A31 APPENDIX D CHAPTER 2 Class Width = Range of data Number of classes (round up to next convenient number) Midpoint = (Lower class limit) + (Upper class limit) 2 Relative Frequency = Class frequency Sample size = f n Population Mean: m = gx N Sample Mean: x = gx n Weighted Mean: x = gxw gw Mean of a Frequency Distribution: x = gxf n Range = (Maximum entry) - (Minimum entry) Population Variance: s 2 = g(x - m) 2 N Population Standard Deviation: s = 2s 2 = Ag(x - m) 2 N Sample Variance: s2 = g(x - x)2 n - 1 Sample Standard Deviation: s = 2s2 = Ag(x - x)2 n - 1 Empirical Rule (or 68-95-99.7 Rule) For data sets with distributions that are approximately symmetric and bell-shaped: 1. About 68% of the data lie within one standard deviation of the mean. 2. About 95% of the data lie within two standard deviations of the mean. 3. About 99.7% of the data lie within three standard deviations of the mean. Chebychev’s Theorem The portion of any data set lying within k standard deviations (k 7 1) of the mean is at least 1 - 1 k2 . Sample Standard Deviation of a Frequency Distribution: s = Ag(x - x)2f n - 1 Population Coefficient of Variation: CV = s m # 100% Sample Coefficient of Variation: CV = s x # 100% Interquartile Range: IQR = Q3 - Q1 Percentile of x = number of data entries less thanx total number of data entries # 100 Standard Score: z = Value - Mean Standard deviation = x - m s Key Formulas D
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