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M1 Statistics

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The mean and the standard deviation of the Liberal Studies test marks of 38 students are 65 and 2*(2)^(1/2) 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.Can you please show me all the... 顯示更多 The mean and the standard deviation of the Liberal Studies test marks of 38 students are 65 and 2*(2)^(1/2) 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. Can you please show me all the steps, thanks!

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Old Mean = 65 Old Total marks / 38 = 65 Correct mean = Correct total marks / 38 = [Old total marks - 50 + 60 ]/38 = Old Total marks / 38 +10/38 = 65 + 10/38 =1240/19 =65.326... =65.3 (3 sig. fig.) [Old S.D]^2 = mean of square - square of mean =(∑xi^2) / 38 - 65^2 = (2√2)^2 = 8 => (∑xi^2) / 38 = 8 + 65^2 = 4233 .............(*) where xi are the old marks. [New S.D,]^2 = mean of square - square of mean = (∑yi^2) / 38 - 65.3^2 , where yi are the old marks. = [(∑xi^2) - 50^2 + 60^2 ]/ 38 - 65.3^2 = (∑xi^2) / 38 +1100/38 - 65.3^2 = 4233 + 1100/38 -65.3^2 [Using (*)] = 2.6676... New S.D. = 1.63 (3 sig. fig.) 2010-07-24 14:41:55 補充： yi are the new(not old) marks. 2010-07-24 14:53:11 補充： I guess if we use: S.D.^2 =∑(xi - u)^2 / N ,u=mean, it very difficult to answer this question becuase: u has changed and it is inside a "square". Rather, if we use S.D.^2 = mean of square - square of mean =(∑xi^2) / N - u^2 u becomes more separable from xi. 2010-07-24 16:59:07 補充： STEVIE-G? : The mean u has already changed, so even you replace x1 by x1+10, the mean in x2-u, x3-u, ..., x38-u doesn't change.

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Thanks for your remainder. I do it wrongly and I appreciate your work.
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