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    Frequency Distribution and Data Samples

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    I have several questions relate to frequency distribution that I need support. Please see my questions below and please post with examples if you can so I have more understanding.

    1. Does it necessarily true that any frequency distribution contains any form of data sample? Please illustrate your answer with examples.

    2. Can we make any comment regarding the distributional (i.e., skewness, Kurtosis, etc.) shape of the data points from a frequency table?

    3. Suppose, you are given a frequency distribution table (not the raw data set), how will you calculate Mean, Median and Mode of the distribution of the data set from the frequency table?

    4. What are the possible applications of normal distribution in Business research?

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    Solution Preview

    Skewness = E[(x-u)^3]/s^3
    = E[(x-u)(x^2-2ux+u^2)]/s^3
    = E[x^3-2ux^2+xu^2-ux^2+2xu^2-u^3]/s^3
    = E[x^3-2ux^2+xu^2-ux^2+2xu^2-u^3]/s^3
    = [E(x^3)-2uE(x^2)+u^3-uE(x^2)+2u^3-u^3]s^3

    Here is what has been done above.
    Take the definition of skewness and multiply out.
    Use the fact that E(aX+bY+c) = aE(x)+bE(Y)+c (where X and Y are variables and c,a,b are constants) to simplify the expression into something we can work with.

    Notation used above includes:
    u = mean
    s = standard deviation.
    E(Y) = the expected value of Y
    Note: E(X) = u in the above since u is the mean of x.
    Note 2: To find E(x^n) do: E(x^n) = SUM[(midpoint of class i)*(frequency of class i)/(number of total observations)] where i ...

    Solution Summary

    The solution discusses questions regarding frequency distribution and data samples.