In some applications, certain values in a data set may be considered more important than others. For example, to determine students’ grades in a course, an instructor may assign a weight to the final exam that is twice as much as that to each of the other exams. In such cases, it is more appropriate to use the weighted mean. In general, for a sequence of n data values x1, x2,..., xn that are assigned weights w1, w2,..., wn, respectively, the weighted mean is found by the formula
Where ∑xw is obtained by multiplying each data value by its weight and then adding the products. Suppose an instructor gives two exams and a final, assigning the final exam a weight twice that of each of the other exams. Find the weighted mean for a student who scores 73 and 67 on the first two exams and 85 on the final. (Hint: Here, x1 = 73, x2 = 67, x3 = 85, w1 = w2 = 1, and w3 = 2.)
Answer to relevant QuestionsWhen studying phenomena such as inflation or population changes that involve periodic increases or decreases, the geometric mean is used to find the average change over the entire period under study. To calculate the ...The following data set belongs to a population: Calculate the range, variance, and standard deviation. The following data give the number of highway collisions with large wild animals, such as deer or moose, in one of the northeastern states during each week of a 9-week period. Find the range, variance, and standard ...The following data are the ages (in years) of six students. Calculate the standard deviation. Is its value zero? If yes, why? The following table gives the frequency distribution of the number of hours spent last week on cell phones (making phone calls and texting) by all 100 students of the tenth grade at a school. Hours per Week Number ...
Post your question