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

How to Use the Statistics Calculator

Enter your dataset; the Statistical Summary and Logic Trace update instantly. See the article below for formulas and when to use each measure.

Quick Start

Input

Paste or type numbers—commas, spaces, or newlines. Geometric mean requires all positive values.

Mode Toggle

Sample (n−1) for subsets; Population (n) for full data. Affects SD and variance.

Logic Trace & Plots

Arithmetic/Geometric Mean tabs show the Logic Trace. Bell curve and box plot visualize distribution.

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

Compute mean, median, mode, standard deviation, variance, and five-number summary from raw data. Logic Trace, box plot, and bell curve. Trusted by students and educators.

What This Statistics Calculator Does

Purpose & Use Cases

Scope:

Geometric mean requires all positive values (N/A otherwise). Sample mode needs n ≥ 2. All calculations run locally—no data stored.

This statistics calculator computes a full descriptive statistics profile from raw data: mean, median, mode, standard deviation, variance, geometric mean, five-number summary (min, Q1, median, Q3, max), sum (Σx), and sum of squares (Σx²). Choose sample (n−1) or population (n) for SD and variance. Includes a tabbed Logic Trace and distribution visualizations (bell curve, box-and-whisker plot). Ideal for homework verification, exploratory data analysis, and learning how to find mean, median, and standard deviation from a list of numbers.

Arithmetic Mean and Geometric Mean

The arithmetic mean is:

\bar{x} = \frac{\sum x_i}{n} = \frac{x_1 + x_2 + \cdots + x_n}{n}

The geometric mean is:

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

—the nth root of the product of all values. Geometric mean applies to growth rates and ratios; it is undefined (N/A) when any value is zero or negative.

Standard Deviation, Variance, and Sum of Squares

Population variance:

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

Sample variance (Bessel's correction):

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

Standard deviation is √variance. The sum of squares Σx² is the sum of each value squared (used in some variance formulas and regression).

Five-Number Summary and Box-and-Whisker Plot

The five-number summary—Min, Q1, Median, Q3, Max—summarizes distribution. Q1 and Q3 are the medians of the lower and upper halves. A box-and-whisker plot (or box plot) draws whiskers to min and max, a box from Q1 to Q3, and a line at the median. Use it to compare spread, center, and skew across datasets.

FAQ

? What statistics does this calculator compute?

Mean, median, mode, standard deviation, variance, geometric mean, five-number summary, sum (Σx), and sum of squares (Σx²). Choose sample or population for SD. Results update live.

? When is the geometric mean N/A?

The geometric mean is defined only for positive numbers. If your dataset contains zero or any negative values, the calculator shows "N/A" because the nth root of a non-positive product is undefined (or complex) in standard statistics.

? What is the five-number summary?

Min, Q1, Median, Q3, and Max. Q1 and Q3 are the medians of the lower and upper halves of the sorted data. Used for box-and-whisker plots and to compare distributions.

? What is the difference between arithmetic and geometric mean?

The arithmetic mean is (Σx)/n—the usual average. The geometric mean is (∏xᵢ)^(1/n)—the nth root of the product. Use geometric mean for growth rates, ratios, or data that multiplies (e.g. investment returns).

? What does the box-and-whisker plot show?

Whiskers to min and max, a box from Q1 to Q3, and a median line. Shows spread (IQR), center, and potential outliers at a glance.