What does this statistics calculator compute?

This statistics calculator computes core descriptive statistics from a list of numbers: count, sum, mean, median, mode, minimum, maximum, range, variance, standard deviation, and coefficient of variation. You can choose whether to treat your data as a whole population or as a sample.

What is the difference between population and sample standard deviation?

The population standard deviation divides the sum of squared deviations by N, the total number of values. The sample standard deviation divides by N−1 instead. The N−1 denominator makes the sample variance an unbiased estimator of the population variance under standard assumptions.

How should I format numbers in the input field?

You can separate numbers with commas, spaces, new lines or semicolons. For example: 3, 4, 5.5, 7 or on separate lines. Non-numeric entries are ignored with a clear warning so that they do not affect the results.

How many data points can I enter?

For practical performance, the calculator is designed for a few tens of thousands of values at most, which is more than enough for typical classroom, lab, or business datasets. For very large datasets, consider using a statistical programming environment such as R or Python.

Statistics Calculator – Descriptive Statistics in One Place

Paste your data and instantly compute mean, median, mode, variance, standard deviation, range and more. Choose between population and sample statistics and see the formulas used, step by step.

Descriptive statistics Mean · median · mode Variance & σ

1. Statistics calculator

Enter your numeric observations below. You can separate values with commas, spaces, new lines, or semicolons. The tool will compute core descriptive statistics and highlight the difference between population and sample measures.

Data (one-dimensional numerical sample)

Allowed separators: comma, space, semicolon, tab, or new line. Non-numeric entries will be ignored with a warning.

Data type

Sample (divide by n − 1) Population (divide by n)

Decimal places

Count, min, max, and range are shown as exact integers when possible.

Output focus

This tool focuses on univariate descriptive statistics. For regressions, tests, and advanced inference, use the dedicated calculators in the sidebar.

Count

–

Number of valid numeric values

Mean

–

Arithmetic average

Median

–

Central value (50th percentile)

Std. deviation

–

Sum
Minimum
Maximum
Range
Variance
Coefficient of variation
Mode(s)

What are statistics?

Statistics is the branch of mathematics that deals with collecting, summarizing, analyzing, and interpreting data. At the most basic level, descriptive statistics compress a set of numbers into a few key summaries: measures of central tendency (mean, median, mode) and variability (range, variance, standard deviation).

Core descriptive statistics and formulas

Suppose you have numerical observations \(x_1, x_2, \dots, x_n\).

Mean (arithmetic average)
\[ \bar{x} = \frac{1}{n}\sum_{i=1}^n x_i \] Sum
\[ S = \sum_{i=1}^n x_i \]

Variance
Population variance: \[ \sigma^2 = \frac{1}{n}\sum_{i=1}^n (x_i - \mu)^2 \] Sample variance: \[ s^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2 \] Standard deviation is the square root of variance: \[ \sigma = \sqrt{\sigma^2}, \quad s = \sqrt{s^2}. \]

The median is the central value when the data are sorted. For odd \(n\) it is the middle observation; for even \(n\) it is the average of the two middle observations. The mode is (are) the most frequent value(s).

Population vs. sample statistics

In many applications, especially in science and economics, you do not measure an entire population; you only have a sample. Using the population variance formula on a small sample tends to underestimate the true variability, which is why the denominator is adjusted from \(n\) to \(n-1\).

Use population formulas when you really have data for every element of the group you care about (for example, the exam scores of a small class).
Use sample formulas when your data are a subset of a larger population and you are trying to infer properties of the whole (for example, a survey sample in official statistics).

Coefficient of variation (CV)

The coefficient of variation measures relative variability: how large the standard deviation is compared to the mean.

\[ \text{CV} = \frac{\text{standard deviation}}{\lvert \text{mean} \rvert} \times 100\% \]

CV is unitless and useful for comparing the variability of different datasets on different scales (for example, heights in centimeters vs. weights in kilograms).

FAQ – Using this statistics calculator

Can I include missing values or text in the input?

The calculator attempts to parse every token as a number. Tokens that cannot be interpreted as valid numbers are ignored and reported in a warning. This way, placeholders like “NA” or “missing” do not contaminate your numerical results.

Why do I get “not defined” for variance or standard deviation?

For sample statistics, variance and standard deviation use a denominator of \(n-1\). If you select “sample” and only provide one valid value, \(n-1 = 0\) and the quantity is not defined. In that case, switch to population statistics if it makes sense contextually, or add more observations.

Does this tool perform hypothesis tests or regression?

No. This page focuses on univariate descriptive statistics. For hypothesis testing (t-tests, ANOVA, chi-square) or modelling (linear/logistic regression, Bayesian inference), use the dedicated calculators in the statistics & probability section, many of which are linked in the sidebar.

How many decimal places should I keep?

In applied work, you usually match the precision of the raw data: if measurements are recorded to one decimal place, reporting summary statistics to two or three decimals is typically appropriate. The rounding selector lets you adjust this without changing the internal precision of the computations.