HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 3.1 Course Grade can be a Weighted Mean – Homework = some %, Exams = some %, etc. With value-added by D.R.S., University of Cordele

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Mean Weighted Mean The weighted mean is the mean of a data set in which each data value in the set does not hold the same relative importance, given by where x i is the i th data value and w i is the weight of the i th data value.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.3: Calculating a Weighted Mean The syllabus in Walter’s US history class states that the final grade is determined by tests (40%), homework (20%), quizzes (10%), and a final exam (30%). Two students in the class, Walter and Virginia, want to calculate their final grades. Below are their average grades in each of the categories for tests, homework, and quizzes. They have also individually guessed at what they might score on their final exam.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.3: Calculating a Weighted Mean (cont.) a.Calculate what Walter’s final grade using the formula. Tests: 83 Homework: 98 Quizzes: 90 Final Exam: 87 Suggestion: Make a data table: Multiply Total right column: Should get 87.9

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.3: Calculating a Weighted Mean (cont.) b.Calculate Virginia’s final grade using 1-Var Stats. Tests: 95 Homework: 45 Quizzes: 66 Final Exam: 90 Organize/Write FIRST (make table), then type. Type data values into list L1. Type weights into list L2. 1-Var Stats L1, L2 must give it BOTH list names, data list first, weight list second. Data values in the “List”, Weights in the “FreqList”

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.3: Calculating a Weighted Mean (the grade for Virginia.) The output, seen in the screenshot on the right, shows the value of along with the other descriptive statistics for this data set. TI-84 calculation for Virginia 1-Var Stats L 1,L 2 ___________ and _______________ n=1 is ___________________

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.3: Calculating a Weighted Mean (cont.) Although Virginia didn’t do as well on her homework and quizzes, if she manages to get a 90 on the final exam like she predicts, she’ll end up with an 80.6 for her final grade. Take a moment and consider the effect on her grade if her test score was low, but the homework and quiz scores were high. Would she come out with the same grade? Yes or No? __________ Because homework weight _____ + quiz weight ______ = _______, but final exam weight = ______.