The Dating Game

Disclaimer: Although this is called the "Dating Game", it is merely intended to help the student gain understanding of the concept of Standard Deviation. It is not intended to help students find dates.

The day after Thanksgiving, 1996, I was driving my sister, brother-in-law, and sister-in-law over to meet my brother in Springfield at the Mission where he and his wife helped out. During this drive, I ask my sister, "How do you know which woman is the right one for you?" Now, my sister was born a Jones, and like the rest of the family, she can make anything sound believable. Without missing a beat, she said, "You take the letters in her name, convert them to numbers, find the standard deviation, and whoever's standard deviation is closest to yours is the woman for you." I was so proud of my sister, that was a really good answer. Then, she followed it up with "Actually, if you can find a woman who knows what a standard deviation is, that's the woman for you."

The first part was easy, take each letter in your name and convert it to a number. The most logical system is to use the conversion an A=1, B=2, ... Z=26.

Conversion Table

A
B
C
D
E
F
G
H
I

1
2
3
4
5
6
7
8
9

J
K
L
M
N
O
P
Q
R

10
11
12
13
14
15
16
17
18

S
T
U
V
W
X
Y
Z

19
20
21
22
23
24
25
26

James

In order to know which woman has a standard deviation that is closest to mine, I first of all need to find my standard deviation. The letters in my name are "JAMES". Let's convert each of those into a number.

The mean of the numbers is 9.6.
The median of the numbers is 10.
The standard deviation of the numbers is 6.986.

Now, let's interpret the results. The mean of my name is 9.6 which rounds to 10 which corresponds to the letter J. The median number is also 10 or "J". So, the letters in my name are "centered" around the letter J.

The standard deviation of my name is 6.986, which would round to be a 7. However, it does not make sense to say that this is a "G" because no one will understand you if you say the average deviation of the letters in your name is a "G". But what the standard deviation tells us is that the "average" (I use that word loosely - close to technically speaking, it is the quadratic mean of the deviations rather than the arithmetic mean of the deviations, but that's not important right now) deviation is 7 letters.

An important thing to remember is that the order of the values does not affect the standard deviation. In other words, the standard deviation of AEJMS would be the same as JAMES (but I'm really glad my parents didn't name me AEJMS).

Sandi

Let's take another name. This time, we'll use the name SANDI (while not her given name, it's important to use the name the person goes by -- or whichever name gives the standard deviation closest to yours)

Looking at the letters in SANDI, you find that they are very similar to the letters in JAMES. In fact, since order of the letters isn't important, let's put both names into alphabetical order to compare the differences.

You can see that the letters are very similar indeed. This is why our means are close to each other. But, her letters are a little bit further away from the mean than mine (her D is one letter less than my E and her N is one letter more than my M). For that reason, her standard deviation is a little, not much, larger than mine.

The mean of the numbers is 9.4.
The median of the numbers is 9.
The standard deviation of the numbers is 7.301.

Brenda

Looking at the letters in her name, we see that the A and E are in common with the JAMES, and that the R and N are close to the S and M. However, she has a couple of other letters, D and B thrown in there. Since those letters are close to the beginning of the alphabet, her mean will be less than JAMES.

Determining the standard deviation is a bit harder, but that's really what the point of this whole exercise is. Since several of her letters are bunched closely together, they will have a small deviation, but the R and N will account for more of the total deviation. Another thing to consider with BRENDA is that there are six letters instead of the five with JAMES. This means that even though there may be more variation in her name, it may actually be less when you find the average.

The mean of the numbers is 7.333.
The median of the numbers is 4.5.
The standard deviation of the numbers is 6.976.

Can you say Wow! 6.976 compared to my 6.986. Only 0.01 off. Maybe Brenda really is the person for me. In an effort to be truthful, I later found out that the person who thought she knew the right person for me thought I was somebody else.

Your name in alphabetical order is
The numbers corresponding to your name are
The mean of your name is
The median of your name is
The standard deviation of your name is