1. 7.5 The Variance and Standard Deviation
Definitions
The Formula
Variance measures the dispersal of the information.
Basically, how spread out is the data?
If the variance is small:
The data is concentrated about the mean
If the variance is large:
The data is more spread out about the mean
Let’s try!
Find the mean
Calculate the variance
Value
Prob
0.1 1
0.3 2
0.5 3

2. 7.5 The Variance and Standard Deviation
Another Formula!!
Another Example!!
This formula calculates the variance as well, but it can be a little simpler than the other…
Try it out… does it work?
Calculate the variance of this information.
Value (X)
Freq 3 1 8 2 5 12 4 13 9
Value (X) X2
Prob
0.1 1
0.3 2 4
0.5 3 9

3. 7.5 The Variance and Standard Deviation
Definitions
Variance:
Definition:
Tells us how spread out the data is.
Formula(s):
Standard Deviation:
Definition:
Statistic used to measure the dispersal about the mean
The reason this is good is because Var(X) is based upon the X values, whereas the standard deviation is “generic”
Formula(s):

4. 7.5 The Variance and Standard Deviation
Examples
State the variance from the previous two examples.
What do they tell us about the data?
Calculate the standard deviation of both.
What does this tell us about the data?

5. 7.5 The Variance and Standard Deviation
Problems to complete from 7.5
Pg #1, 2