How is the SEM calculated?

The SEM is calculated by dividing the SD by the square root of N. This relationship is worth remembering, as it can help you interpret published data.

If the SEM is presented, but you want to know the SD, multiply the SEM by the square root of N.

Calculating the SEM with Excel

Excel does not have a function to compute the standard error of a mean. It is easy enough to compute the SEM from the SD, using this formula.

=STDEV()/SQRT(COUNT())

For example, if you want to compute the SEM of values in cells B1 through B10, use this formula:

=STDEV(B1:B10)/SQRT(COUNT(B1:B10))

The COUNT() function counts the number of numbers in the range. If you are not worried about missing values, you can just enter N directly. In that case, the formula becomes:

=STDEV(B1:B10)/SQRT(10)