# Thread: standard deviation

1. ## standard deviation

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

2. 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.

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

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

Glad I can help.

5. 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

6. Originally Posted by JohnM
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
Well said John. My comments on sd would not hold in many cases. Thanks for pointing it out.

Welcome to the community.

7. Thanks.

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