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All articles standard error Calculate standard error of mean (SEM) in Excel

Calculate standard error of mean (SEM) in Excel

The Standard Error of Mean, also known as SEM is another measure of variability of data.  It is an estimate of the deviation of a sample mean from the population mean.  SEM is not as popular as standard deviation, and it is sometimes just referred to as “standard error”.  

Its formula is the quotient of standard deviation and the square root of sample size.  

Formula for SEM

Figure 1. Standard error of mean formula

There is no built-in function that directly computes for the standard error of mean.  We can calculate the standard error of mean by using the functions STDEV.S, SQRT and COUNT.  

Standard error of mean formula:

= STDEV.S(sample)/SQRT(COUNT(sample))

Parameters:

  • STDEV.S function returns the standard deviation of a sample
  • SQRT function returns the square root of a number
  • COUNT function returns the number of data points in a sample

How to find standard error

By using the above formula, we can calculate the standard error of mean through these steps:

  • Prepare data in worksheet

Figure 2.  Sample data for standard error of mean

  • Select cell E3 and enter the formula for SEM:

=STDEV.S(C3:C12)/SQRT(COUNT(C3:C12))

Figure 3.  Final result:  Standard error of mean

As a result, the standard error of mean is 1.693, as calculated in cell E3.  

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