Standard Error Formula

I searched the standard error formula in Excel Help and found this:

I tried the formula using this data set:

1

2

3

4

5

and the result is 1.65831. This is wrong, because the standard error should be 0.70711.

I know that the standard error is equal to the sample standard deviation over the square root of the size of the sample. If I use this formula, the result is 0.70711.

There are different statistics called "standard error".

0.70711 is the standard error of the mean of the data {1,2,3,4,5}.

As you say, it is defined as =STDEV(data)/SQRT(n) or, equivalently, =STDEVP(data)/SQRT(n-1).

There is also the standard error of the regression.  See the reference cited in

The function STEYX is the "standard error of the predicted y-value for each x in the regression".

You stumbled onto the mathematical formula used to calculate "standard error" error bars in Excel charts.

I find that help page by searching "online" help in Excel 2010.  I don't know if you are quoting it out of context, or if Excel 2013 continues the "tradition" of broken help information, started in Excel 2010. :-(

Note that the formula for the standard error of the mean can be written as:

=SQRT( SUMPRODUCT((data-AVERAGE(data))^2) / ( (n-1)*n ) )

And for a single series, the formula for "standard error" error bars can written as:

=SQRT( SUMPRODUCT((data-0)^2) / ( (n-1)*n ) )