Briefly |
Use N-1 if you're estimating the standard deviation of the population based on a sample. |
There are two formulas for standard deviation. The main one,
(in Fathom, popStdDev(x) )
is correct when you have all the data and you want the standard deviation to help describe the data.
The other one is almost the same:
(in Fathom, s(x) )
Because the denominator is smaller, this SD is slightly larger. It is correct when you have a sample and you're estimating the standard deviation of the population. You need this "larger" SD because, when you sample, your sample's standard deviation will be, on the average, slightly smaller than that of the parent population. (You can construct a simulation in Fathom to show that this is true, and how it depends on the sample size, N.)
Most statistics books use (lower-case Greek sigma) for the "original" standard deviation, and s for the "sample" standard deviation.