Statistics Calculator

How to use this statistics calculator

Paste or type a data set of two or more numbers, separated by commas, spaces, or line breaks. As a descriptive statistics calculator, it returns the main summary values in one pass: the count, sum, mean, median, mode, largest and smallest values, range, geometric mean, and both the population and sample variance and standard deviation. It also lists the data in sorted order and plots it on a number line.

Mean, median, mode, and range

These four values describe the center and the extent of the data, which is why this page also works as a mean median mode range calculator.

• Mean = (x₁ + x₂ + … + xₙ) ÷ n, the sum divided by the count.
• Median = the middle value of the sorted data, or the average of the two middle values when the count is even.
• Mode = the value that appears most often. A data set can have more than one mode, and if every value appears once there is no mode.
• Range = largest value − smallest value.
• Geometric mean = the nth root of the product of the values. This calculator shows 0 if any value is 0 and "Not defined" when the product is negative.

For the data set 3, 7, 7, 12, 5, 9, 7, 14, the mean is 64 ÷ 8 = 8, the median is 7, the mode is 7 (it appears 3 times), and the range is 14 − 3 = 11.

Variance calculator: population vs. sample

Variance measures how far the values spread from the mean, and the standard deviation is its square root, in the same units as the data. Both are shown two ways:

• Population variance σ² = Σ(xᵢ − μ)² ÷ N, used when the data includes every member of the group.
• Sample variance s² = Σ(xᵢ − x̄)² ÷ (n − 1), used when the data is a sample of a larger group. Dividing by n − 1 corrects for the sample mean sitting closer to the sample values than the true mean does, so use this value when you need a sample variance calculator.

In the example above, the sum of squared deviations is 90, so the population variance is 90 ÷ 8 = 11.25 (σ ≈ 3.354) and the sample variance is 90 ÷ 7 ≈ 12.857 (s ≈ 3.586).

Frequently asked questions

What does a stats calculator calculate?

A stats calculator summarizes a list of numbers with descriptive statistics—measures of the center (mean, median, mode) and of the spread (range, variance, standard deviation). It does not run hypothesis tests or regressions.

Should I use the population or sample standard deviation?

Use the population value when your numbers cover the entire group you care about, such as every test score in one class. Use the sample value when the numbers are a sample drawn to estimate a larger group, which is the more common case in research.

How do I find the mode when two values tie?

When two or more values share the highest count, the data set is bimodal or multimodal, and every tied value is a mode. The calculator lists all of them.

Why is the geometric mean "Not defined"?

The geometric mean is normally used for positive values such as growth rates. This calculator takes the nth root of the product: if any value is 0 the result is 0, and if the product is negative (an odd count of negative values) it shows "Not defined" rather than a value. Remove negative values or use the arithmetic mean instead.