Statistics Calculator

Paste a data set to get its descriptive statistics: mean, median, standard deviation, variance, quartiles and more.

How to use the Statistics Calculator

  1. Type or paste your data, separated by commas, spaces or new lines.
  2. Read the mean and standard deviation at the top.
  3. Use the grid below for variance, quartiles, range, standard error and the sorted data.

Formulas used

  • Mean: x̄ = Σx ÷ n
  • Sample variance: s² = Σ(x − x̄)² ÷ (n − 1)
  • Population variance: σ² = Σ(x − x̄)² ÷ n
  • Standard deviation: the square root of the variance
  • Standard error: s ÷ √n
  • Coefficient of variation: s ÷ |x̄| × 100%

Sample or population?

Use the sample figures when your data is a subset of a larger group and you want to estimate that group’s spread; this is the usual case. Use the population figures when your data includes every member of the group.

Quartiles

Q1, the median and Q3 split the sorted data into four equal parts. This calculator uses linear interpolation between data points, the same method as the QUARTILE.INC function in Excel and Google Sheets. The interquartile range (IQR = Q3 − Q1) measures the spread of the middle half of the data.

Frequently asked questions

What is standard deviation?

A measure of how spread out the values are around the mean. A small standard deviation means the values are close to the mean.

When do I divide by n − 1 instead of n?

Divide by n − 1 for a sample taken from a larger population. Divide by n only when the data covers the whole population.

How are the quartiles calculated?

By linear interpolation on the sorted data, matching QUARTILE.INC in Excel. Other methods can give slightly different values for small data sets.

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