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Math Help - Variance, and Standard Deviation

  1. #1
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    Variance, and Standard Deviation

    I have the following problem I'm working on and although I understand the formula's for mean, variance, and standard deviation I don't know which numbers need to be plugged into the formulas.

    Here's the Probability Model

    # of transactions 0 1 2 3 4 5
    Number of Clients56 122 180 140 132 90

    I came up with the following porportions
    .08 .17 .25 .19 .18 .13

    Now for the mean, variance, and standard deviation...The questions states "calculate the mean, variance, and standard deviation for the number of transaction per client for this firm"
    -Does this mean I should use # of transactions and porportions for my formula or should I use number of clients and proportions? I also need to know the units of measure for the variance and standard deviation.
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  2. #2
    MHF Contributor
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    Why did you round to two decimal places? Losing accuracy should be deliberate. I do hope you did that on purpose.

    You simply MUST get these basic ideas in your head. Calculating the first two moments of a distribution should be concepts and practices that you keep in your back pocket. Take them out and put them on your nightstand while sleeping. Make them your friends.

    There are three pieces:


    a = First Moment = Mean = \sum x \cdot p(x)


    b = Second Moment = \sum x^2 \cdot p(x)


    Variance = b - a^{2}

    First Moment = Mean = 0*0.08 + 1*0.17 + 2*0.25 + 3*0.19 + 4*0.18 + 5*0.13

    Second Moment = 0*0.08 + 1*0.17 + 4*0.25 + 9*0.19 + 16*0.18 + 25*0.13

    You do the arithmetic and calculate the Variance.
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  3. #3
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    Is this correct,
    Variance= 2.1979
    and thus,
    SD=1.483

    So would the defintion of unit of measure be "number of transactions"
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  4. #4
    MHF Contributor
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    Well, I get 2.1599 and 1.4697, but I already commented on the rounding problem. On the other hand, any physical scientist would slap your hands for writing what you have written. I explain...

    1) You calculated probabilities to two significant figures.
    2) You calculated variance and standard deviation from these probabilities and somehow, magically came up with four or five significant digits.
    3) Very bad!

    I retained probabilities to 15 significant figures and reported variance and standard deviation to five significant figures. This is acceptable behavior, even to my hand-slapping friends.

    You have the unit of measure correct.
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