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Copyright © 2009 Pearson Education, Inc.
Chapter 13 Section 6 - Slide 1
Chapter 13
Statistics
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Chapter 13 Section 6 - Slide 2
WHAT YOU WILL LEARN
• Range and standard deviation
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Chapter 13 Section 6 - Slide 3
Section 6
Measures of Dispersion
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Chapter 13 Section 6 - Slide 4
Measures of Dispersion

Measures of dispersion are used to indicate the
spread of the data.

The range is the difference between the highest
and lowest values; it indicates the total spread
of the data.
Range = highest value – lowest value
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Chapter 13 Section 6 - Slide 5
Example: Range


Nine different employees were selected and the
amount of their salary was recorded. Find the
range of the salaries.
$24,000
$32,000 $26,500
$56,000 $48,000 $27,000
$28,500 $34,500 $56,750
Range = $56,750  $24,000 = $32,750
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Chapter 13 Section 6 - Slide 6
Standard Deviation

The standard deviation measures how much
the data differ from the mean. It is symbolized
with s when it is calculated for a sample, and
with  (Greek letter sigma) when it is calculated
for a population.
 x  x 
2
s
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n 1
Chapter 13 Section 6 - Slide 7
To Find the Standard Deviation of a
Set of Data
1. Find the mean of the set of data.
2. Make a chart having three columns:
Data
Data  Mean
(Data  Mean)2
3. List the data vertically under the column
marked Data.
4. Subtract the mean from each piece of data and
place the difference in the Data  Mean
column.
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Chapter 13 Section 6 - Slide 8
To Find the Standard Deviation of a
Set of Data (continued)
5. Square the values obtained in the Data  Mean
column and record these values in the
(Data  Mean)2 column.
6. Determine the sum of the values in the
(Data  Mean)2 column.
7. Divide the sum obtained in step 6 by n  1,
where n is the number of pieces of data.
8. Determine the square root of the number
obtained in step 7. This number is the standard
deviation of the set of data.
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Chapter 13 Section 6 - Slide 9
Example

Find the standard deviation of the following
prices of selected washing machines:
$280, $217, $665, $684, $939, $299
Find the mean.
x 280  217  665  684  939  299

x

n
3084

 514
6
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6
Chapter 13 Section 6 - Slide 10
Example (continued), mean = 514
Data
217
280
299
665
684
939
Data  Mean
297
234
215
151
170
425
0
Copyright © 2009 Pearson Education, Inc.
(Data  Mean)2
(297)2 = 88,209
54,756
46,225
22,801
28,900
180,625
421,516
Chapter 13 Section 6 - Slide 11
Example (continued), mean = 514

421,516
s
6 1
421,516
s
 290.35
5

The standard deviation is $290.35.
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Chapter 13 Section 6 - Slide 12