# 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 *technically* be better, but he could still be off by a wide margin. Thus, incrementing

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