- #1

olgerm

Gold Member

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- TL;DR Summary
- population std vs sample std

I know that standard deviation of whatever data is defined as sqaure root of square difference from mean value:

##\sigma(data)=\frac{\sum_{x \in data}((x-x_{mean\ of\ data})^2)}{|data|}=\frac{\sum_{x \in data}((x-\sum_{y \in data}(y)/|data|)^2)}{|data|}##

but sometimes formula ##\sigma_2(data)=\frac{\sum_{x \in data}((x-x_{mean\ of\ data})^2)}{|data|-1}=\frac{\sum_{x \in data}((x-\sum_{y \in data}(y)/|data|)^2)}{|data|-1}## is used.

Does the 2. formula:

##\sigma(data)=\frac{\sum_{x \in data}((x-x_{mean\ of\ data})^2)}{|data|}=\frac{\sum_{x \in data}((x-\sum_{y \in data}(y)/|data|)^2)}{|data|}##

but sometimes formula ##\sigma_2(data)=\frac{\sum_{x \in data}((x-x_{mean\ of\ data})^2)}{|data|-1}=\frac{\sum_{x \in data}((x-\sum_{y \in data}(y)/|data|)^2)}{|data|-1}## is used.

Does the 2. formula:

- estimate population standard deviation based on sample?
- estimate of standard deviation of means of all samples(with the same size) that can be taken from population?
- is ##\sigma_2/\sqrt{n}## estimation of standard deviation of means of all samples(with the same size) that can be taken from population?
- assume that population is much larger than sample?
- assume something more?

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