FRAME 37.

For example:

(X-u ) 2

X

X-u

15

- 15

(-15)(-15) =

225

Note that a minus times

20

- 10

(-10)(-10) =

100

a minus always equals

25

-5

(-5)(-5) =

25

a plus.

30

0

(0)(0)

=

0

35

5

(5)(5)

=

25

40

10

(10)(10) =

100

45

15

(15)(15) =

225

Σ(X-u) =0,

Σ(X-u) 2

700

By squaring the differences, we have eliminated the problem of a total being equal to zero.

But this total of the squares does not consider the number of observations that contributed to the

result is a value called variance. For our example:

variance = Σ(X-u)2 = 700 = 100

N

7

FRAME 38.

Squaring the individual differences increased their magnitude. We must adjust or correct for this

increased magnitude or our measure of dispersion will be far too large and thus not

representative. The method for correcting this is to perform the opposite operation. Since we

squared the individual differences, the opposite operation would be to take the square root of the

variance. The square root of the variance is called standard deviation. Standard deviation is a

measure of dispersion Just like the centimeter is a measure of distance. Just as 5 centimeters

represents a greater distance than 2 centimeters, a standard deviation of 4 represents a greater

dispersion than a standard deviation of 2. The more variability or scatter in a group of

observations, the larger the standard deviation will be. To find the standard deviations when the

variance is 100, the following equation is used.:

standard deviation =

variance =

10

= 10