Using R for Introductory Statistics : John Verzani

Univariate data 43compare different data sets quantitatively. In this section we cover central tendency; inthe next we cover measures of spread.The most familiar notion of the center of a numeric data set is the average value of thenumbers. In statistics, the average of a data set is called the sample mean and is denotedbyThe sample meanThe sample mean of the numeric data set, x 1 , x 2 , …, x n , is(2.1)The mean() function will compute the sample mean for a data vector. Additionalarguments include trim= to perform a trimmed mean and na.rm= for removal of missingdata.The mean can be found directly from the formula, as in> x = scan()1:2 3 16 23 14 12 4 13 2 0 0 0 6 28 31 14 4 8 2 521:Read 20 items> sum(x)/length(x)[1] 9.35Using the mean() function is preferable, though:> mean(x)[1] 9.35The mean is the most familiar notion of center, but there are times when it isn’t the best.Consider, for example, the average wealth of the patrons of a bar before and afterMicrosoft co-founder Bill Gates steps in. Really large values can skew the average,making a misleading measure of center.The medianA more resistant measure of the center is the sample median, which is the “middle”value of a distribution of numbers. Arrange the data from smallest to biggest. When thereis an odd number of data points, the median is the middle one; when there is an evennumber of data points, the median is the average of the two middle ones.The sample medianThe sample median, m, of x 1 , x 2 ,…,x n is the middle value of the sorted values. Let thesorted data be denoted by x (1) ≤ x (2) ≤ …≤x (n) . Then