Stats Calculator | Mean, Median, Mode & SD

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

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.

Scope:

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

How the Math Works: Key Descriptive Statistics Formulas

The calculator applies standard descriptive statistics formulas to your dataset. The arithmetic mean is the sum divided by count:

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

Sample standard deviation uses Bessel's correction (n−1 denominator) to produce an unbiased estimate from a subset:

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

Population standard deviation uses n. The geometric mean, defined only for positive values, is the nth root of the product:

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

The five-number summary (Min, Q1, Median, Q3, Max) and IQR = Q3 − Q1 complete the descriptive profile.

Worked Example:

Dataset: 4, 8, 6, 5, 3, 7. Mean = 33/6 = 5.5. Sorted: 3, 4, 5, 6, 7, 8. Median = (5+6)/2 = 5.5. Q1 = 4, Q3 = 7, IQR = 3. Sample SD ≈ 1.87.

How to Use This Calculator

Enter your dataset to get a full descriptive statistics profile with visualizations.

Data Input:

Paste or type numbers separated by commas, spaces, or new lines. The geometric mean requires all positive values (shows N/A otherwise).
Sample vs. Population Toggle:

Choose Sample (n−1) for subsets of a larger population or Population (n) for complete datasets. This affects standard deviation and variance.
Statistical Summary:

Displays mean, median, mode, standard deviation, variance, geometric mean, five-number summary (Min, Q1, Median, Q3, Max), sum (Σx), and sum of squares (Σx²).
Logic Trace & Visualizations:

Tabbed Logic Trace shows arithmetic and geometric mean calculations step by step. The bell curve and box-and-whisker plot visualize your distribution.

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.

Statistics Calculator