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    Hello, I'm not too sure how to use to formula



    in order to work out the standard variance of a sample.

    Say my sample goes:

    1-10 cm 8 people
    11-20 cm 12 people
    21-30 cm 7 people

    and the mean is 15.3.

    Thank you
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    bump?
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    Would it be just

    (8 - 15.3)^2 + (12-15.3)^2 + (7-15.3)^3
    ________________________________ __

    (8+12+7)


    = 32.13?
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    Your data is given as a frequency distribution.
    Do you have a version of this formula for frequency distributions? Involves f...
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    (Original post by vc94)
    Your data is given as a frequency distribution.
    Do you have a version of this formula for frequency distributions? Involves f...
    I think this is it:
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    This formula is equivalent:

    sample variance = (n/(n-1))*( (sum of f*(y^2))/n - (mean)^2 )

    Where y is the midpoint of each group and f is the group's frequency.
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    (Original post by vc94)
    This formula is equivalent:

    sample variance = (n/(n-1))*( (sum of f*(y^2))/n - (mean)^2 )

    Where y is the midpoint of each group and f is the group's frequency.
    Could you please use the numbers in the example to show how it'd work? I'd really appreciate it. Thanks.
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    Isn't this the unbiased estimate of the variance from a sample?
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    (Original post by hollywoodbudgie)
    Hello, I'm not too sure how to use to formula



    in order to work out the standard variance of a sample.

    Say my sample goes:

    1-10 cm 8 people
    11-20 cm 12 people
    21-30 cm 7 people

    and the mean is 15.3.

    Thank you
    if this was a table, the measurements would be column x, you would have to work out the mid-class values for column x before you can work with them. I would make a few more columns, the frequency can be f, you would have an xf column and an x^2 x f column, and the totals at the bottom, then I would use Vc94's formula because its easier to use
    just plug in values, should be easy.
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    \frac{n}{n-1}(\Sigma \frac{fy^2}{n}-\mu^2)

    The midpoints of the groups are 5.5, 15.5 and 25.5

    So calculate:

    \frac{27}{26}(\frac{8\times 5.5^2 +12\times 15.5^2 +7\times 25.5^2}{27}-15.1^2)

    I make your mean 15.129 ?
 
 
 
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