Do we calculate the Standard Deviation of a population the same no matter how small (say less than 30) population size gets? Does distribution type play any roles in this?
Thank you in advance
Solved – Standard Deviation of small population (less than 30)
distributionspopulationstandard deviation
Best Answer
While it's true that the standard deviation of the sample is defined the same way regardless of the distribution type, the convergence of the sample s.d. to the true process s.d. can be slower or faster depending on the distribution type. In most real world settings, you'd also be concerned with robustness, i.e. preventing a single or few corrupted points (e.g. probe malfunction) to skew the s.d. estimation. if you are expecting a certain distribution type, you can try to fit the empirical cdf to that distribution's cdf, and kolmogorv- smirnoff test may be used to hypothesis-test a specific distribution.