Calculators

Winsorized Mean Calculator

Calculate a winsorized mean by replacing a chosen percentage of each tail with boundary values, privately in your browser.

Replace a percentage of the lowest and highest values with the nearest retained boundary, then average all values. Your data stays in your browser.

Separate values with commas, semicolons, spaces, or newlines. Use decimal points without thousands separators. Scientific notation is supported. Enter up to 10000 finite signed numbers, including zero.

Use 0 to less than 50%. The number of positions replaced at each end is rounded down. For five values and 20%, one position is replaced at each end. Ties may leave values unchanged.

Your winsorized mean will appear here.

Reduce the influence of extremes while preserving the dataset size.

Sort n values and set k = floor(n × p / 100), where p is the percentage per end. Replace the lowest k positions with the value at sorted position k + 1, and the highest k positions with the value at position n − k (positions start at 1). Average all n resulting values. For 1, 2, 3, 4, 100 and 20% per end, the transformed data is 2, 2, 3, 4, 4 and the winsorized mean is 3. Unlike trimming, winsorization preserves the observation count. A 0% setting gives the arithmetic mean; small datasets may replace no positions. Tied boundary values may mean fewer numerical changes than replaced positions. Report the percentage and rounding convention with your result. Enter 1 to 10000 finite signed values with consistent units, separated by commas, semicolons, spaces or newlines. Scientific notation is accepted; omit thousands separators. Results use browser floating-point arithmetic displayed to 12 significant digits. All processing stays in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

How is a winsorized mean calculated?

Sort n values and set k = floor(n × p / 100), where p is the percentage per end. Replace the lowest k positions with the value at sorted position k + 1, and the highest k positions with the value at position n − k (positions start at 1). Average all n resulting values. For 1, 2, 3, 4, 100 and 20% per end, the transformed data is 2, 2, 3, 4, 4 and the winsorized mean is 3.

Is the percentage per end?

Yes. A 10% setting replaces floor(n × 0.10) positions at each end. Counts are rounded down. Ties can leave some values unchanged.

How does this differ from a trimmed mean?

A trimmed mean removes observations. A winsorized mean replaces tail values and averages the original number of observations.

What percentages and inputs are supported?

Use a percentage from zero up to but not including 50, and 1 to 10000 finite signed numbers. Zero percent gives the arithmetic mean. A single number returns itself. Scientific notation is accepted; results use up to 12 significant digits and stay in your browser.