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Measures of Variability Chapter 2 (Page 60) (Page 60) Measures of Variability –shows the spread of the data. (Page 60) Range – the difference between the largest and the smallest measurements. Range = 9.4 – 5.6 = 3.8 The range is easy to calculate, easy to interpret and is an adequate measure of variation for small sets of data. (Page 62) Variance of a Population – is the average of the squares of the deviations of the measurements about their mean µ. ( x i ) N 2 2 The population standard deviation – is equal 2 to the positive square root of . 2 Page 61 2 ( x ) 2 i N ( xi ) xi ( xi ) 2 22.80 4.56 5 2 4.56 2.14 2 Variance of a Sample – is the sum of the squared deviations of the measurements about their mean 2 x. ( x x ) 2 i s n 1 2 ( x x ) 22.80 2 i s 5.7 n 1 4 Sample Standard Deviation – is the positive square 2 root of s . s s2 5.7 2.39 (Page 63) 5, 7, 1, 2, 4 x 2 i 25 49 1 4 16 95 ( xi ) 2 (5 7 1 2 4) 2 (19) 2 361 2 ( x ) 361 2 i x i 95 95 72.2 22.8 2 n 5 s 5.7 n 1 5 1 4 4 Answer 2 – 15 Page 65