# Interquartile Range (IQR) Calculator

Free IQR calculator. Calculate the interquartile range, outlier fences, and mid-hinge from Q1 and Q3 values. Identify mild and extreme outliers.

## What this calculates

Calculate the interquartile range and detect outliers using the IQR method. Enter Q1 and Q3 to find the IQR, outlier fences, and mid-hinge.

## Inputs

- **First Quartile (Q1)** — The 25th percentile value.
- **Third Quartile (Q3)** — The 75th percentile value.
- **Median (Q2)** — The 50th percentile value (optional, for reporting).

## Outputs

- **Interquartile Range (IQR)** — Q3 - Q1, the range of the middle 50% of data.
- **Lower Fence** — Q1 - 1.5 × IQR. Values below are mild outliers.
- **Upper Fence** — Q3 + 1.5 × IQR. Values above are mild outliers.
- **Lower Extreme Fence** — Q1 - 3 × IQR. Values below are extreme outliers.
- **Upper Extreme Fence** — Q3 + 3 × IQR. Values above are extreme outliers.
- **Mid-Hinge** — (Q1 + Q3) / 2, the average of the two quartiles.

## Details

The interquartile range (IQR) is a robust measure of statistical dispersion.

Formula:
IQR = Q3 - Q1

Outlier Fences

- Mild outlier: value < Q1 - 1.5×IQR or value > Q3 + 1.5×IQR

- Extreme outlier: value < Q1 - 3×IQR or value > Q3 + 3×IQR

Advantages of IQR

- Not affected by extreme outliers (unlike range or standard deviation)

- Works well with skewed distributions

- Used in box plots for visualization

## Frequently Asked Questions

**Q: Why use IQR instead of standard deviation?**

A: IQR is resistant to outliers and does not assume a normal distribution. Standard deviation is affected by extreme values. Use IQR when your data is skewed or contains outliers. Use standard deviation when data is approximately normal and outliers are unlikely.

**Q: What is the 1.5 × IQR rule?**

A: The 1.5 × IQR rule (Tukey's fences) identifies potential outliers. Any value below Q1 - 1.5×IQR or above Q3 + 1.5×IQR is flagged as a mild outlier. Values beyond Q1 - 3×IQR or Q3 + 3×IQR are considered extreme outliers. For a normal distribution, about 0.7% of data falls beyond the 1.5×IQR fences.

**Q: What is the mid-hinge?**

A: The mid-hinge is (Q1 + Q3) / 2, the average of the first and third quartiles. It provides a robust estimate of the center of the data, similar to the median but calculated from the quartiles. For symmetric distributions, the mid-hinge equals the median.

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Source: https://vastcalc.com/calculators/statistics/interquartile-range
Category: Statistics
Last updated: 2026-04-21