Transcript Standard Deviation

9.7: Standard Deviation
Analyzing Data
 Consider these sets of data:
 60, 70, 80, 90, 100

The mean is:
80
 78, 79, 80, 81, 82

The mean is:
80
Average or Mean doesn’t always
tell the whole story!
 That’s where standard deviation
comes into play.
 Standard Deviation tells us how
spread out our data is.
___________
Standard Deviation
 The higher the standard deviation is,
the more the data is varied, therefore
less reliable
making it ______________.
 The lower the standard deviation is,
the more consistent your data is,
more reliable
making it ________________.
Steps to find standard deviation
1. Find the mean of your data (the
average!) We’ll call it m.
2. Take the difference between each
member of the set and the mean.
x-m
3. Square each of these numbers.
(x – m)2.
Steps to find standard deviation
(continued)
4. Take the average of this set of
numbers. (this is called the
variance
_______).
5. Take the square root of this number….
now you’ve found the standard
deviation.
Ex. 1:
x
2
6
7
9
11
2, 6, 7, 9, 11
Mean: m =
7
(x – m) (x – m)2
-5
-1
0
2
25
4
16
1
0
4
Variance:
9.2
Standard
Deviation:
3.03
Ex. 2:
x
90
65
78
92
84
90, 65, 78, 92, 84
Mean: m =
81.8
(x – m) (x – m)2
Variance:
8.2
-16.8
-3.8
10.2
67.24
94.56
282.24
14.44
104.04
Standard
Deviation:
2.2
4.84
9.72
Which of the previous sets of data
would be more reliable?
Compare Standard Deviations!!!
3.03 and 9.73
Data is less varied
so more reliable!!