Download Lesson 17 Feb IV 1b

Math Tech IIII, Feb 17
Measures of Variation
Book Sections: 2.4
Essential Questions: How do I compute and use statistical values? What
are measures of variation and how can I compute them?
Standards: PS.SP.ID.1, .2
What are Measures of Variation?
• Values that show how data is spread out with
respect to the center.
 The center value used today is the mean
Today’s Measures of Variation
When measures of central tendency are just not enough
Measure
Symbol
Calculator
Symbol
• Range
• Variance
s2
• Standard Deviation
s
sx
• Mean
x
x
Range
• The range (R) is an indication of the spread of
a data set, and is computed by:
R = highest value – lowest value
Example
The salaries for the staff of the XYZ Manufacturing Co. are
shown in the following table. Find the range of this data.
Staff
Owner
Manager
Sales Rep
Workers
Salary ($)
100,000
40,000
30,000
25,000
15,000
18,000
Variance and Standard Deviation
• Statistics that show how dispersed a data
set is about its mean.
• Variance (s2)
• Standard Deviation (s) – the square root of
variance. s  s 2
Computational Formulas for s2 and s
Variance
Standard Deviation
 X  (( X ) / n)
s 
n 1
2
2
2
s s
2
Squares and Square Roots, Why?
• We find the distance from the mean to
every data point, and square it because we
don’t want negative values in the
computation. That gives us variance.
• Finding the square root of variance as
standard deviation puts that value, s, into
the same units as the raw data.
Variance and Standard Deviation
Need to Know
• Variance (s2)
If you have standard deviation and want
variance  square the standard deviation
• Standard Deviation (s)
If you have variance and want standard
deviation  take the square root of the
variance
• Know this: standard deviation is the
square root of variance
Examples
The variance of a data set is 134.5, what is the standard
deviation?:
If the standard deviation of a data set was 2.8, about what would
be the variance of that set?
Calculator Language
• s is sx on the calculator. The calculator has no s2,
how do I get it. Square s! or [List]  [Math] 8
Help Me Mr. Texas
The calculator can compute what you need here:
How?
1-Var Stats
Example 1
Find the sample variance and standard deviation for the following
data set:
35, 45, 30, 35, 40, 25
Example 2
Compute the mean and standard deviation of the following data
set::
34, 32, 30, 27, 35, 30, 28, 32, 36, 26
Variability – The Concept
• Variability is how spread out a set of data is.
• In comparing two data sets to see which one is more
variable – compute both standard deviations. The one
with the largest s is more spread out and is said to be
more variable.
• You can sometimes see variability in a data set, but
most of the time you can’t. You can always compute
and compare s’s.
Examples
The average daily high temps for January for 10 selected cities is:
50, 37, 29, 54, 30, 61, 47, 38, 34, 61
And their normal monthly precipitation for January is:
48, 26, 15, 18, 18, 33, 51, 11, 18, 25
Which set is more variable?
Variability by Sight
Which data set is more variable:
Variability by Sight
Which data set is more variable:
(a)
Data 101
S1: 34, 32, 30, 27, 35, 30, 28, 32, 36, 26
    
10
15
20
25
30
35
40
45
50
S2: 15, 47, 11, 32, 30, 51, 26, 46, 16, 36

10

15

20
25
 
30

35

40
45

50
S3: 34, 32, 30, 27, 35, 30, 28, 32, 36, 26

10
15
 
   
 
20
25
30
35
40
45
50
Data 102
S4: 11, 27, 30, 28, 30, 32, 34, 32, 35, 51
    

10
15
20
25
30

35
40
45
50
S2: 15, 47, 11, 32, 30, 51, 26, 46, 16, 36

10

15

20
25
 
30

35

40
45

50
S5: 15, 16, 17, 16, 18, 44, 46, 45, 46, 47


10
15
20
 
25
30
35
40
45
50
Which set Is More Variable
12, 20, 18, 14, 26, 24, 16, 22, 30, 24
18, 30, 27, 21, 34, 36, 24, 33, 40, 36
Class work: CW 2/17/17 1b, 1-8
Homework: None