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    Question

    The mean and standard deviation of 6 observations are 10

    and 3 respectively. If each observation is multiplied by 4 and then 5 is added to each result, find the new mean and new standard deviation.
    A 10 Correct Answer Incorrect Answer
    B 18 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer

    Solution

    If original data has mean ╬╝ and SD ╧Г, and we transform x to y = a x + b: New mean = a╬╝ + b New SD = |a| ╧Г Here ╬╝ = 10, ╧Г = 3, a = 4, b = 5 New mean = 4├Ч10 + 5 = 45 New SD = 4├Ч3 = 12.

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