Which quartile method is used here?

We use the Hyndman–Fan Type‑7 estimator (h = 1 + (n−1)p), the default in R. This provides linear interpolation between order statistics for percentiles.

How are outliers defined?

Tukey's boxplot rule: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are mild outliers; beyond 3×IQR are extreme outliers.

When should I use the geometric mean?

For strictly positive data involving multiplicative processes (e.g., growth rates, fold-changes, investment returns).

Why might trimmed mean be preferable?

Trimming reduces the influence of extreme values. It's a robust alternative that balances efficiency and resistance to outliers.

Why is harmonic mean not always available?

Harmonic mean is undefined if any value is zero. It's appropriate for averaging rates or ratios.

Mean, Median, Mode Calculator for Statistical Analysis

Calculate statistical measures including mean (average), median, mode, and range for any data set.

Quick Examples

Use weightsExclude outliers

Trim (%)

Decimals

Data values

Parsed 0 values.

Weights (optional)

When to prefer each measure

Mean: efficient for symmetric distributions; sensitive to outliers.
Median: robust against outliers/skew; preferred for skewed data or with outliers.
Mode: useful for discrete or categorical-like numeric data and repeated measurements.
Weighted mean: when observations contribute unequally (e.g., credits, sample sizes).
Trimmed mean: reduces influence of extremes; common in robust statistics.
Geometric mean: ratios/growth rates and strictly positive data (e.g., returns, fold-changes).
Harmonic mean: rates and ratios where averaging denominators makes sense (e.g., speeds).

How to analyze central tendency with this tool

Enter your data

Paste or type your dataset (comma, space, or newline separated). Optionally provide weights.

Set options

Choose decimals, enable outlier exclusion (Tukey), and specify trimmed mean percentage per tail.

Review the outputs

See mean, median, mode, extended means, quartiles (Type‑7), IQR, skewness, and outliers.

Interpret results

Use the summary and educational tips below to guide your conclusions.

Pro Tips

Use weighted mean when measurements have different reliability or sizes.
Prefer median or trimmed mean in heavy-tailed or skewed data.
Geometric mean applies only to strictly positive values.
Harmonic mean is for rates; avoid zeros.

Interpreting your results

Mean ≈ Median and Bowley skewness ≈ 0

Distribution is roughly symmetric with limited outlier influence.

Mean > Median and positive Bowley skewness

Right-skewed distribution; high-end values pull the mean upward.

Mean < Median and negative Bowley skewness

Left-skewed distribution; low-end values pull the mean downward.

Large IQR and outliers present

Substantial spread and possible anomalies; consider robust measures (median, trimmed mean).

Frequently Asked Questions

Related Calculators

Central tendency at a glance

Paste a dataset to get mean, median (Type-7), mode, quartiles, IQR, Tukey outliers, Bowley skewness, and extended means (weighted, trimmed, geometric, harmonic).

Central Tendency & Robust Statistics

Mean, Median, Mode Calculator: Quartiles, IQR, Outliers, and Robust Means

Compute mean, median (Type‑7), and mode alongside quartiles, IQR, Tukey outliers, Bowley skewness, and extended means (weighted, trimmed, geometric, harmonic). Evidence‑based methods match common statistical software defaults for reproducible results.

Comprehensive Outputs

Mean, median, mode, quartiles (Type‑7), IQR, Bowley skewness, range, min, max, and sum.

Robust & Specialized Means

Weighted mean, trimmed mean, geometric mean for positive data, and harmonic mean for non‑zero values.

Outlier Diagnostics

Tukey fences at ±1.5×IQR (mild) and ±3×IQR (extreme), with optional exclusion for robust summaries.

Comprehensive Methods & Features

Statistical Methods

• Mean (arithmetic): x̄ = Σx / n
• Median & Quartiles: Hyndman–Fan Type‑7 quantiles (h = 1 + (n−1)p) with linear interpolation
• Mode: maxima in the empirical frequency distribution (multi‑modal supported)
• IQR: Q3 − Q1 and Tukey outlier fences (1.5×IQR, 3×IQR)
• Weighted mean: x̄_w = Σ(wᵢxᵢ) / Σwᵢ; Trimmed mean: symmetric tail removal
• Geometric mean: (∏xᵢ)^(1/n), strictly positive xᵢ
• Harmonic mean: n / Σ(1/xᵢ), xᵢ ≠ 0
• Bowley skewness: (Q3 + Q1 − 2·Median) / IQR

Statistical Topics Covered

Mean Median Mode CalculatorStatistical Average CalculatorData Summary ToolCentral Tendency CalculatorStatistical Summary ToolQuartiles CalculatorIQR CalculatorOutlier Detection ToolBowley Skewness CalculatorWeighted Mean CalculatorTrimmed Mean CalculatorGeometric Mean CalculatorHarmonic Mean CalculatorData Analysis Tool

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Important: This statistical calculator provides accurate calculations for central tendency measures using standard statistical methods including the Hyndman-Fan Type-7 quantile estimator for quartiles and Tukey's method for outlier detection. While calculations are mathematically precise, statistical interpretation depends heavily on data quality, sampling methodology, distribution characteristics, and the specific context of your analysis. Results should be independently verified for critical applications including academic research, scientific studies, quality control processes, or professional statistical analysis. Users should ensure their data meets the assumptions of the statistical methods being applied and consult qualified statisticians or data analysts for complex analyses, hypothesis testing, or when statistical significance assessment is required.

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