SECTION 2.3 Measures of Central Tendency 71 Weighted Mean and Mean of Grouped Data Sometimes data sets contain entries that have a greater effect on the mean than do other entries. To find the mean of such a data set, you must find the weighted mean. A weighted mean is the mean of a data set whose entries have varying weights. The weighted mean is given by x = Σxw Σw Sum of the products of the entries and the weights Sum of the weights where w is the weight of each entry x. DEFINITION Finding a Weighted Mean Your grades from last semester are in the table. The grading system assigns points as follows: A = 4, B = 3, C = 2, D = 1, F = 0. Determine your grade point average (weighted mean). Final grade Credit hours C 3 C 4 D 1 A 3 C 2 B 3 SOLUTION Let x be the points assigned to the letter grade and w be the credit hours. You can organize the points and hours in a table. Points, x Credit hours, w xw 2 3 6 2 4 8 1 1 1 4 3 12 2 2 4 3 3 9 Σw = 16 Σ(x# w) = 40 x = Σxw Σw = 40 16 = 2.5 Last semester, your grade point average was 2.5. TRY IT YOURSELF 7 In Example 7, your grade in the two-credit course is changed to a B. What is your new weighted mean? Answer: Page A36 EXAMPLE 7 Tech Tip You can use technology such as Minitab, Excel, StatCrunch, or the TI-84 Plus to find the weighted mean. For instance, to find the weighted mean in Example 7 on a TI-84 Plus, enter the points in L1 and the credit hours in L2. Then, use the 1-Var Stats feature with L1 as the list and L2 as the frequency list to calculate the mean (and other statistics), as shown below. TI-84 PLUS 1-Var Stats x=2.5 Mean Σx=40 Σx2=112 Sx=.894427191 sx=.8660254038 Èn=16
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