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10 July, 14:42

Find the sample standard deviation and the population standard deviation of the data set.

52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51

5 - 1572

- 1519

S - 15.19

- 15.72

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  1. 10 July, 18:42
    0
    See below in bold.

    Step-by-step explanation:

    52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51

    The mean = 35.6

    The absolute differences from the mean =

    16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4

    The squares of these differences =

    268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.

    The Sum of these squares = 3459.6

    Sample Variance 3459.6 / 14 = 247.11 and

    Population Variance = 3459.6 / 15 = 230.64

    Sample standard deviation = √247.11 = 15.72

    Population Standard deviation = √230.64 = 15.19.
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