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11 September, 01:35

What is the standard deviation of the following data set rounded to the nearest tenth? 3, 17, 18, 15, 12, 21, 9

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  1. 11 September, 03:52
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    The standard deviation of the data set is 5.7 to the nearest tenth

    Step-by-step explanation:

    * Lets explain how to find the standard deviation

    # Step 1: find the mean of the data set

    ∵ The mean = the sum of the data : the number of the data

    ∵ The data set is 3, 17, 18, 15, 12, 21, 9

    ∵ Their sum = 3 + 17 + 18 + 15 + 12 + 21 + 9 = 95

    ∵ They are seven

    ∴ The mean = 95 : 7 = 13.6

    # Step 2: subtract the mean from each data and square the answer

    ∴ (3 - 13.6) ² = 112.36

    ∴ (17 - 13.6) ² = 11.56

    ∴ (18 - 13.6) ² = 19.36

    ∴ (15 - 13.6) ² = 1.96

    ∴ (12 - 13.6) ² = 2.56

    ∴ (21 - 13.6) ² = 54.76

    ∴ (9 - 13.6) ² = 21.16

    # Step 3: find the mean of these squared difference

    ∵ The mean = the sum of the data : the number of the data

    ∵ The sum = 112.36 + 11.56 + 19.36 + 1.96 + 2.56 + 54.76 + 21.16 = 223.72

    ∴ The mean = 223.72 : 7 = 31.96

    # Step 4: the standard deviation is the square root of this mean

    ∴ The standard deviation = √ (31.96) = 5.6533 ≅ 5.7

    * The standard deviation of the data set is 5.7 to the nearest tenth
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