Maths

Statistics Calculator (Mean, Median, Mode, Variance)

Full descriptive statistics — mean, median, mode, range, variance and standard deviation — with step-by-step working.

Data values (separate by commas, spaces or semicolons)

Use population variance (divide by n) — uncheck for sample (n − 1)

Result

Mean (x̄)

Median

15.5

Mode

No mode (all values unique)

Range

Variance

151.6667

Population (÷n)

Std Deviation

12.3153

Sum

108

Count (n)

Concept

Measures of central tendency — mean, median and mode each capture the "typical" value differently. The mean is sensitive to outliers, the median is robust, and the mode identifies the most frequent value.

Measures of spread — variance measures the average squared distance from the mean; standard deviation converts this back to the original unit by taking the square root.

When to use each: use the mean for symmetric distributions without outliers, the median for skewed data or data with outliers (e.g. incomes), and the mode for categorical or discrete data.

Formula

Mean (x̄)=Σ xᵢn

Variance (σ²)=Σ (xᵢ − x̄)²n

Std Dev (σ)=√Variance

Variables

n: Count of data points.
xᵢ: Each individual value in the dataset.
x̄: Arithmetic mean = sum of all values ÷ n.
Median: The middle value when data is sorted — average of two middle values if n is even.
Mode: The most frequently occurring value — a dataset can have none, one or multiple modes.
σ²: Population variance.
σ: Population standard deviation.