Mean, Median, Mode, Range Calculator

Descriptive Statistics & Central Tendency

In statistical analysis, measures of central tendency describe the single most representative value of a numerical dataset.

The Fundamental Statistical Formulas

• Arithmetic Mean: x = (1) / (N) Σ_i=1^N x_i

• Median: The 50th percentile value separating the higher half from the lower half.

• Mode: Argmax(f(x)) — the value with highest frequency.

• Range: R = x_max - x_min

Mean vs Median in Skewed Distributions

• Right-skewed (Positive Skew): Mean > Median > Mode

• Symmetric Normal Distribution: Mean = Median = Mode

• Left-skewed (Negative Skew): Mean < Median < Mode

Bimodal & Multimodal Distributions

A dataset can have more than one mode if multiple values share the highest frequency (bimodal for 2 modes, multimodal for 3 modes). If all values occur with equal frequency, the dataset has no mode.

Interquartile Range & Dispersion Measures

While range measures total spread from minimum to maximum, advanced statistical reporting pairs range with variance (σ^2) and standard deviation (σ) to quantify internal spread around the mean.

How to Use This Calculator

Enter your Data Set (comma or space separated) (e.g. 12, 15, 18, 15, 22, 30, 15, 24). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

range = max - min

median = (numbers[mid - 1] + numbers[mid]) / 2

Worked Example

Analyzing dataset [12, 15, 18, 15, 22, 30, 15, 24]: Yields Mean = 18.8750, Median = 16.5000, Mode = 15, and Range = 18.

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Understanding Your Result

Statistical results require context: a mean alone is misleading without knowing the standard deviation (spread). Normal distribution reference: 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, 99.7% within ±3 SD. For small sample sizes (n < 30), use t-distributions rather than z-scores. Statistical significance (p < 0.05) does not imply practical significance — effect size (Cohen's d, R², odds ratio) measures real-world importance. Correlation coefficient r: |r| < 0.3 weak, 0.3–0.7 moderate, > 0.7 strong.