Smile 發問時間: 科學及數學數學 · 3 星期前

Maths problem: how to do (a), (b) thanks?

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  • 3 星期前
    最佳解答

    (a)

    First of all, we calculate the mean as

    μ

    = [(k + 4) + (k - 3) + (k + 1) + (k - 7) + k] ÷ 5

    = k - 1.

    The variance is then

    σ²

    = [(k + 4 - μ)² + (k - 3 - μ)² + (k + 1 - μ)² + (k - 7 - μ)² + (k - μ)²] ÷ 5

    = [(5)² + (-2)² + (2)² + (-6)² + (1)²] ÷ 5

    = (25 + 4 + 4 + 36 + 1) ÷ 5

    = 70 ÷ 5

    = 14.

    The s.d. is σ = √14.

    (b)

    Standard deviation is a measure of dispersion.

    For each datum added to the same number, the dispersion among the data remains the same, so the new s.d. is still σ = √14.

    (c)

    For each datum multiply to the same number, the dispersion among the data is also scaled by the same number, so the new s.d. is 3σ = 3√14.

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