The mean (arithmetic average) is the sum of all values divided by the count. It measures the central tendency of a data set.

The median is the middle value when data is sorted. For even counts, it is the average of the two middle values. It is less affected by outliers than the mean.

The mode is the value that appears most frequently. A data set can have no mode (all values unique), one mode, or multiple modes.

What is standard deviation?

Standard deviation measures how spread out values are from the mean. A low value means data points cluster near the mean; a high value means they are spread widely.

Is this population or sample variance?

This calculator uses population variance (divides by N). For sample variance, divide by N-1 instead. The difference matters mainly for small samples.

MATMathematics

Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, range, and more from a list of numbers. Enter comma-separated values.

Numbers (comma-separated)

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How It Works

Formula

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

\sigma^2 = \frac{1}{n}\sum_{i=1}^{n} (x_i - \bar{x})^2

\sigma = \sqrt{\sigma^2}

\text{Range} = x_{\max} - x_{\min}

Where

$x_i$: The i-th value in the data set
$n$: Number of values (the count)
$\bar{x}$: Mean (arithmetic average) of the data set
$\sigma^2$: Population variance
$\sigma$: Population standard deviation
$x_{\min},\; x_{\max}$: Smallest and largest values in the data set

Enter numbers separated by commas. The calculator sorts them and computes: mean (sum/count), median (middle value), mode (most frequent), variance (average squared deviation from mean), standard deviation (square root of variance), range (max - min).

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