Statistics Calculator

Compute count, sum, mean, median, mode, range, variance, and standard deviation from a list of numbers.

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Statistics

Mean: 30

5 values ranging from 10 to 50 with a mean of 30.00 and mode of none.

Count
5
Sum
150
Mean
30
Median
30
Mode
None
Range
40
Min
10
Max
50
Std Dev (Population)
14.14
Sample Std Dev
15.81

Population vs sample standard deviation

Population standard deviation divides by N and is used when your data represents the entire population. Sample standard deviation divides by N−1 (Bessel's correction) and is used when your data is a sample from a larger population.

Also in Statistics

Descriptive Statistics

Statistics calculator: compute mean, median, mode, standard deviation, and more

A statistics calculator takes a set of numbers and computes all the key descriptive statistics in one step: count, sum, mean, median, mode, range, minimum, maximum, population standard deviation, and sample standard deviation. Enter numbers separated by commas, spaces, or newlines.

Key measures of central tendency and spread

The mean (average) is the sum of all values divided by the count. The median is the middle value when data is sorted — for an even count, it is the average of the two middle values. The mode is the most frequently occurring value; a data set can have no mode, one mode, or multiple modes.

Standard deviation measures how spread out values are from the mean. Population standard deviation (σ) divides by N and is appropriate when your data includes every member of the population. Sample standard deviation (s) divides by N−1, applying Bessel's correction to provide an unbiased estimate when working with a sample from a larger population.

Mean = Σx / n

Sum of all values divided by count.

σ = √(Σ(x−μ)² / N)

Population standard deviation.

s = √(Σ(x−x̄)² / (N−1))

Sample standard deviation with Bessel's correction.

Frequently asked questions

When should I use population vs. sample standard deviation?

Use population standard deviation when your data set includes every member of the group you are studying. Use sample standard deviation when your data is a subset drawn from a larger population and you want to estimate that population's variability.

What does it mean when there is no mode?

If every value appears the same number of times (all unique, or all equally frequent), there is no single most-common value, so the data set has no mode.

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