Stats Calculator | Mean, Median, Mode & SD

Statistics Calculator: Mean, Median, Mode, SD, Variance & More

This calculator builds a descriptive statistics profile from numbers you type or paste: mean, median, mode, SD, variance, geometric mean, and a five-number summary. It includes a logic trace and bell-curve and box plots, and everything runs locally in your browser.

What This Calculator Does

This statistics calculator is a descriptive tool — it summarizes one dataset you enter (type or paste numbers separated by commas, spaces, or new lines). Outputs: arithmetic mean, median, mode, sample or population standard deviation and variance, geometric mean (positive data only), range, five-number summary with IQR, Σx, and Σx². A four-card Statistical summary updates live; Logic trace tabs prove the arithmetic and geometric mean; Distribution visualization shows a normal curve N(μ, σ²) and a box-and-whisker plot. Sample mode requires n ≥ 2; population mode allows n ≥ 1. It does not run hypothesis tests or regression. All math runs locally.

How the Math Works

Arithmetic mean:

\bar{x} = \frac{\sum x_i}{n}

Sample variance (Bessel):

s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}

Population variance divides by n. Geometric mean (all xᵢ > 0):

G = \left(\prod x_i\right)^{1/n}

Example 2, 4, 4, 5, 5, 7, 9: x̄ = 36/7, median 5, sample s ≈ 2.27, Q₁ = 4, Q₃ = 7.

How to Use This Calculator

Control reference:

Data:

Multi-line field; commas, spaces, or newlines separate values.
SD / Variance toggle:

Sample (n−1) or Population (n).
Statistical summary:

Four cards — Averages, Variability, Five-number summary, Sums (+ mode).
Logic trace:

Arithmetic Mean vs Geometric Mean tabs; Copy for plain text.
Distribution visualization:

Normal curve and box plot when quartiles and SD allow.

Arithmetic Mean vs Geometric Mean

Use the arithmetic mean for ordinary averages. Use the geometric mean for multiplicative data (growth rates, ratios). Any zero or negative value makes G undefined — the calculator shows N/A rather than a misleading number.

Five-Number Summary and Box Plot

Quartiles split the sorted list: Q₁ is the median of the lower half, Q₃ of the upper half. The box plot whiskers run to min and max; the box spans Q₁–Q₃ with a median line. Compare spread and center across datasets at a glance.

FAQ

What statistics does this calculator compute?

Enter any list of numbers (type or paste, separated by commas, spaces, or new lines) and you get arithmetic mean, median, mode, sample or population standard deviation and variance, geometric mean (when all values are positive), range, five-number summary (Min, Q₁, Median, Q₃, Max), IQR, Σx, and Σx². Results update as you type.

What is the difference between sample and population SD?

Sample (n−1) divides squared deviations by n−1 (Bessel’s correction) — use when your list is a subset of a larger population. Population (n) divides by n — use when the list is the entire group. The SD / Variance toggle switches the denominator; mean and median are unchanged.

How many data points do I need?

Population mode needs at least 1 number. Sample mode needs at least 2 (n−1 in the denominator). Quartiles and the box plot need at least 2 values. The bell curve appears when SD > 0.

When is the geometric mean N/A?

The geometric mean requires every value to be positive. Zeros or negatives make the product zero or undefined, so the summary shows N/A and the Geometric Mean logic trace tab has no steps.

What is the five-number summary?

Min, Q₁, Median, Q₃, and Max. Q₁ and Q₃ are medians of the lower and upper halves of the sorted list (same split the calculator uses). IQR = Q₃ − Q₁. The box plot draws whiskers to min/max, a box from Q₁ to Q₃, and a red median line.

What if there is no mode?

When every value appears once, the summary shows No mode. When two or more values tie for highest frequency, all tied values are listed (e.g. 4, 5).

What does the bell curve show?

It plots a normal PDF N(μ, σ²) using your list’s mean μ and the SD from the current sample/population toggle — a visual reference, not a claim that your data are perfectly normal. A dashed red line marks μ.

Statistics Calculator

Enter your data

Reading the statistical summary

Worked example: 2, 4, 4, 5, 5, 7, 9

Card 1: Averages

Card 2: Variability (Sample n−1)

Card 3: Five-number summary

Card 4: Sums & mode