In some applications, certain values in a data set may be considered more important than others. For

Question:

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 ˆ‘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.)