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and

✤

= s

n−1

✤ = s

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:

stddevp(x)

Func

©(list) population std dev of list

stddev(x)*√(1-1/dim(x))

EndFunc

Population variance:

variancp(x)

Func

©(list) population variance of list

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

EndFunc

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)

Func

stddev(x,f)*√(1-1/sum(f))

EndFunc

Population variance, with frequencies:

varianpf(x,f)

Func

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

EndFunc

6 - 76

Texas Instruments TI-92+ User Manual

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