I know that sx is the standard deviation of a sample and σx is the standard deviation of a population. My question is, does the TI-Nspire think that the data I entered is a sample or the population? If it think’s (A) my data is a sample, how is σx calculated? If it thinks (B) my data is the population, how is it taking a “sample”?
I think (A) makes sense and the calculator is somehow estimating a population standard deviation (σx) through some normal distribution approximation.
Possibly ... https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
However, I can’t find any reference to confirm this and I want to be sure.
Note: Actually using the TI-Nspire CX CAS.
After cross-checking in Excel and reading Bessel’s correction and Unbiased estimation of standard deviation on Wikipedia …
σx gives the “regular” standard deviation and sx applies Bessel’s correction. In other words, σx is the exact standard deviation of the data given (with n in the denominator), and sx is an unbiased estimation of the standard deviation of a larger population assuming that the data given is only a sample of that population (i.e. with n-1 in the denominator).