQR and Q3 + 1.5×IQR.

Supported inputs

Precision and limits

Model and design

Fence exceedance is a screening rule, not proof that an observation is erroneous.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

IQR is resistant to extreme values and is especially useful for skewed data.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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