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Unformatted text preview: Chapter 4 : Other points about Standard Deviation A: Classification of performance For data set A, 15.2, 9.2 6.7, 12.4, 20.5, is 12.8. Three deviations, 2.4, 3.6, and 0.4 (i.e. 60%) are small, and two deviations , 6.1, 7.7 (i.e. 40%) are large. We can see that it is easier to get small deviations than large deviations. When data are plenty (i.e. when N is large), we would probably have this situation: μ Thus most people (about two thirds, 67%) are of ordinary ability. Only very, very few people (about 0.1% each) can be extremely brilliant or extremely silly. How are these percentages obtained? They are obtained from the Normal Distribution. (We will cover this topic in chapter 7 & 8.) B: Standardized Score or SignalSigma Ratio We often have this idea: “Getting 70 marks in Composition is quite good; but, getting 75 marks in Mathematics is not that great.” Why? Answer : In Composition, marks are rather stable: it is not easy to get 70, nor easy to get 45. In other words, the s.d. of the marks is small. In Mathematics, marks are rather volatile: it is quite common to get 75 or 90 as well as 30 or even 0. In other words, the s.d. of these marks is big. It would only be fair to compare abilities by means of the SignalSigma ratio (S/S Ratio) Q : Who performed better? Based on (a) raw marks, (b) S/S ratio Solution : (a) In terms of raw marks, John achieved 145, while Mary obtained 148. Therefore, Mary is better. Over the class Raw marks Subject John Mary Composition 62 5 70 66 Mathematics 70 10 75 82 total XXXXXX XXXXX 145 148 ) ( ratio S S sigma signal x z = = = σ μ μ σ Therefore, John is better.Therefore, John is better....
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 Spring '11
 Gabrille
 Standard Deviation, Sample standard deviation, S.D.

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