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Math Help - Sum of squares for variance Help!

  1. #1
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    Sum of squares for variance Help!

    Heres the question:

    The Royal Automobile Association defines peak-time as 6 am to 6 pm, Monday to Friday. It records the number of vehicle breakdowns reported per hour. The figures for a random sample of 40 peak-time hours in a certain area are as follows.




    i. Find the mean and variance of the data.
    I worked out the mean to be 0.5, which is right, but im stuck on the variance part.

    I know the formula for variance to be s^2=\frac{S_{xx}}{n-1}

    So i need to find S_{xx}, which is S_{xx}=\sum{x^2}-n\overline{x}^2

    Im a bit stuck on the S_{xx} part due to one of the x values being '4 or more'. Normally i wouldn't have a problem with these sorts of questions, but they usually just have single values for x.

    How would i use '4 or more' in the formula. Should i just do 0^2+1^2+2^2+3^2+4^2... etc, or is there something else i need to do?

    Any hints?

    Thanks in advanced.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by nugiboy View Post
    Heres the question:



    I worked out the mean to be 0.5, which is right, but im stuck on the variance part.

    I know the formula for variance to be s^2=\frac{S_{xx}}{n-1}

    So i need to find S_{xx}, which is S_{xx}=\sum{x^2}-n\overline{x}^2

    Im a bit stuck on the S_{xx} part due to one of the x values being '4 or more'. Normally i wouldn't have a problem with these sorts of questions, but they usually just have single values for x.

    How would i use '4 or more' in the formula. Should i just do 0^2+1^2+2^2+3^2+4^2... etc, or is there something else i need to do?

    Any hints?

    Thanks in advanced.
    You can ignore the 4 or more because its frequency count is 0.



    and you should have:

    <br />
S_{xx}=\left(\sum{f_i x_i^2}\right)-n\overline{x}^2<br />

    and for that matter:

    <br />
\bar{x}=\frac{1}{n}\sum{f_i x_i}<br />

    CB
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  3. #3
    Junior Member
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    Quote Originally Posted by CaptainBlack View Post
    You can ignore the 4 or more because its frequency count is 0.



    and you should have:

    <br />
S_{xx}=\left(\sum{f_i x_i^2}\right)-n\overline{x}^2<br />

    and for that matter:

    <br />
\bar{x}=\frac{1}{n}\sum{f_i x_i}<br />

    CB
    ok il try the other formula it looks a it easier.
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