This time, lk at
the scores of
4. Standard Deviation
Team a and
team b.
Okay...
Draw a
number line.
Write down the names of
the players aording to
their scores.
Even though the
average score
of each team
was 87...
Team A
AVERAGE
AVERAGE
Team B
the trends
described by the
number lines are
quite dierent.
Rui-Rui
Jun
Yumi
ShizukaTouko
Kaede
Kimiko
Megumi
Yoshimi
Mei
Kaori
Yukiko
48 Chapter 2
Rui-Rui
Jun
Kaede
They sure are.
Team A's scores
vary from low to
high, but Team B's
scores are more
similar.
Standard deviation
is used to describe
such scaering of
data.
Another
new term?!
In short, standard
deviation is an
indicator to show
the dierence
from the mean of
each value in that
set.
Indicator to show
the dierence...?
0 (Minimum)
no scaering
(a values are the same)
scaered
The minimum standard deviation is
zero, and as the "scaering of data"
increases, so does the standard
deviation.
Gue which standard
deviation is larger, Team a's
or Team b's?
HM...
MAYBE Team A's?
Geing the Big Picture: Understanding Numerical Data 49
Right. The formula
is as foows.
sum of (each value − mean)²
number of values
It is suenly
Starting to
sound like
mathematics.
It's easy. You just
put some numbers
into the formula.
Okay, I'
give it a
try.
First, team a.
It's easier
than I
thought. I
think I can
do this.
Then try figuring
out the standard
deviation of Team B
by yourself.
Team A
Let's try it
together.
50 Chapter 2
≈
I put this number
here, and...
What is the square
rt of 89.6?
Coect!
S? You can
do it!
Finished!
Sure, piece of
cake!
Members of team b
had scores similar to
each other. thus the
standard deviation is
smaer than team a's.
Team B
About
9.5
Standard Deviation
WONDERFUL!
Clap
Clap
Team A Team B
Geing the Big Picture: Understanding Numerical Data 51
≈
Team B
You subtract 1
from the total
number of
values?
Yes.
Another
formula?
The second formula is
alied when calculating
the standard deviation of
a sample.
Generay speaking...
So, a population
is the real
group you
actuay want to
examine.
And a sample is a
group of people
selected from the
population.
population
SAMPLE
number of values
sum of (each value − mean)²
sum of (each value − mean)²
number of values − 1
I told you that the formula for standard
deviation is:
There's also a dierent formula, which is:
The first formula is alied
when calculating the
standard deviation of an
entire statistical population.
52 Chapter 2

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