1. ## Population Variance.

Ok, so I messed up displaying the questions in a previous thread now. Here is the question straight from my worksheet.

For the data set s={x_1,x_2,...,x_n}

Show /sigma x^2= (\sum \frac{x_i^2}{N})-\mu x^2

Where /mu x= /frac{\sum x_i}{N}

All sums between i=1

2. ## Re: Population Variance.

Sorry, I have no clue as to how to make the website display the actual formula visually.

3. ## Re: Population Variance.

Originally Posted by Joyeux
Ok, so I messed up displaying the questions in a previous thread now. Here is the question straight from my worksheet.

For the data set $s={x_1,x_2,...,x_n}$

Show $\sigma_x^2= (\sum \frac{x_i^2}{N})-\mu_x^2$

Where $\mu_x= \frac{\sum x_i}{N}$

All sums between i=1
Hi Joyeux!

I took the liberty to make your formulas work.
If you click Reply with quote, you'll be able to see what I did.

I suspect you are supposed to start with the definition of variance.

$\sigma_x^2= \frac{\sum (x_i - \mu_x)^2}{N}$

Can you simplify this?

4. ## Re: Population Variance.

I don't think that is what the question is asking, the question right after that one in the sheet asks for that. This one is just to substitute the /mu x into the first equation and simply to get the equation displayed.

6. ## Re: Population Variance.

From the definition of variance which Serena gave

$\sigma_x^2= \frac{\sum (x_i - \mu_x)^2}{N}$

Expand the squared values
$\sigma_x^2= \sum \frac{x_i^2- 2x_i\mu_x+\mu_x^2}{N}$

$\sigma_x^2= \sum \frac{x_i^2}{N}- \sum \frac{2x_i\mu_x}{N}+\sum \frac{\mu_x^2}{N}$

Use what you are given to simplify this.

Note: Since $\mu_x$ does not change with i

$\sum \mu_x= N\mu_x$

7. ## Re: Population Variance.

How do I get from

This: /sigma x^2= (\sum \frac{x_i^2}{N})-(\frac {\sum x_i}{N})^2

To this: /sigma x^2= (\sum \frac{x_i^2}{N})-\mu x^2