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Thread: [ASK] Is Expected Frequency Rounded Up or Down?

  1. #1
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    [ASK] Is Expected Frequency Rounded Up or Down?

    A die is tossed 100 times. What's the expected frequency that the number appears will be 4?

    The probability is 1/6, so the expected frequency is 1/6 100, but that results in a fraction (16 2/3). Do we need to round it up or down? Is the answer 16 or 17?
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  2. #2
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    Re: [ASK] Is Expected Frequency Rounded Up or Down?

    You don't need to round it at all. The correct answer is $\dfrac{50}{3}$

    True you won't see 2/3 of a die but that doesn't matter. An expectation is an average and as such there's no reason to expect it must be an integer.
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    Re: [ASK] Is Expected Frequency Rounded Up or Down?

    Okay then, thanks.
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    Re: [ASK] Is Expected Frequency Rounded Up or Down?

    If you are forced to round, for whatever reason, you will need to decide exactly how to do that.

    Typically, a simple up or down methodology will prove unsatisfactory as you will violate the definition of a probability distribution:

    Down 2 dp
    1/3 = 0.33
    1/3 = 0.33
    1/3 = 0.33
    0.33 * 3 = 0.99 and that is NOT 1.00

    Likewise, fudging (forced footing) proves unsatisfactory:

    1/3 = 0.33
    1/3 = 0.33
    1/3 = 0.34

    They are not really equal, are they.

    Unless you are in a purely theoretical pursuit, you just have to make up your mind what is and is not suitable.
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  5. #5
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    Re: [ASK] Is Expected Frequency Rounded Up or Down?

    Oh well, no rounding then, thanks.
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