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Math Help - Need help with a question:

  1. #1
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    Need help with a question:

    Q) Suppose a sample consisting of n=12 different data values has a mean of 5. One of the data values is -4 and another is 4.

    a) A student calculates the sample variance of this sample and claims that S(squared) = 7.2. Explain why this value is incorrect.

    b) If the two value -4 and 4 are removed what is the mean of the remaining data values?


    Would much appreciate any help, not so much just the answers, but also how i get to them and the formulas used.

    Thanks.
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  2. #2
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    Not to sure how to answer the first one as we don't know much about the data. I'm guessing it has something to do with 4 and -4 being samples.

    For the second consider

     \frac{x_1+x_2+\dots+x_{12}}{12}=5

    so

     x_1+x_2+\dots+x_{12}=60

    now removing 2 data points -4 and 4 will not change the sum of all data points therefore you get

     x_1+x_2+\dots+x_{10}=60

    and dividing by 10

     \frac{x_1+x_2+\dots+x_{10}}{10}=6

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  3. #3
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    Thanks thats very helpful

    Yes still dont quite understand the first myself.
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  4. #4
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    Quote Originally Posted by Dogfighters View Post
    Q) Suppose a sample consisting of n=12 different data values has a mean of 5. One of the data values is -4 and another is 4.

    a) A student calculates the sample variance of this sample and claims that S(squared) = 7.2. Explain why this value is incorrect.

    b) If the two value -4 and 4 are removed what is the mean of the remaining data values?


    Would much appreciate any help, not so much just the answers, but also how i get to them and the formulas used.

    Thanks.
    a) By definition,
    S^2 = \frac{\sum_{i=1}^{12} (X_i - \bar{X})^2}{11}
    so
    S^2 \geq \frac{((-4) -5)^2 + (4 - 5)^2}{11} \approx 7.45
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