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Unit 9 Seminar Agenda
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Final Project and Due Dates
Measures of Central Tendency
Measures of Dispersion
Celebrate!
Copyright © 2009 Pearson Education, Inc.
Slide 13 - 1
Final Project and Due Dates
• Final project is due to the dropbox by Tuesday,
September 6th by 11:59 PM ET.
• Late final projects will be docked 5% per day late and will
not be accepted after 4 days late.
• If you have any questions about the assignment
requirements there is a page in the Unit 9 introduction
with all of the info you should need, as well as some
sample projects to give you an idea of what I'm
expecting from the finished product.
• Late assignments: The last day to submit any late
assignments or message board posts will be Sunday,
September 11th, 11:59 PM ET.
Copyright © 2009 Pearson Education, Inc.
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9.1 Measures of Central Tendency
• An average is a number that is representative
of a group of data.
• The arithmetic mean, or simply the mean is
symbolized by x , when it is a sample of a
population or by the Greek letter mu,  ,
when it is the entire population.
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Mean
• The mean, is the sum of the data divided by
the number of pieces of data. The formula for
calculating the mean is
Sx
x
n
• where Sx represents the sum of all the data
and n represents the number of pieces of
data.
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Slide 13 - 4
Example-find the mean
• Find the mean amount of money parents
spent on new school supplies and clothes if 5
parents randomly surveyed replied as follows:
$327 $465 $672 $150 $230
327  465  672  150  230 1844
x

 368.8
5
5
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Median
• The median is the value in the middle of a set
of ranked data.
• Example: Determine the median of
$327 $465 $672 $150 $230.
Rank the data from smallest to largest.
$150 $230 $327 $465 $672
middle value
(median)
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Example: Median (even data)
• Determine the median of the following set of data: 8, 15, 9, 3,
4, 7, 11, 12, 6, 4.
Rank the data:
3 4 4 6 7 8 9 11 12 15
There are 10 pieces of data so the median will
lie halfway between the two middle pieces the 7
and 8.
The median is (7 + 8)/2 = 7.5
3 4 4 6 7 8 9 11 12 15
(median) middle value
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Mode
• The mode is the piece of data that occurs
most frequently.
• Example: Determine the mode of the data set:
3, 4, 4, 6, 7, 8, 9, 11, 12, 15.
• The mode is 4 since it occurs twice and the
other values only occur once.
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Example
• The weights of eight Labrador retrievers
rounded to the nearest pound are 85, 92, 88,
75, 94, 88, 84, and 101. Determine the
a) mean
c) mode
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b) median
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Example--dog weights 85, 92, 88, 75,
94, 88, 84, 101
a. Mean
85  92  88  75  94  88  84  101 707
x

 88.375
8
8
b. Median
Rank the data:
75, 84, 85, 88, 88, 92, 94, 101
The median is 88.
c. Mode-the number that occurs most
frequently. The mode is 88.
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Measures of Position
• Measures of position are often used to make
comparisons.
• Two measures of position are percentiles and
quartiles.
• Both measure how many data points are less
than the given value.
• 1st Quartile – 25% of the data values are less
than the 1st Quartile
• 99th Percentile – 99% of the data values are
less than the 99th Percentile
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To Find the Quartiles of a Set of Data
1. Order the data from smallest to largest.
2. Find the median, or 2nd quartile, of the set of
data. If there are an odd number of pieces of
data, the median is the middle value. If there
are an even number of pieces of data, the
median will be halfway between the two
middle pieces of data.
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Slide 13 - 12
To Find the Quartiles of a Set of Data
continued
3. The first quartile, Q1, is the median of the
lower half of the data; that is, Q1, is the
median of the data less than Q2.
4. The third quartile, Q3, is the median of the
upper half of the data; that is, Q3 is the
median of the data greater than Q2.
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Slide 13 - 13
Example: Quartiles
• The weekly grocery bills for 23 families are as
follows. Determine Q1, Q2, and Q3.
170
330
225
75
95
210
80
225
160
172
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270
170
215
130
190
270
240
310
74
280
270
50
81
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Example: Quartiles continued
• Order the data:
50
75
74
160 170 170
225 225 240
310 330
80
172
270
81
190
270
95
210
270
130
215
280
Q2 is the median of the entire data set which
is 190.
Q1 is the median of the numbers from 50 to
172 which is 95.
Q3 is the median of the numbers from 210 to
330 which is 270.
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Slide 13 - 15
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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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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Slide 13 - 17
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.
s
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
S xx

2
n 1
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To compute mean and standard deviation
using a calculator
•In Windows choose Start > Accessories >
Calculator
• Select View > Statistics
• Enter numbers then the Add key to create a
list
• Use the x-bar key for mean
• Use the σ(n-1) key for sample standard
deviation
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Slide 13 - 19
To compute mean and standard deviation using the web/Excel
http://www.easycalculation.com/statistics/statistics.php
In Excel use the Average() function for mean.
Use the Stdev() function for sample standard deviation.
Copyright © 2009 Pearson Education, Inc.
Slide 13 - 20
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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Slide 13 - 21
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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Slide 13 - 22
Example
• Find the standard deviation of the following
prices of selected washing machines:
$280, $217, $665, $684, $939, $299
Find the mean.
280  217  665  684  939  299 3084
x

 514
6
6
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Slide 13 - 23
Example continued, mean = 514
Data
217
280
299
665
684
939
Data  Mean
297
234
215
151
170
425
0
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(Data  Mean)2
(297)2 = 88,209
54,756
46,225
22,801
28,900
180,625
421,516
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Example continued, mean = 514
s

S xx

2
n 1
421,516

 84303.2  290.35
5
• The standard deviation is $290.35.
Copyright © 2009 Pearson Education, Inc.
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