1 The “Perfect” Date Prepared for SSAC by Semra Kilic-Bahi - Colby-Sawyer College, New London, NH © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved, Excel Skills Absolute cell Sort Function SSAC2007:BF448.SKB1.3 Core Quantitative Concepts and Skills Weighted sums Decision Making-A Ranking and Rating Spreadsheet to Find the “Perfect” Date eMATcH Online Dating Service

Background and Overview When we need to make a decision, we often need to consider many factors. The process can easily get complicated when the number of factors and objectives involved is increased. Another difficulty is the mix of quantitative and qualitative aspects involved in the process. However, we often make decisions based on ratings. Every year, we are given a list of “Best Colleges to Attend” or “Best Cities to Live in.” In this module, we will informally explore how these rating systems might be set up to give us some insight into these types of studies. This includes: –the factors involved –how the factors are rated according to a scaling criteria –how each factor is weighed in the final ranking process. 2

Background and Overview The term ranking is used to ascribe a level or position in a hierarchy. The term rating is used to assess the quality or worth of things. Throughout this module, we will use the term rating when we are appraising the value of the things. We will use the term ranking when we are doing the overall ordering of the choices according to the magnitude of the weighted sums. 3 Slides 4 presents the problem to be solved. Slides 5-6 give an example to demonstrate the basic concepts. Slides 7-11 solve the problem. Slide present the end of module assignments.

4 Problem – eMATcH Dating Service Problem: Suppose you have subscribed to an online dating service, eMATcH, to find a partner. Here is the compilation of the dating profiles of eight candidates who responded to the personal profile you provided. Candidates rate the last six attributes on a scale of 1 to 7, with “7” being the most and “1” being the least favorable. Decide which candidate will make the most-compatible date from the information in the table.

5 Example-which job to choose? Before working through the eMATcH dating table, we will consider a less- involved problem. Suppose we are trying to decide between two job offers and we are basing our decision on two factors, the “salary” and the “location.” We like the higher salary of Job B, but we prefer the location for Job A. So, if we try to rate each factor on a scale of 1 to 2, where “2” is the most preferred, we will have JobSalaryLocation A48,000Bestville B67, 000Troublecity JobSalaryLocation A12 B2 1

6 Example-which job to choose? Now, we need to decide which attribute is more important for us, the salary or the location. If “salary” is more important than the “location”, then by using the same scale, we will assign “2” points for salary, and “1” point for the location. Then, the weighted sum for each job can be calculated as:

7 Rating - AGE Now, let’s go back to the problem –eMATcH dating service- presented at the beginning of the module. For the characteristic of AGE, we will set up a rating by using a scale of 1 to 7, where our most-preferred age receives a “7” and the least preferred gets a “1.” We observe that the youngest candidate is 18 years old and oldest candidate is 46 years old. The following is a possible rating: (Note that some rating scores are used more than once, and some are not used at all. The choice is up to the person making the decision.)

8 Rating Continued Let’s continue rating for the characteristics of SALARY, HEIGHT, HOW FAR AWAY THE PERSON LIVES, and EDUCATION LEVEL by using the same scale, 1 to 7, in which our most-preferred rating receives a “7” and the least preferred gets a “1.” Here is a possible rating:

9 Weighting the attributes Now we convert our rating tool into a spreadsheet to calculate an overall ranking on the next slide. We start by inserting a row of weights (Row 3). Recreate this spreadsheet. For homework, you will need to assign weights for each characteristic, using a scale of 1 to 7, where 7 is the most-important characteristic, and 1 is the least important for you. For now, use the values in this spreadsheet so you can check your calculation when you complete the spreadsheet in the next slide. = Cell with a number in it = Cell with a formula in it

Add a column to your spreadsheet to calculate the weighted sums. For each characteristic, we will multiply rating for the candidate by the assigned weight for the characteristic and then add them all up to find the weighted sum for each candidate. That is, we have the following formula in Cell N4 for candidate A: 10 Weighted Sums =C4*$C$3+D4*$D$3+E4*$E$3+F4*$F$3+G4*$G$3+H4*$H$3+I4*$I$ 3+J4*$J$3+K4*$K$3+L4*$L$3+M4*$M$3 To extend this formula to calculate the weighted sum for other candidates, click on N4, move the cursor to the lower- right corner of the cell, drag the fill handle down to N11. Isn’t this long formula equivalent to =SUMPRODUCT(C4:M4, $C$3:$M$3) ?

If we order the weighted sums from the largest to smallest values by using the “SORT” function, we will rank the compatibility of each candidate according to our ranking process. 11 Weighted Sums SORTING: Highlight the “Weighted Sums” column. On the Home tab, in the Editing group, click Sort & Filter, select “Expand the selection” option and then click Sort Largest to Smallest. Candidate A received the highest ranking according to this ranking criteria and Candidate F received the lowest ranking.

12 End of Module Assignments 1. Copy and paste the following table into an Excel worksheet. a)Rate the characteristics of AGE, SALARY, HEIGHT, HOW FAR AWAY THE PERSON LIVES, and EDUCATION LEVEL, on a scale of 1 to 7, where “7” is the most and “1” is the least preferred. b)Determine the weight you want to assign to each characteristic as we did in Slide # 9, by using a scale of 1 to 7 where “7” is the most and “1” is the least preferred. c)Calculate the weighted sum for each candidate. Which candidate has the highest weighted sum? Which candidate has the lowest weighted sum? d)In part b, use a scale of 1 to 10, where “10” is the most and “1” is the least preferred and recalculate the weighted sum for each candidate. Which candidate has the highest weighted sum? Which candidate has the lowest weighted sum?

13 End of Module Assignments 2. WHICH ONE OF THE FOLLOWING CITIES WOULD YOU LIKE TO LIVE IN? Use the following data and rate the characteristic of POPULATION, MEDIAN FAMILY INCOME, SALES TAX, JOB GROWTH, MEDIAN HOUSING PRICE, HIGHEST TEMPERATURE IN JULY, AND LOWEST TEMPERATURE IN JANUARY by using a scale of 1 to 7, where “7” is the most and “1” is the least. Determine the weight for each characteristic. Calculate the weighted sum for each city. Which city has the highest weighted sum? Which city has the lowest weighted sum?