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Math Help - Population Variance.

  1. #1
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    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
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  2. #2
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    Re: Population Variance.

    Sorry, I have no clue as to how to make the website display the actual formula visually.
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  3. #3
    Super Member ILikeSerena's Avatar
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    Re: Population Variance.

    Quote Originally Posted by Joyeux View Post
    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?
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  4. #4
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    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.
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  5. #5
    Super Member ILikeSerena's Avatar
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    Re: Population Variance.

    What is your question then?
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  6. #6
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    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
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  7. #7
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    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
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  8. #8
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    Re: Population Variance.

    Bumping for answer.
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  9. #9
    Super Member ILikeSerena's Avatar
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    Re: Population Variance.

    I find it hard to read your post.
    The latex is messed up.

    Did you try to use the hints Shakarri provided?
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