How do I enter my numbers?

Type or paste them into the box, separated by commas, spaces, or new lines. You can mix separators; the calculator reads every number it finds.

What is the difference between the mean and the median?

The mean is the arithmetic average of every value. The median is the middle value when the list is sorted. The median is less affected by extreme values, so it often describes skewed data better.

What does it mean when there is no mode?

There is no mode when every value appears the same number of times, for example 1, 2, 3, 4. If two or more values tie for the most frequent, all of them are shown.

Should I use the population or sample standard deviation?

Use the population version when your list is the whole group. Use the sample version when your list is a sample from a larger group; it divides by n − 1 and needs at least two values.

Why are the two standard deviations different?

The sample standard deviation divides by n − 1 instead of n, which makes it slightly larger. This corrects for the tendency of a sample to underestimate the spread of the full group.

Can I share my results?

Yes. Use Share to copy a link that reopens the calculator with the same list of numbers.

Statistics calculator

Type or paste your numbers, separated by commas, spaces, or new lines. The calculator works out the full set of descriptive statistics as you type.

Enter a list of numbers to get the mean, median, mode, range, variance, and both the population and sample standard deviation.

Mean

6.4286

Median

Statistic	Value
Count	7
Sum	45
Mode	7
Minimum	3
Maximum	10
Range	7
Variance (population)	5.6735
Std dev (population)	2.3819
Std dev (sample)	2.5728

The mean and median are shown first as the headline averages. The table below breaks down every other statistic, including both standard deviations.

How does it work?

Use the population standard deviation when the list is the whole group, and the sample version when it is a sample drawn from a larger group.

Descriptive statistics formulas

\begin{aligned} &\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i\\[4pt] &\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2,\quad \sigma = \sqrt{\sigma^2}\\[4pt] &s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2} \end{aligned}

x_i: Each value in the data set.
n: The count of values.
\bar{x}: The mean (average).
\sigma: The population standard deviation (divides by n).
s: The sample standard deviation (divides by n − 1).

For 1, 2, 2, 3, 4 the mean is 2.4, the median is 2, and the mode is 2.

Method & sources

Every entry is treated as an independent numeric data point; order does not affect the result. The mode is the most frequent value; when every value is equally frequent there is no mode, and several values can tie. Variance and the population standard deviation divide by n; the sample standard deviation divides by n − 1 and needs at least two values.

Sources

Where this method comes from — use these references to understand the formula, assumptions, and limits.

NIST/SEMATECH e-Handbook of Statistical Methods — National Institute of Standards and Technology, verified 2026-06-10

How we calculate

Every entry is treated as an independent numeric data point; order does not affect the result.
The mode is the most frequent value; when every value is equally frequent there is no mode, and several values can tie.
Variance and the population standard deviation divide by n; the sample standard deviation divides by n − 1 and needs at least two values.

Rounding

Results are rounded to four decimals for display. The calculation itself uses full precision.

What this calculator does

Descriptive statistics summarise a list of numbers with a handful of figures. This calculator reads your list and reports the count, sum, mean, median, mode, minimum, maximum, range, variance, and standard deviation, so you can describe a data set at a glance.

How to use it

Type or paste your numbers into the box.
Separate them with commas, spaces, or new lines.
Read the mean and median at the top and the full breakdown in the table.

Mean, median, and mode

The mean is the sum of every value divided by how many there are. The median is the middle value once the list is sorted, or the average of the two middle values when the count is even. The mode is the value that appears most often. A list can have one mode, several modes, or no mode at all when every value is equally common.

Mean: sensitive to outliers, because every value pulls on the average.
Median: resistant to outliers, which makes it useful for skewed data such as incomes.
Mode: the only average that works for non-numeric categories, though here all inputs are numbers.

Range, variance, and standard deviation

The range is the largest value minus the smallest. Variance and standard deviation measure how spread out the values are around the mean. The standard deviation is the square root of the variance and is expressed in the same units as the data, which makes it easier to interpret.

Population vs sample standard deviation

If your list is the entire group you care about, use the population standard deviation, which divides by n. If your list is a sample drawn from a larger group, use the sample standard deviation, which divides by n − 1 to correct for the smaller spread you tend to see in a sample. The sample version needs at least two numbers.

A worked example

Take 1, 2, 2, 3, 4. The count is 5, the sum is 12, the mean is 2.4, the median is 2, the mode is 2, the range is 3, the population standard deviation is about 1.02, and the sample standard deviation is about 1.14.

FAQ

How do I enter my numbers?: Type or paste them into the box, separated by commas, spaces, or new lines. You can mix separators; the calculator reads every number it finds.
What is the difference between the mean and the median?: The mean is the arithmetic average of every value. The median is the middle value when the list is sorted. The median is less affected by extreme values, so it often describes skewed data better.
What does it mean when there is no mode?: There is no mode when every value appears the same number of times, for example 1, 2, 3, 4. If two or more values tie for the most frequent, all of them are shown.
Should I use the population or sample standard deviation?: Use the population version when your list is the whole group. Use the sample version when your list is a sample from a larger group; it divides by n − 1 and needs at least two values.
Why are the two standard deviations different?: The sample standard deviation divides by n − 1 instead of n, which makes it slightly larger. This corrects for the tendency of a sample to underestimate the spread of the full group.
Can I share my results?: Yes. Use Share to copy a link that reopens the calculator with the same list of numbers.

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