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Measures of Variation Notes Spring

# Measures of Variation Notes Spring - 2 of 8 1.2 Measures of...

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2 of 8 1.2 Measures of variation Figure 1: Image and its histogram. Please welcome our special visitor to the class today: Add Mini-Me (Verne Troyer) 2’ 8” to the class: R: load ( ”ClassData . RData”) R: height = c l a s s . data \$ height R: height . skewed = c ( height , 32) R: par ( mfrow = c (1 , 2) ) R: h i s t ( height ) R: h i s t ( height . skewed ) Histogram of height height Frequency 65 70 75 0 1 2 3 4 5 Histogram of height.skewed height.skewed Frequency 30 40 50 60 70 80 0 5 10 15 1.2 Measures of variation Variation Anthony Tanbakuchi MAT167

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Measures of Variation 3 of 8 Figure 2: Mini-Me. (2’ 11”). How can we measure how much the data varies from the center? We need quantitatively describe the dispersion in the data. RANGE Range. Definition 1.1 The max - min of a data set. range = max - min (1) Easy to compute but very susceptible to outliers. Range: max(x)-min(x) Where x is a vector. Note that typing range(x) in R will return the min and max values. R Command Need better measure of average variation from center. Example 1 . Range and skewed distributions: R: max( height ) - min( height ) Anthony Tanbakuchi MAT167
4 of 8 1.2 Measures of variation [ 1 ] 15 R: max( height . skewed ) - min( height . skewed ) [ 1 ] 45 STANDARD DEVIATION Standard deviation: σ , s . Definition 1.2 average variation from the mean value.

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