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The “Perfect” Date

Prepared for SSAC bySemra Kilic-Bahi - Colby-Sawyer College, New London, NH

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved, 2007.

Excel SkillsAbsolute cellSort Function

SSAC2007:BF448.SKB1.3

Core Quantitative Concepts and SkillsWeighted sums

Decision Making-A Ranking and Rating Spreadsheet to Find the

“Perfect” Date

eMATcHOnline 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.

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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.

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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 12-13 present the end of module assignments.

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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.

B C D E F G H I J K L M

2 Can

did

ate

Age

Sal

ary

Hei

ght (

inch

es)

How

far

away

th

e pe

rson

live

s (m

iles)

Edu

catio

n Le

vel

Sty

lish

Fit

Like

s A

nim

als

Like

s D

inin

g ou

t

Like

s R

eadi

ng

Org

aniz

ed

3 A 35 $48,000 64 60 Ph.D. 7 1 2 5 7 64 B 46 $57,000 60 30 High School 2 3 3 1 4 75 C 28 $40,000 62 90 Master 1 5 7 2 1 56 D 18 $3,000 68 235 High School 5 4 3 4 6 37 E 21 $18,000 67 130 Bachelor 6 6 5 7 7 48 F 22 $15,000 66 69 High School 3 1 7 3 2 2

9G 31 $29,000 69 12 Middle

School2 2 4 2 7 6

10 H 26 $50,000 71 56 Master 5 7 6 5 4 3

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

Job Salary Location

A 48,000 Bestville

B 67, 000 Troublecity

Job Salary Location

A 1 2

B 2 1

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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:

WeightLocationLocationWeightSalarySalaryJob 4 1221 AJob 5 1122B Job

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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.)

B C

2 Can

dida

te

Age

3 A 354 B 465 C 286 D 187 E 218 F 229 G 31

10 H 26

B C

2 Can

dida

te

Age

3 A 54 B 75 C 26 D 17 E 18 F 19 G 3

10 H 2

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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:

B C D E F G H I J K L M

2 Ca

ndid

ate

Ag

e

Sa

lary

He

igh

t (i

nch

es)

Ho

w f

ar

awa

y th

e p

ers

on

liv

es

(mile

s)

Ed

uca

tion

L

eve

l

Sty

lish

Fit

Lik

es

Ani

ma

ls

Lik

es

Din

ing

o

ut

Lik

es

Re

ad

ing

Org

an

ize

d

3 A 5 5 6 5 7 7 1 2 5 7 64 B 7 7 4 6 3 2 3 3 1 4 75 C 2 4 4 3 6 1 5 7 2 1 56 D 1 1 7 1 3 5 4 3 4 6 37 E 1 2 7 2 5 6 6 5 7 7 48 F 1 2 7 4 3 3 1 7 3 2 29 G 3 3 7 7 1 2 2 4 2 7 6

10 H 2 6 6 5 6 5 7 6 5 4 3

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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

B C D E F G H I J K L M

2 Can

dida

te

Age

Sal

ary

Hei

ght (

inch

es)

How

far

away

th

e pe

rson

live

s (m

iles)

Edu

catio

n Le

vel

Sty

lish

Fit

Like

s A

nim

als

Like

s D

inin

g ou

t

Like

s R

eadi

ng

Org

aniz

ed

3 WEIGHTS 6 5 3 4 7 4 4 4 6 6 54 A 5 5 6 5 7 7 1 2 5 7 65 B 7 7 4 6 3 2 3 3 1 4 76 C 2 4 4 3 6 1 5 7 2 1 57 D 1 1 7 1 3 5 4 3 4 6 38 E 1 2 7 2 5 6 6 5 7 7 49 F 1 2 7 4 3 3 1 7 3 2 2

10 G 3 3 7 7 1 2 2 4 2 7 611 H 2 6 6 5 6 5 7 6 5 4 3

B C D E F G H I J K L M N

2 Ca

nd

ida

te

Ag

e

Sa

lary

He

igh

t (in

ch

es)

Ho

w fa

r a

wa

y

the

pe

rso

n li

ve

s

(mile

s)

Ed

uca

tion

Le

ve

l

Sty

lish

Fit

Lik

es A

nim

als

Lik

es D

inin

g o

ut

Lik

es R

ea

din

g

Org

an

ize

d

WEI

GH

TED

SU

M

3 WEIGHTS 6 5 3 4 7 4 4 4 6 6 54 A 5 5 6 5 7 7 1 2 5 7 6 2845 B 7 7 4 6 3 2 3 3 1 4 7 2316 C 2 4 4 3 6 1 5 7 2 1 5 1937 D 1 1 7 1 3 5 4 3 4 6 3 1808 E 1 2 7 2 5 6 6 5 7 7 4 2529 F 1 2 7 4 3 3 1 7 3 2 2 158

10 G 3 3 7 7 1 2 2 4 2 7 6 20511 H 2 6 6 5 6 5 7 6 5 4 3 263

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:

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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, dragthe fill handle down to N11.

Isn’t this long formula equivalent to =SUMPRODUCT(C4:M4,$C$3:$M$3) ?

B C D E F G H I J K L M N

2 Ca

nd

ida

te

Ag

e

Sa

lary

He

igh

t (in

ch

es)

Ho

w fa

r a

wa

y

the

pe

rso

n li

ve

s

(mile

s)

Ed

uca

tion

Le

ve

l

Sty

lish

Fit

Lik

es A

nim

als

Lik

es D

inin

g o

ut

Lik

es R

ea

din

g

Org

an

ize

d

WEI

GH

TED

SU

M

3 WEIGHTS 6 5 3 4 7 4 4 4 6 6 54 A 5 5 6 5 7 7 1 2 5 7 6 2845 H 2 6 6 5 6 5 7 6 5 4 3 2636 E 1 2 7 2 5 6 6 5 7 7 4 2527 B 7 7 4 6 3 2 3 3 1 4 7 2318 G 3 3 7 7 1 2 2 4 2 7 6 2059 C 2 4 4 3 6 1 5 7 2 1 5 193

10 D 1 1 7 1 3 5 4 3 4 6 3 18011 F 1 2 7 4 3 3 1 7 3 2 2 158

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.

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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.

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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?

B C D E F G H I J K L M

2 Can

did

ate

Age

Sala

ry

Heig

ht (inches)

How

far

aw

ay

the p

ers

on li

ves

(mile

s)

Educatio

n L

evel

Sty

lish

Fit

Lik

es A

nim

als

Lik

es D

inin

g o

ut

Lik

es R

eadin

g

Org

aniz

ed

3 A 35 $48,000 64 60 Ph.D. 7 1 2 5 7 64 B 46 $57,000 60 30 High School 2 3 3 1 4 75 C 28 $40,000 62 90 Master 1 5 7 2 1 5

6 D 18 $3,000 68 235 High School 5 4 3 4 6 3

7 E 21 $18,000 67 130 Bachelor 6 6 5 7 7 4

8 F 22 $15,000 66 69 High School 3 1 7 3 2 2

9 G 31 $29,000 69 12 Middle School 2 2 4 2 7 610 H 26 $50,000 71 56 Master 5 7 6 5 4 3

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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?

B C D E F G H I

2 Cities Po

pu

lati

on

Med

ian

fam

ily

inco

me

Sale

s T

ax

Jo

b G

row

th

Med

ian

Ho

usin

g P

rice

Hig

hest

Tem

pera

ture

in

Ju

ly7

Lo

west

Tem

pera

ture

in

Jan

uary

3 A 17,400 $60,126 0.00% 10.81% $326,223 81.4° 7.7°4 B 8,500 $48,824 5.50% 13.02% $290,269 80.6° 6.2°5 C 19,500 $58,231 0.00% 10.17% $428,329 82.9° 8.7°6 D 13,200 $72,334 8.10% 3.68% $322,812 87.2° 19.2°7 E 35,900 $60,758 7.00% 18.22% $321,173 91.9° 47.0°8 F 18,800 $84,267 8.30% -0.76% $643,549 88.7° 41.5°9 G 25,700 $102,456 7.00% 35.22% $173,774 87.4° 11.6°10 H 22,500 $94,385 5.00% 2.79% $527,670 81.2° 18.1°