Statistics Calculator – Tutorial

Statistics — Mean, Median, Variance, Standard Deviation

Statistics summarizes a dataset with a few key numbers instead of listing every value.

1) Mean (Arithmetic Average)

x̄ = Sum / n

Affected by outliers. A single extreme value can shift the mean significantly.

2) Median

The middle value of a sorted list. Less affected by outliers than the mean.

• Odd count: the middle element
• Even count: average of the two middle elements

3) Variance and Standard Deviation

Variance (pop) = Σ(xᵢ − x̄)² / n

Variance (sample) = Σ(xᵢ − x̄)² / (n−1)

Standard deviation = √Variance — measures the "typical distance" from the mean.

• Small std: data points are close together
• Large std: data points are spread out

Note: This tool does not calculate mode.