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18 June, 11:55

A student union cafeteria worker checked the weight of ten half-pound bags of whole bean coffee and recorded the following weights in pounds: 0.48, 0.51, 0.47, 0.49, 0.49, 0.50, 0.52, 0.48, 0.49, 0.51. What is the standard deviation of the weight of these coffee bags?

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  1. 18 June, 12:05
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    Answer: σ = 0.0154

    Step-by-step explanation:

    1. Calculate the mean for the recorded data.

    (0.48 + 0.51 + 0.47 + 0.49 + 0.49 + 0.50 + 0.52 + 0.48 + 0.49 + 0.51) / 10 =

    4.94 / 10 = 0.49

    The mean is represented with the greek letter μ, so μ = 0.49

    2. For each element in the serie, subtract the mean (0.49) and square the result

    (0.48 - 0.49) ^2 = (-0.01) ^2 = 0.0001

    (0.51 - 0.49) ^2 = (0.02) ^2 = 0.0004

    (0.47 - 0.49) ^2 = (-0.02) ^2 = 0.0004

    (0.49 - 0.49) ^2 = 0

    (0.49 - 0.49) ^2 = 0

    (0.50 - 0.49) ^2 = (0.01) ^2 = 0.0001

    (0.52 - 0.49) ^2 = (0.03) ^2 = 0.0009

    (0.48 - 0.49) ^2 = (-0.01) ^2 = 0.0001

    (0.49 - 0.49) ^2 = 0

    (0.51 - 0.49) ^2 = (0.02) ^2 = 0.0004

    So we get these results: 0.0001, 0.0004, 0.0004, 0, 0, 0.0001, 0.0009, 0.0001, 0, 0.0004

    3. Now, we calculate the mean of these squared differences

    (0.0001 + 0.0004 + 0.0004 + 0 + 0 + 0.0001 + 0.0009 + 0.0001 + 0 + 0.0004) / 10 =

    (0.0024) / 10 = 0.00024

    4. Now to get the standard deviation, we need to get the root of this last value (0.00024).

    √ (0.00024) = 0.0154

    5. So that will be our standard deviation value:

    σ = 0.0154

    DONE!
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