Which is greater: the sample standard deviation or the population standard deviation? Explain.

waldo7852p

waldo7852p

Answered question

2022-09-25

Which is greater: the sample standard deviation or the population standard deviation? Explain.

Answer & Explanation

Jacey Humphrey

Jacey Humphrey

Beginner2022-09-26Added 7 answers

If a data set { x 1 , x 2 , , x n } is a sample, the formula for standard deviation is
i = 1 n ( x i x ¯ ) 2 n 1
(Note that we are dividing with n-1.)
If the data set { x 1 , x 2 , , x n } is a population, the expression in the formula for standard deviation is
i = 1 n ( x i μ ) 2 n
(Note that we are dividing with n, a higher number than in the sample.)
Dividing a quantity with a higher positive number, the result is smaller.
Sample standard deviation is the greater of the two.

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