Читать книгу Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP - Bhisham C. Gupta, Irwin Guttman - Страница 72

Sometimes, we are interested in finding the sample average of a data set where each observation is given a relative importance expressed numerically by a set of values called weights. We illustrate the concept of weighted mean with the following example.

Example 2.5.5 (GPA data) Elizabeth took five courses in a given semester with 5, 4, 3, 3, and 2 credit hours. The grade points she earned in these courses at the end of the semester were 3.7, 4.0, 3.3, 3.7, and 4.0, respectively. Find her GPA for that semester.

Solution: Note that in this example, the data points 3.7, 4.0, 3.3, 3.7, and 4.0 have different weights attached to them; that is, the weights are the credit hours for each course. Thus, to find Elizabeth's GPA, we cannot simply find the arithmetic mean. Rather, in this case, we need to find the mean called the weighted mean, which is defined as

(2.5.4)

where are the weights attached to , respectively. Thus, her GPA is given by