1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 3.1-mean-backwards When you’re told “the mean is ____” and you have to find a missing data value. With value-added by D.R.S., University of Cordele

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.2 The Mean We know the mean. We’re missing one data value. Work backwards to find it.

3. Outline – Ten Big Topics 1.Example 3.2 – Rutherford’s songs – the mean is given but one of the data values is unknown. Work backwards to find the missing data value. 2.Example 3.4 – Virginia’s course grade, a weighted mean. What does she need to get to attain the final course grade she wants to get?

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.2: Working backwards: They tell you the mean but a data value is unknown Rutherford downloaded five new songs from the Internet. He knows that, on average (mean), the songs cost $1.23. If four of the songs cost $1.29 each, what was the price of the fifth song he downloaded? Solution Since we are given the value of the mean, we can use algebra on the formula to find the missing value. Substituting all the values we are given into the formula for the mean, we have the following.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.2: Using the Mean to Find a Data Value (cont.) So the cost of Rutherford’s fifth song was $0.99. μ= “Clear the Fractions” – multiply each side by 5. Important algebra technique to remember.

6. Excel: Data, What-if Analysis, Goal Seek to reach the target mean These are the inputs: four of them at $1.29, fifth one unknown. We want the mean in B2 to be set equal to $1.23 and we want to achieve it by having the “right” value in cell A5.

7. Excel: Data, What-if Analysis, Goal Seek to reach the target mean And here is the result. Goal Seek figured out that a price of $0.99 in cell A5 leads to a mean of $1.23 in cell B2.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.4 Weighted Mean Heather wants an “A”, what does she need to get on the Final Exam?

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.4: Calculating a Weighted Mean Working backward to find missing value At the end of the semester, Heather knows all of her grades in her sculpting class except for the final exam. Here’s a breakdown of her points and how much each category counts toward the final course grade. Tests (35%): 78 Class Assignments (20%): 92 Semester Project (35%): 93 Final Exam (10%): ?

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.4: Calculating a Weighted Mean (cont.) a.Calculate the weighted mean for the portion of the grade that she has completed. Use 1-Var Stats. Put __________ in list _____ and __________ in list _____ Result: _______ = _________ and by the way, n = _______ which is:

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Excel Weighted Mean Observe completely blank Final Exam line

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.4: Calculating a Weighted Mean (cont.) b.What grade must Heather make on her final exam in order to have a final grade of 90%, which would be the A that she desires? Assume that the final exam is worth 100 points. In this problem, we know the __________ ___________ and we have to work backwards to find the _______________________.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. What does Heather need to reach 90% overall? ScoreWeightMultiply Tests Assign. Project Final Total: To achieve an overall weighted average grade of ________, Heather needs a score of ______ on the final exam, which is __________________________.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. What does Heather need to reach 90% overall? If you use the formula, it looks like this. The calculator cannot do the entire work-backwards-to-find-what’s-needed. You have to understand weighted mean and figure it out yourself. The calculator can only assist with arithmetic along the way.

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.4: Calculating a Weighted Mean (cont.) Since x > 100, it appears as though it is mathematically impossible for Heather to make an A in the course. The highest final grade that Heather could achieve in the class is 88.25. We will leave this for you to verify on your own. How would you figure out the maximum possible grade?

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3.4: Calculating a Weighted Mean (cont.) c.What grade must Heather make on her final exam in order to have a final grade of 80% and a B in the course? Again, assume that the final exam is worth 100 points. Use either table or formula. ScoreWeightMultiply Tests Assign. Project Final Total:

18. Weighted Mean and Excel Goal Seek Final Exam line is filled in now. The 117.5 is leftover from a Goal Seek attempt at 90% (part b of the example). Here are Goal Seek inputs for part c, where we want to know “What Final Exam grade is needed to attain an overall 80% in the course?”