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Lecture 3 notes - 2.2 NUMERICAL SUMMARIES OF DATA FROM A...

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2.2 NUMERICAL SUMMARIES OF DATA FROM A SINGLE SAMPLE Data X 1 , X 2 , ..., X n a. Measures of location or center (Devore 7e, Sec.1.3) Sample Mean X = 1 n n i =1 X i “center of gravity” — See Devore Fig. 1.14 Sample Median X = “middle” X -value if n odd half-way between 2 middle values if n even Sample Mode most frequent value Trimmed mean (5% MINITAB,) (Why? - mean susceptible to outliers) b. Measures of variability or spread (Devore 7e, Sec.1.4) Sample variance : S 2 = 1 n - 1 n i =1 ( X i - X ) 2 (Note: some use n in division, not n - 1) Handy computing formula: n i =1 ( X i - X ) 2 = n i =1 X 2 i - n X 2 This result is very simple to show — see Devore 7e, p.34. Sample standard deviation : S = S 2 Sample Range : X max - X min Sample Coefficient of variation : S/ X or 100 S/ X % MINITAB: menu sequence is: Stat Basic Statistics Descriptive Statistics... 1
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2.3 ORDER STATISTICS AND QUANTILES Order Statistics: Arrange data in increasing order X (1) X (2) ... X ( n ) Quantiles and percentiles Roughly speaking for p (0 < p < 1) the p quantile of a set of values is such that a fraction p
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