The Standard Deviation Calculator an online tool which shows Standard Deviation for the given input. Byju's Standard Deviation Calculator is a tool

which makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number.

Standard Deviation Calculator is used to calculate the variance, mean, and standard deviation of a set of numbers. This is an online tool that shows the standard deviation for the given input. The Standard Deviation Calculator from Byju’s makes it easy to calculate the mean, variance, and standard deviation of the given numbers. The value used to calculate the confidence range is the sample standard deviation value.

What Is Standard Deviation?

Standard deviation is the square root of the given variance. It is a tool to measures the dispersion, that can be found by how much the values in the given set of data are likely to differ from the mean.

Standard Deviation Definition

Standard Deviation is a measure of dispersion in statistics. It gives an inkling of how the individual data in a data set is detached from the mean. Standard deviation is described as the square root of the mean of the squares of the deviations of all the values of a series derived from the arithmetic mean. It is also known as the root mean square deviation. The symbol used for standard deviation is σ.

Standard Deviation Formula

Variance and standard deviation both are depended on the mean of a given set of numbers. Calculating these set of numbers depends on whether the given set is a sample standard deviation or the population standard deviation.

Variance and Standard Deviation of a Population Formula:

The population standard deviation is used to measure the variability of data in the population. The Variance is denoted as σ2 and Standard Deviation as σ and the formula of population are given by:

\(\large \sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}\left ( x_{i}-\mu \right )^{2}}\)

\(\large \sigma^{2} = \frac{1}{N}\sum_{i=1}^{N}\left ( x_{i}-\mu \right )^{2}\)

Where:

σ = population standard deviation

σ2 = population variance

x1, …, xN = the population data set

μ = mean of the population data set

N = size of the population data set

Variance and Standard Deviation of a Sample:

The sample standard deviation is an estimate of a population standard deviation which is based on a given sample. The variance is denoted as s2 and standard deviation as s and the formula for sample standard deviation are given by:

\(\large s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left ( x_{i}-\overline{x} \right )^{2}}\)

\(\large s^{2}=\frac{1}{N-1}\sum_{i=1}^{N}\left ( x_{i}-\overline{x} \right )^{2}\)

Where:

s = sample standard deviation

s2 = sample variance

x1, …, xN = the sample data set

x̄ = mean value of the sample data set

N = size of the sample data set