Texas Instruments TI-89 Tip List page 234

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✤ 2 = s 2 n−1

The last line shows the identities we want, in which the desired population variance and standard

deviation are functions of the sample variance and standard deviation.

If desired, these definitions can be coded as simple functions:

Population standard deviation:

stddev(x)*√(1-1/dim(x))

Population variance:

variance(x)*(1-1/dim(x))

The built-in stddev() and variance() functions can both accept an optional second argument which is a

list of the frequencies of the first list elements. This feature is easily added with these two functions:

Population standard deviation, with frequencies:

stddevpf(x,f)

stddev(x,f)*√(1-1/sum(f))

Population variance, with frequencies:

varianpf(x,f)

variance(x,f)*(1-1/sum(f))

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