This standard deviation calculator can help you calculate the population & sample standard deviations, standard variance, sum and the mean of a data set. Below the form you can find the equations used.

Instruction: Please input the numbers separated by semicolon (;)!

Understanding the concept of standard deviation

In statistics, standard deviation refers to an indicator that shows by how much the individual members of a data set/group vary from the mean value for the data set. It can be calculated both for a population case in which it is referred to as population standard deviation and for a sample case in which is called sample standard deviation. Its formula takes account of the:

■ Data set members (xi);

■ Mean of the data being analyzed x̄ in case of sample; respectively the expected mean of the population data set denoted with μ;

■ Total number of members in the group which is the count of values in the data set (N).

Standard deviation is denoted by “s” in case of a sample, respectively “σ” in case of a population. In statistics this measure is related to the concept of variance symbolized with “s2“/“σ2” since it is the square root of its variance.

Variance and standard deviation of a sample

Sample standard deviation formula

Sample Standard Deviation Formula Explained

Sample variance formula

Sample Variance Formula Explained

s = sample standard deviation
s2 = sample variance
x1, ..., xi = individual members of the sample data set
x̄ = data set mean value
N = size of the sample data set

Variance and standard deviation of a population

Population standard deviation formula

Population Standard Deviation Formula Explained

Population variance formula

Population Variance Formula Explained

σ = population standard deviation
σ2 = population variance
x1, ..., xi = members of the data set
μ = expected mean of the population data set
N = size of the population

Interpretation of the levels of the standard deviation

In regard of the interpretation of the standard deviation levels, typically a low standard deviation indicates that the members/values within the group/data set tend to be close to the mean, while a high standard deviation is an evidence of the contrary (values tend to differ significantly in comparison to the average).

15 Apr, 2015