Outlier Calculator

What Is an Outlier?

An outlier is a value that sits much lower or much higher than the rest of a dataset. Outliers can point to data entry mistakes, unusual observations, or genuinely rare events. This outlier calculator uses the standard interquartile-range method to flag values that lie beyond the lower or upper fence.

Outlier Formula

First, compute the first quartile $Q_1$, median, and third quartile $Q_3$. Then find the interquartile range:

$$IQR = Q_3 - Q_1$$

The outlier fences are:

$$\text{Lower fence} = Q_1 - 1.5 \times IQR$$ $$\text{Upper fence} = Q_3 + 1.5 \times IQR$$

Any value below the lower fence or above the upper fence is treated as an outlier.

How This Outlier Calculator Works

1. Sort the dataset from smallest to largest.
2. Find $Q_1$, the median, and $Q_3$.
3. Compute the interquartile range.
4. Build the lower and upper fences.
5. Return low outliers, high outliers, and the sorted list.

Why Outliers Matter

Outliers can distort averages, variance, and regression results. They matter in grading systems, experimental measurements, business metrics, and quality-control datasets. For a wider summary of your data, pair this tool with the Box Plot Calculator, Quartile Calculator, and Descriptive Statistics Calculator.