Statistics Calculator

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

Examples

Test scores

Statistics for 85, 90, 78, 92, 88

Numbers (comma-separated): 85, 90, 78, 92, 88

Mean (Average)

86.6

Median

Standard Deviation

4.882622

Mode

No mode

Range

Variance

23.84

Count

Sum

433

Minimum

Maximum

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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}

Variables, symbols and units

$x_i$: 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

Calculation method explained

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).

Examples

Test scores85, 90, 78, 92, 88 → 86.6

Statistics for 85, 90, 78, 92, 88

Numbers (comma-separated): 85, 90, 78, 92, 88

Mean (Average): 86.6

With repeated values3, 7, 3, 9, 3, 5 → 5

Find the mode of 3, 7, 3, 9, 3, 5

Numbers (comma-separated): 3, 7, 3, 9, 3, 5

Mean (Average): 5

Simple data set1, 2, 3, 4, 5, 6, 7, 8, 9, 10 → 5.5

Statistics for 1 through 10

Numbers (comma-separated): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Mean (Average): 5.5

Frequently Asked Questions

What is the mean?

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

What is the median?

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.

What is the mode?

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.

Statistics Calculator

Test scores

How It Works

Examples

Frequently Asked Questions

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