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descriptive statistics (2).docx

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September 14 , 2012 Stats 2B03: Statistical Methods for Science Descriptive Statistics (2) Measures of variation - the coefficient of variation is a measure of variation that can be used to compare the variation of two different data sets, possibly measured in different units. It is defined by c.v.= (S/avg)(100). Values can be greater than 100 because they are not percentages.  example: a) Ages in years: 3, 4, 5, 6 2 X 1avg4.5, s1=1.667 b) The same ages in months: 36, 48, 60, 72 X 2avg54, s2=240  Which data set has more variation: same amount of variation just different units a) c.v.=(√1.667/4.5)(100)=28.69 b) c.v.=(√240/54)(100)=28.69 Percentiles and quartiles th - the p percentile is the number X with the property that p percent of the data is less than X and (100-p) percent of the data is bigger than X  e.g. the 50 percentile is the median - the quartiles Q ,1Q 2 Q 3ivide the data set into roughly four equal parts, data set doesn’t have to be equally spaced, quartiles have to be equally spaced  e.g. 25%3 where Q 4s the medi2n  Q 1s at position (n+1)/4 in ordered da
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