What happens to the sample standard deviation when the sample size is increased?
1 Answer
It depends on the actual data added to the sample, but generally, the sample S.D. will approach the actual population S.D.
Explanation:
The formula for sample standard deviation is
#s=sqrt((sum_(i=1)^n (x_i-bar x)^2)/(n-1))#
while the formula for the population standard deviation is
#sigma=sqrt((sum_(i=1)^N(x_i-mu)^2)/(N-1))#
where
#n# is the sample size,#N# is the population size,#bar x# is the sample mean, and#mu# is the population mean.
As
Thus, as
Note:
When
It is only over time, as the archer keeps stepping forward—and as we continue adding data points to our sample—that our aim gets better, and the accuracy of