Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 50symmetrically distributed, as a stem-and-leaf plot will show. Let’s use the quantile()function to look at the data:> sum(exec.pay > 100)/length(exec.pay) # proportionmore[1] 0.09045 # 9% make more than 1million> quantile(exec.pay,0.9) # 914,000 dollars is 90percentile90%91.4> quantile(exec.pay,0.99) # 9 million is top 1percentile997,906.6> sum(exec.pay quantile(exec.pay,.10) # the 10 percentile is90,00010%9Quantiles versus proportions For a data vector x we can ask two related but inversequestions : what proportion of the data is less than or equal to a specified value? Or for aspecified proportion, what value has this proportion of the data less than or equal? Thelatter question is answered by the quantile function.The inter-quartile rangeReturning to the idea of the middle 50% of the data, this would be the distance betweenthe 75th percentile and the 25th percentile. This is known as the interquartile range andis found in R with the IQR() function.For the executive pay data the IQR is> IQR(exec.pay)[1] 27.5Whereas, for comparison, the standard deviation is> sd(exec.pay)[1] 207.0This is much bigger, as the largest values of exec. pay are much larger than the others andskew the results.z-scoresThe z-score of a value is the number of standard deviations the value is from the samplemean of the data set. That is,