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1.
Homework, Page 768
Make a stemplot of the data in table 9.11.
Year
Home Runs
1957
14
1958
28
1959
16
1960
39
1961
61
1962
33
1963
23
1964
26
1965
8
1966
13
1967
9
1968
5
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0
1
2
3
4
5
6
5
3
3
3
8 9
4 6
6 8
9
1
Slide 9- 1
Homework, Page 768
5. Make a back-to-back stemplot of the life
expectancies of males and females in South
America. Use whole years and split stems.
Male Age Female
3
0
6
8 8 8
7
6
5
8
3 3 3 2 2
1
7
1
2
7
5
6 7 7 9 9
8
0
0
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Slide 9- 2
Homework, Page 768
9. Draw a histogram of the frequency table in
Exercise 7.
y
Age
Frequency
60.0  64.9
2
65.0  69.9
4
70.0  74.9
6
60
65
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70
75
x
Slide 9- 3
Homework, Page 768
13. Make a time plot of Willie Mays’ annual
home run totals.
Home Runs by Willie Mays
60
Home Runs
50
40
30
Home Runs
20
10
0
1940
1950
1960
1970
1980
Year
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Slide 9- 4
Homework, Page 768
17. Make a time plot of men’s winnings.
PGA Top Winners' Winnings
Winnings ($1,000)
10000
8000
6000
4000
2000
0
1960 1970 1980 1990 2000 2010
Year
Winnings growth was approximately linear until the late 1990s
when it became almost exponential for several years.
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Slide 9- 5
Homework, Page 768
21. Make a time plot comparing the home run
totals of Willie Mays and Mickey Mantle.
Home Run comparison
60
Home Runs
50
40
Mays
30
Mantle
20
10
0
1940
1950
1960
1970
1980
Year
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Slide 9- 6
Homework, Page 768
25.
Compare the populations of California, New York, and
Texas from 1900 t0 2000.
Population (Millions)
Population comparison for CA, NY, and TX
40
35
30
25
20
15
10
5
0
1850
CA
NY
TX
1900
1950
2000
2050
Year
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Slide 9- 7
Homework, Page 768
29.
A.
B.
C.
D.
E.
A time plot is an example of a
Histogram
Bar graph
Line graph
Pie chart
Table
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Slide 9- 8
Homework, Page 768
31.
The histogram below would most likely result from which
set of data?
A. test scores for a fairly easy test
B. weights of children in a third-grade class
C. winning soccer scores for a team over the course of a year
D. ages of all people visiting the Bronx Zoo at a given point in
time
E. prices of all the desserts on the menu at a certain restaurant
y
x
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Slide 9- 9
9.8
Statistics and Data (Algebraic)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Quick Review
Write the sum in expanded form.
5
1.  x
i
i 0
1
2.  x
3
1
3.  x  x
3
Write the sum in sigma notation
4. x f  x f  x f  x f
3
i
i 1
3
i 1
2
2
1
5.
20


i
3
3
4
4
5
5
 x  x    x  x    x  x    x  x  
2
1
2
2
2
3
2
4
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Slide 9- 11
Quick Review Solutions
Write the sum in expanded form.
x x  x x  x x
5
1.  x
i 0
i
0
1
2
3
4
5
1
1
2.  x
x  x  x 
3
3
1
1
3.  x  x
x x x xx x
3
3
Write the sum in sigma notation
3
i
i 1
3
i 1

1
2
 
i
3
1
2
4. x f  x f  x f  x f
2
2
1
5.
20
3
3
4
4
5
3

5
5
x f
i
i 2
i
 x  x    x  x    x  x    x  x  
2
1
2
2
2
3
2
4
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
1
 x x
20
4
i 1
i

2
Slide 9- 12
What you’ll learn about






Parameters and Statistics
Mean, Median, and Mode
The Five-Number Summary
Boxplots
Variance and Standard Deviation
Normal Distributions
… and why
The language of statistics is becoming more commonplace in our
everyday world.
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Slide 9- 13
Mean
The mean, commonly called the average, of a
list of n numbers  x , x ,..., x  is
1
2
n
x  x  ...  x 1
x
 x.
n
n
n
1
2
n
i 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
i
Slide 9- 14
Median
The median of a list of n numbers {x1,x2,…,xn}
arranged in order (either ascending or
descending) is
 the middle number if n is odd, and
 the mean of the two middle numbers if n is
even.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 9- 15
Mode
The mode of a list of numbers is the number that
appears most frequently in the list.
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Slide 9- 16
Finding Mean, Median, and Mode
To find the Mean and Median, enter the data in one of the lists,
then, on the Stat menu, select Calc, and then select 1-Var Stats
and press enter. In the parentheses after 1-Var Stats on the home
screen, enter the list containing the data and close the parentheses
and press enter. The stats will be displayed on the screen. x
indicates the mean. Median is indicated by Med.
 To find the mode, return to the Stat menu and select either Sort
A or Sort D, and press enter. Indicate the list in which your data
is located and close the parentheses and press enter. When the
screen displays Done, return to the list and it will be in numerical
order. Go through it and find which number appears most
frequently and that is the mode.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 9- 17
Example Finding Mean, Median, and
Mode
Find the (a) mean, (b) median, and (c) mode of the data:
3, 6, 5, 7, 8, 10, 6, 2, 4, 6
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Slide 9- 18
Weighted Mean
The formula for finding the mean of a list of numbers  x , x ,..., x  with
1
2
n
n
frequencies  f , f ,..., f
1
2
n

x f
x f  x f  ...  x f
is x 

.
f  f  ...  f
f
1
1
2
2
n
n
i 1
i
i
n
1
2
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n
i 1
i
Slide 9- 19
Quartiles and Percentiles
If a set of data is arranged in order, it may be divided into
fourths. Each fourth is called a quartile.
 The first quartile, Q1,is the median of the lower half of the
data, the second quartile, Q2, is the median, and the third quartile,
Q3, is the median of the upper half.
 The interquartile range (IQR) measures the spread between
the first and third quartiles, the middle half of the data.

IQR  Q3  Q1
If your test results say you are in the 60th percentile, that
means that you scored better than 60% of the test takers.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 9- 20
Five-Number Summary
The five - number summary of a data set is the collection
minimum, Q , median, Q , maximum .
1
3
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Slide 9- 21
Boxplot
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Slide 9- 22
Box and Whisker or Box Plot
The box and whisker or box plot is a graph that depicts the
five-number summary of a data set.
 To graph a box plot, do the following:
 Enter the data in one of the lists in the stats menu
 Use second and Y= to select one of the plot menus
 Under type, select the icon in the middle of the second row
 Indicate which list contains the data at Xlist:
 Press zoom 9 to see the box plot

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Slide 9- 23
Box and Whisker or Box Plot Continued
Using the trace command and the right and left
arrows, we can find the values of the five numbers in
the five number summary:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 9- 24
Outlier
A number in a data set can be considered an
outlier if it is more than 1.5×IQR below the first
quartile or above the third quartile.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 9- 25
Standard Deviation
The standard deviation of the numbers  x , x ,..., x  is
1


2
n
1

 x  x , where x denotes the mean.
n
The variance is  , the square of the standard deviation.
n
i 1
i
2
2
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Slide 9- 26
Normal Curve
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Slide 9- 27
The 68-95-99.7 Rule
If the data for a population are normally distributed
with mean μ and standard deviation σ, then
 Approximately 68% of the data lie between
μ – 1σ and μ + 1σ.
 Approximately 95% of the data lie between
μ – 2σ and μ + 2σ.
 Approximately 99.7% of the data lie between
μ – 3σ and μ + 3σ.
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Slide 9- 28
The 68-95-99.7 Rule
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Slide 9- 29
Example, Page 782
Find the mean of the data set.
6. {27.4, 3.1, 9.7, 32.3, 12.8, 39.4, 73.7}
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Slide 9- 30
Example, Page 782
14.
A painting crew in College Station, PA painted 12 houses
in 5 days and a crew in College Station, TX painted 15 houses in
7 days. Determine the average number of houses each crew
painted per day. Which crew had the greater rate?
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Slide 9- 31
Example, Page 782
A) Find the average of the indicated temperatures in Beijing.
B) Find the weighted average using the number of days in the month.
Month
High
Low
January
2
-9
February
5
March
High
Low
July
32
22
-7
August
31
21
12
-1
September
27
14
April
20
7
October
21
7
May
27
13
November
10
-1
June
31
18
December
3
-7
20.
Month
The monthly high temperatures.
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Slide 9- 32
Example, Page 782
B) Find the weighted average using the number of days in the month.
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Slide 9- 33
Homework




Homework Assignment #34
Read Section 10.1
Page 782, Exercises: 1 – 45(EOO), 47
Quiz next time
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Slide 9- 34