12­4 Standard Deviation 2011
February 16, 2011
12­4
Standard Deviation
Objective: To calculate the standard
deviation of a set of values
Feb 8­12:35 PM
1
12­4 Standard Deviation 2011
February 16, 2011
Warm­Up
Find the Mean, Median and Mode of data sets.
#1
5, 6, 7, 8, 9, 10, 11, 12, 13
#2
1, 4, 8, 2, 12, 6, 28, 14, 6
Feb 16­9:09 AM
2
12­4 Standard Deviation 2011
February 16, 2011
What is Standard Deviation?
Definition: The measure of how much the values in a data
set vary from the mean.
Notation: Sigma =
How do we find Standard Deviation?
Feb 8­12:38 PM
3
12­4 Standard Deviation 2011
February 16, 2011
Example: Find the standard deviation for the following values:
48, 53, 52, 46, 49
__
Find: x
__
x
__
x
__
x ­ x
__
__
(x ­ x)2
Find:
Find:
Find:
Feb 8­12:44 PM
4
12­4 Standard Deviation 2011
February 16, 2011
Colombia
Kuwait
Colorado
Feb 16­8:36 AM
5
12­4 Standard Deviation 2011
February 16, 2011
Colombia
Kuwait
__
x
__
x
__
__
x ­ x
__
(x ­ x)2
Colorado
Feb 16­8:42 AM
6
12­4 Standard Deviation 2011
February 16, 2011
Definition
The interquartile range is the difference between the third and first quartiles. Feb 16­8:46 AM
7
12­4 Standard Deviation 2011
February 16, 2011
Definition
The number of standard deviations a value is from the mean is called the Z­Score.
z­score
value ­ mean
standard deviation
__
= x­x
Example: A set of values has a mean of 85 and a standard
deviation of 6. Find the z­score of the value 76.
Feb 16­8:52 AM
8
12­4 Standard Deviation 2011
February 16, 2011
Example: A set of values has a mean of 28 and a standard
deviation of 3.5. Find the value if the z­score is 4.
Feb 8­1:35 PM
9
12­4 Standard Deviation 2011
February 16, 2011
Homework
12­4
Pg. 672 # 1, 3, 4, 5,
10­16 even, 17­20, 30
Feb 8­1:54 PM
10