# Interquartile Range Calculator

Calculate Q1, Q3, IQR, and optional 1.5 x IQR outlier fences for a numeric dataset

> Canonical page: https://elysiatools.com/en/tools/interquartile-range-calculator

- **Category:** Math & Numbers

- **Keywords:** interquartile range, iqr, quartile, q1, q3, outliers, box plot

## Overview

Calculate the interquartile range for a numeric dataset.

IQR = Q3 - Q1

The IQR measures the spread of the middle 50% of sorted data. It is robust against extreme values and is commonly used for box plots and outlier screening.

## Inputs

- **Dataset** (textarea): e.g. 7, 15, 36, 39, 40, 41
- **Quartile Method** (select)
- **Decimal Places** (number)
- **Include Outlier Fences** (checkbox)

## When to use

- When you need to measure the statistical dispersion of a dataset while ignoring extreme high or low values.
- When preparing data for a box plot visualization and you need exact quartile values.
- When screening a dataset for potential outliers using the standard 1.5 x IQR rule.

## How it works

- Paste your comma-separated or space-separated numeric dataset into the input field.
- Select your preferred quartile calculation method, such as linear interpolation or nearest rank.
- Choose whether to include Tukey's 1.5 x IQR outlier fences and set your desired decimal precision.
- View the calculated Q1, Q3, interquartile range, and outlier boundaries in the results.

## Use cases

- Data analysts cleaning raw datasets by identifying and filtering out anomalous data points.
- Students and researchers calculating summary statistics for academic papers and lab reports.
- Quality control engineers monitoring manufacturing variations without being misled by isolated measurement errors.

## Frequently asked questions

### What is the Interquartile Range (IQR)?

The IQR is a measure of statistical dispersion representing the difference between the third quartile (Q3) and the first quartile (Q1), capturing the middle 50% of a dataset.

### Why use IQR instead of the standard range?

Unlike the standard range which only looks at the absolute minimum and maximum, the IQR is not skewed by extreme outliers, providing a more reliable view of the central data spread.

### What are outlier fences?

Outlier fences are boundaries calculated using the IQR (typically Q1 - 1.5 * IQR and Q3 + 1.5 * IQR). Any data points falling outside these fences are generally considered outliers.

### What quartile calculation methods are supported?

The tool supports linear interpolation, nearest rank, and exclusive percentile methods to match different statistical software standards.

### Can I adjust the decimal precision of the results?

Yes, you can configure the output to display anywhere from 0 to 10 decimal places depending on your reporting needs.

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