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Descriptive Statistics Calculator

Enter your dataset to compute summary statistics, five-number summary, and visualize distributions with box plots and histograms. All calculations run in your browser.

Tip: Press Ctrl+Enter (Cmd+Enter on Mac) to calculate.

Reference Guide

Measures of Central Tendency

Mean The arithmetic average.
xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i
Median The middle value when data is sorted. For even-count datasets, it is the average of the two middle values.
Mode The most frequently occurring value(s). A dataset can have one mode, multiple modes, or no mode if all values are unique.

Measures of Spread

Sample Variance
s2=1n−1∑i=1n(xi−xˉ)2s^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2
Population Variance Uses nn instead of n−1n-1 in the denominator.
Standard Deviation The square root of variance. s=s2s = \sqrt{s^2}
Interquartile Range (IQR) IQR=Q3−Q1IQR = Q_3 - Q_1. Measures the spread of the middle 50% of data.

Five-Number Summary and Box Plots

The five-number summary consists of Min, Q1, Median, Q3, and Max. These five values form the basis of the box plot.

Quartiles (Tukey's Hinges) Q1 is the median of the lower half, Q3 is the median of the upper half.
Outlier Detection Points below Q1−1.5×IQRQ_1 - 1.5 \times IQR or above Q3+1.5×IQRQ_3 + 1.5 \times IQR are considered outliers and displayed as individual dots on the box plot.

Histograms and Distribution Shape

A histogram groups data into bins and shows frequency counts. Adjusting the number of bins can reveal different patterns in the data.

Skewness Measures asymmetry. Positive skewness means a longer right tail (mean > median). Negative skewness means a longer left tail (mean < median).
Kurtosis Measures tail heaviness relative to a normal distribution. Excess kurtosis of 0 means normal-like tails. Positive values indicate heavier tails.
Sturges' Rule The default bin count is ⌈log⁡2(n)+1⌉\lceil \log_2(n) + 1 \rceil, which works well for moderate-sized datasets.