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匿名 發問於 科學及數學數學 · 9 年 前

NSS MI (Statistic Part) 急急急

Question:

The mean and the standard deviation of the Liberal Studies test marks of 38 students are 65 and 2√2 respectively. After checking the marks, the teacher finds that a mark of 60 is wrongly recorded as 50. Find the correct mean and standard deviation of the test marks.

I have already the mean but i don't know how to find standard deviation.

The mean is 65.26(4 sig. fig.)

Sources: Mathematics In Action Module 1 Calculus and Statistic (Volume 2) (Longman) Chapter 9 Review on Basic Statistics and Probability (Exercise 9A no. 19) P. 9.24

1 個解答

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  • 9 年 前
    最佳解答

    If the mark is 50, then the toal mark ∑ x_i =38*65=2470. Also

    ∑ (x_i - 65)^2 / 38 = (2√2)^2 => ∑ (x_i - 65)^2 = 304

    ∑ (x_i)^2 - 130 ∑x_i + 38*4225 = 304

    ∑ (x_i)^2 =160854

    Now one recorded is changed to 60. So the new ∑ x_i is 2470-50+60 = 2480 and the mean is 2480/38 = 65.2632

    New ∑ (x_i)^2 = 160854 - 50^2 + 60^2 = 161954

    New Var(x) = E(x^2)-[E(x)]^2 = 161954 / 38 - [2480 / 38]^2 = 2.6676

    So the new standard deviation = 1.633

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