# standard deviation

#### marginovera

##### New Member
If you have a random sample of 100 in a population and it has some SD and then you do another sample, this time of 300, what happens to the SD, and why? thanks

#### quark

Hi marginovera,

The sd decreases as sample size increases. sd estimates the spread of individual values about the population mean. The more data we have, the more accurately we can estimate the population mean, ie the spread is smaller.

#### marginovera

##### New Member
Thanks quark. Will the sd decrease be proportional to the sample size increase, or is that impossible to know?

#### quark

It is related to the square root of n but not proportional. You can check the formula for sd.

#### JohnM

##### TS Contributor
As the sample size (n) increases, the standard deviation will tend to get closer to the true population standard deviation.

- it will not necessarily get larger or smaller, regardless of the sample size - it will "bounce" around a bit

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