SSAC2007:BF448.SKB1.3
The “Perfect” Date
Decision Making-A Ranking and
Rating Spreadsheet to Find the
“Perfect” Date
Core Quantitative Concepts and Skills
Weighted sums
eMATcH
Online Dating Service
Excel Skills
Absolute cell
Sort Function
Prepared for SSAC by
Semra Kilic-Bahi - Colby-Sawyer College, New London, NH
1
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved, 2007.
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.
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.
3
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.
A
B
C
D
E
F
G
35
46
28
18
21
22
31
$48,000
$57,000
$40,000
$3,000
$18,000
$15,000
$29,000
64
60
62
68
67
66
69
60
30
90
235
130
69
12
H
26
$50,000
71
56
Ph.D.
High School
Master
High School
Bachelor
High School
Middle
School
Master
Organized
M
Likes Reading
L
Likes Dining out
K
Likes Animals
J
Fit
I
Stylish
H
Education Level
G
How far away
the person lives
(miles)
F
Height (inches)
E
Salary
9
10
D
Age
2
3
4
5
6
7
8
C
Candidate
B
7
2
1
5
6
3
2
1
3
5
4
6
1
2
2
3
7
3
5
7
4
5
1
2
4
7
3
2
7
4
1
6
7
2
7
6
7
5
3
4
2
6
5
7
6
5
4
3
4
Example-which job to choose?
Before working through the eMATcH dating table, we will consider a lessinvolved 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.”
Job
Salary
Location
A
48,000
Bestville
B
67, 000
Troublecity
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
1
2
B
2
1
5
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:
Job  Salary  Salary Weight  Location  Location Weight
Job A  1 2  2  1  4
Job B  2  2  1 1  5
6
Rating - AGE
35
46
28
18
21
22
31
26
C
Age
A
B
C
D
E
F
G
H
2
3
4
5
6
7
8
9
10
B
Candidate
C
Age
2
3
4
5
6
7
8
9
10
B
Candidate
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.)
A
B
C
D
E
F
G
H
5
7
2
1
1
1
3
2
7
Rating Continued
C
D
E
F
G
H
I
Age
Salary
Height
(inches)
How far away
the person
lives (miles)
Education
Level
Stylish
Fit
Likes Animals
Likes Dining
out
Likes Reading
Organized
2
3
4
5
6
7
8
9
10
B
Candidate
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:
A
B
C
D
E
F
G
H
5
7
2
1
1
1
3
2
5
7
4
1
2
2
3
6
6
4
4
7
7
7
7
6
5
6
3
1
2
4
7
5
7
3
6
3
5
3
1
6
7
2
1
5
6
3
2
5
1
3
5
4
6
1
2
7
2
3
7
3
5
7
4
6
6
7
5
3
4
2
6
3
J
K
5
1
2
4
7
3
2
5
L
7
4
1
6
7
2
7
4
M
8
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.
Organized
M
Likes Reading
L
Likes Dining out
K
Likes Animals
J
Fit
I
Stylish
H
Education Level
G
How far away
the person lives
(miles)
F
Height (inches)
E
Salary
D
Age
2
3
4
5
6
7
8
9
10
11
C
Candidate
B
WEIGHTS
A
B
C
D
E
F
G
H
6
5
7
2
1
1
1
3
2
5
5
7
4
1
2
2
3
6
3
6
4
4
7
7
7
7
6
4
5
6
3
1
2
4
7
5
7
7
3
6
3
5
3
1
6
4
7
2
1
5
6
3
2
5
4
1
3
5
4
6
1
2
7
4
2
3
7
3
5
7
4
6
6
5
1
2
4
7
3
2
5
6
7
4
1
6
7
2
7
4
5
6
7
5
3
4
2
6
3
= Cell with a
number in it
= Cell with a
formula in it
9
Weighted Sums
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:
Isn’t this long formula
equivalent to
=SUMPRODUCT(C4:M4,
$C$3:$M$3) ?
C
D
E
F
G
H
I
J
K
L
M
Age
Salary
Height (inches)
How far away
the person lives
(miles)
Education Level
Stylish
Fit
Likes Animals
Likes Dining out
Likes Reading
Organized
WEIGHTED SUM
2
3
4
5
6
7
8
9
10
11
B
Candidate
=C4*$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
N
WEIGHTS
A
B
C
D
E
F
G
H
6
5
7
2
1
1
1
3
2
5
5
7
4
1
2
2
3
6
3
6
4
4
7
7
7
7
6
4To extend
7 this 4formula
4 to4
6
5calculate7 the weighted
7
1 sum
2 for
5
6other candidates,
3
2 click
3 on
3 N4,1
3move the
6 cursor
1 to the
5 lower7
2
1right corner
3 of 5the cell,
4 drag
3
4
2the fill handle
5
6
6 down
5
7
to
4N11.
3
3
1
7
3
7
1
2
2
4
2
5
6
5
7
6
5
6
7
4
1
6
7
2
7
4
5
6
7
5
3
4
2
6
3
284
231
193
180
252
158
205
263
10
Weighted Sums
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.
B
C
D
E
F
G
H
I
J
K
L
M
Candidate
Age
Salary
Height (inches)
How far away
the person lives
(miles)
Education Level
Stylish
Fit
Likes Animals
Likes Dining out
Likes Reading
Organized
WEIGHTED SUM
2
3
4
5
6
7
8
9
10
11
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.
N
WEIGHTS
A
H
E
B
G
C
D
F
6
5
2
1
7
3
2
1
1
5
5
6
2
7
3
4
1
2
3
6
6
7
4
7
4
7
7
4
5
5
2
6
7
3
1
4
7
7
6
5
3
1
6
3
3
4
7
5
6
2
2
1
5
3
4
1
7
6
3
2
5
4
1
4
2
6
5
3
4
7
3
7
6
5
5
7
1
2
2
4
3
6
7
4
7
4
7
1
6
2
5
6
3
4
7
6
5
3
2
284
263
252
231
205
193
180
158
11
End of Module Assignments
1. Copy and paste the following table into an Excel worksheet.
M
Organized
L
Likes Reading
K
Likes Dining out
J
Likes Animals
I
Fit
H
Stylish
9
10
G
7
2
1
3
2
3
5
1
7
4
6
7
Master
High School
1
5
5
4
7
3
2
4
1
6
5
3
130
69
Bachelor
High School
6
3
6
1
5
7
7
3
7
2
4
2
69
12
Middle School
2
2
4
2
7
6
71
56
Master
5
7
6
5
4
3
How far away
the person lives
(miles)
8
F
Height (inches)
6
7
E
Salary
4
5
D
Age
2
3
C
Candidate
B
Education Level
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?
A
B
35
46
$48,000
$57,000
64
60
60
30
C
D
28
18
$40,000
$3,000
62
68
90
235
E
F
21
22
$18,000
$15,000
67
66
G
31
$29,000
H
26
$50,000
Ph.D.
High School
12
End of Module Assignments
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?
H
I
Cities
Lowest
Temperature in
January
G
Highest
Temperature in
July7
F
Median
Housing Price
E
Job Growth
D
Sales Tax
2
3
4
5
6
7
8
9
10
C
Median family
income
B
Population
2.
A
B
C
D
E
F
G
H
17,400
8,500
19,500
13,200
35,900
18,800
25,700
22,500
$60,126
$48,824
$58,231
$72,334
$60,758
$84,267
$102,456
$94,385
0.00%
5.50%
0.00%
8.10%
7.00%
8.30%
7.00%
5.00%
10.81%
13.02%
10.17%
3.68%
18.22%
-0.76%
35.22%
2.79%
$326,223
$290,269
$428,329
$322,812
$321,173
$643,549
$173,774
$527,670
81.4°
80.6°
82.9°
87.2°
91.9°
88.7°
87.4°
81.2°
7.7°
6.2°
8.7°
19.2°
47.0°
41.5°
11.6°
18.1°
13