Calculate Standard Deviation from Standard Error

This worksheet help users to understand the relationship between the standard deviation and standard error. The step by step calculation for for calculating standard deviation from standard error illustrates how the values are being exchanged and used in the formula to find the standard deviation.

Standard Deviation
In the theory of statistics and probability for data analysis, standard deviation is a widely used method to measure the variability or dispersion value or to estimate the degree of dispersion of the individual data of sample population.

Standard Error
In the theory of statistics and probability for data analysis, Standard Error is the term used in statistics to estimate the sample mean dispersion from the population mean.

The relationship between standard deviation and standard error can be understood by the below formula
formula to estimate standard error (SE) of mean (SEM)

From the above formula
Standard deviation (s) = Standard Error * √n
Variance = s2

The below solved example problem illustrates how to calculate standard deviation from standard error.

Solved Example Problem

For the set of 9 inputs, the standard error is 20.31 then what is the value standard deviation?
Standard deviation (s) = Standard Error * √n
= 20.31 x √9
= 20.31 x 3
s = 60.93

variance = σ2
= 60.932
= 3712.46

For more information for dispersion value estimation, go to how to estimate sample & population standard deviation.