What happens to the sample standard deviation when the sample size is increased?

Chloe Arnold

Chloe Arnold

Answered question

2022-10-13

What happens to the sample standard deviation when the sample size is increased?

Answer & Explanation

Cavalascamq

Cavalascamq

Beginner2022-10-14Added 21 answers

The formula for sample standard deviation is
s = i = 1 n ( x i x ¯ ) 2 n 1
while the formula for the population standard deviation is
σ = i = 1 N ( x i μ ) 2 N 1
where
n is the sample size,
N is the population size,
x ¯ is the sample mean, and
μ is the population mean.
As n increases towards N, the sample mean x ¯ will approach the population mean μ , and so the formula for s gets closer to the formula for σ
Thus, as n N , s σ

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