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z - score table

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發問:

z - score table shows 2 decimal places of z only, if I want to find the z - score of z = 1.2649 in public examination, should I simply round off to z = 1.26 ( = 0.3962) or use z = 1.265 ( = average of 0.3962 and 0.3980)? What is the common practice in public examination,e.g HKALE? Similarly, if z = 1.2651, should I... 顯示更多 z - score table shows 2 decimal places of z only, if I want to find the z - score of z = 1.2649 in public examination, should I simply round off to z = 1.26 ( = 0.3962) or use z = 1.265 ( = average of 0.3962 and 0.3980)? What is the common practice in public examination,e.g HKALE? Similarly, if z = 1.2651, should I use z = 1.26, or z = 1.265 or z = 1.27?

最佳解答:

For example,.assume you want to find the z-score for z=1.2649. For AS Maths & Stat. of HKALE, you may round it down and use z=1.26. You will then find that the z-score is 0.3962. As far as I know, this is the method applied in the NSS M1 maths subject, as the method of approximation is not taught in the subject. For AL/AS Applied Maths in HKALE, you have to use the method of interpolation to approximate the z-value. The simplest method is to use linear approximation: z z-score 1.26 0.3962 1.27 0.3980 The z-score for z=1.2649 = (0.3962)(0.51) + (0.3980)(0.49) =0.397082

其他解答:

答得好.補充一下the method of interpolation, 或所謂的 weighted mean, 其實即是一種mean, 只是有比重而已.在例子中,0.51和0.49便是比重。 . 舉另一例,已知f(0.34)和f(0.35),則求f(0.3481)時, f(0.34)的比重是19,f(0.35)的比重是81, 因近0.35多一點,所以比重大點. f(0.3481) = f(0.34)*0.19 + f(0.35)*0.81
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