Statistics Calculator

Mean, median, mode, range, variance, standard deviation, quartiles, percentiles, IQR and outliers for a data set — sample or population.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Statistics Calculator

Summarises a list of numbers: count, sum, mean, median, mode, minimum, maximum, range, quartiles, interquartile range, variance, standard deviation, standard error, and any outliers by the 1.5 × IQR rule.

Sample and population statistics differ: the sample variance divides by n − 1 (Bessel’s correction), the population variance by n. Choose which one your data represents; both standard deviations are always listed so you can compare.

Limitations

Quartiles and percentiles use linear interpolation between closest ranks (the method called R-7, used by Excel’s PERCENTILE.INC and NumPy). Other textbooks use slightly different conventions and can give slightly different quartiles for small data sets.

How to use it

Paste or type your data.
Choose whether it is a sample or a whole population.
Optionally enter a percentile to look up, then press Calculate.

Example

2, 4, 6, 8

→ Mean 5, median 5, sample SD 2.582

Formulas used

\bar{x} = \frac{1}{n}\sum x_i

Arithmetic mean.

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

Sample and population variance.

\text{IQR} = Q_3 - Q_1

Interquartile range: the spread of the middle half of the data.

Questions and answers

Should I use the sample or the population standard deviation?

Use population if your data includes every member of the group you care about. Use sample if the data is a subset used to estimate a larger group — this is the usual case.

Data VisualizerTurn a data set into a histogram, box plot, bar chart, line chart or scatter plot, with a fitted normal curve and shape analysis.Frequency Table GeneratorBuild a frequency table with relative and cumulative frequencies, or group data into class intervals; export to CSV.Z-Score CalculatorStandard score of a value, the percentile it corresponds to under a normal distribution, and the tail probabilities.Correlation CalculatorPearson and Spearman correlation coefficients for paired data, with r² and a plain-language strength description.

About the Statistics Calculator

Limitations

How to use it

Formulas used

Questions and answers

Related tools

About the Statistics Calculator

Limitations

How to use it

Formulas used

Questions and answers