1. Normalization and Standard Score
Today's leon is in
a co shop. Rui's
friend Yumi joins the
cla.
Am I
bothering
you two
lovebirds?
EXCUSE ME...
No! IT's
nothing like
that.
So, what
should I teach
you today?
Sir! Please
teach us about
standard
score.*
Standard
score?!
That might
be a gd
topic.
We both scored 90,
but on dierent
tests.
This is
yumi.
Heo.
Nice to
mt you.
On an
english
test.
On a
claical
japanese
test.
66 Chapter 4
* Adjusting test results based on standard score is coonly known as grading on a curve.
But somehow, yumi got
a higher adjusted score
(and standard score) in
claical Japanese than
I got in English.
That is because the
range of scores
and the average
scores are dierent
betwn English and
claical Japanese.
If you can show me a of your
clamates' raw scores, I can
explain...
What?!
That's
impoible.
I have them!
Great!
I s...
Raw Test Scores (Out of 100)
English
Rui
Yumi
Claical
Japanese
I don't
know
why,
either...
Rustle
Rustle
Why?
Yumi, how
did you...
Low
High
English
Claical
Japanese
Standard Score and Deviation Score 67
Student Student
Calculate the
mean of each
subject.
OK.
Done!
Average
Average
Compare
each score's
distance from
the average.
This should make
you understand the
dierence betwn
your score of 90
and her score of 90.
This is so
discouraging...
Oh, don't be
disaointed.
90 is a gd
score, after
a.
I' buy a piece
of cake for
each of you.
Cake!
English
Claical
Japanese
English
Claical
Japanese
Average
Huay!
Huay!
68 Chapter 4
But come
to think
of it...
The cla
average for
both history
and biology
was 53.
But our adjusted
scores were
dierent in this
case as we.
Even though the
dierences betwn
our scores and the
averages were the
same!
Hm...
What is the
standard
deviation
of these
subjects?
We, standard
deviation is...
An index to
describe "the
range of
scaering!"
And my history
score and her
biology score
were the same,
t!
Best
friends!
*Whsh!
History
Biology
History
Rui
Yumi
Biology
Average
Wow! You're
smart, Rui!
Low
High
*
History
Biology
Standard Score and Deviation Score 69
Student
Student
Its formula
is...
Standard deviation
History
History
average
Biology
Biology
There!
The smaer the standard
deviation is, the smaer
the "range of scaering"
of the data...
So, your clamates
had more similar
scores in biology
than in history.
What do
you mean?
If I were a high
schl junior
alying for
coege, I'd study
hard for biology.
One or two points
may aect your
rank greatly.
sum of (each value − mean)²
 
Number of values
T-h!
A high schl
uniform suits him
so we!
average
70 Chapter 4

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