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Lesson 1-1
Collecting Data
FST - Notes
Name:________________________
Date:_________________________
Objectives
Use sampling and the capture-recapture method to make estimations about a population.
Analyze, interpret and evaluate data for its validity.
Book Notes - Vocabulary
Statistics
Data (qualitative vs. quantitative)
Variable
Population
Sample
Random
Bias
Capture Recapture Method
Class Notes
Examples
Reading Data
Use this table from The Statistical Abstract of the United States 1990
Characteristic
Travel by U. S. Residents by Selected Trip Characteristics: 1983 to 1988 (in Millions)
Trips
Person-Trips1
1984
1985
1986
1987
1988
1983
1984
1985
1986
528.2
558.4
592.3
636.3
656.1
1057.8
1012.0
1077.6
1121.5
1983
Total
540.9
Purpose
Visit friends
and relatives
181.9
180.5
206.8
214.9
210.5
213.8
384.6
384.6
Other Pleasure
189.6
170.5
177.6
200.3
234.4
241.5
401.4
349.7
Business or
convention
103.6
114.5
1333
140.0
157.5
155.6
146.4
15301
Other
65.8
62.7
40.7
37.1
33.9
45.1
125.4
121.6
Mode of transport
Auto, truck,
recreation
vehicle
396.1
380.9
376.1
405.6
433.7
472.6
839.8
794.0
Airplane
116.2
118.8
140.5
143.4
160.7
154.6
174.2
174.5
Other
28.6
28.5
41.8
43.3
41.9
28.9
43.8
43.5
Vacation Trip
307.8
333.3
339.8
354.3
366.2
396.2
642.3
689.8
Weekend Trip
225.5
211.4
224.0
252.0
274.4
27127
485.0
424.9
1
A count of times each person (child or adult) goes on a trip.
Source: US Travel Data Center, Washington, DC, National Travel Survey, annual. (Copyright.)
1987
1191.1
1988
1232.5
430.8
376.0
442.5
418.9
437.1
464.6
425.8
502.1
185.2
85.6
189.0
71.1
206.2
83.2
211.7
92.9
797.7
217.3
62.6
728.7
470.1
832.1
231.0
58.4
752.4
513.5
889.4
239.9
61.8
775.2
559.4
952.2
238.6
41.7
830.9
560.0
1.
Explain the information conveyed by the number 214.9 in the fourth column (1986)
under Trips.
2.
Which numbers in the fourth column total 592.3?
3.
How many trips were taken by airplane in 1987?
4.
How many people took trips by airplane in 1987??
Population, Sample, Variable, Bias, Random
For 1 and 2, identify the population, sample and the variable of interest
1.
Before cleaning a sofa with a new cleaning solution, a man cleans a 5 cm by 5 cm section
which is not visible.
2.
In July 1990 the city of Chicago announced that it would set up roadside checkpoints to
stop motorists at random in order to check for drunken drivers.
In 3 and 4 determine why a sample is used rather than a survey of the total population.
3.
The Nielsen television rating service determines the U.S. television ratings with a sample
of 1200 homes.
4.
A Fireworks company tests some of the sparklers it manufactures.
Population problems (Capture-Recapture Method)
1.
In order to estimate the number of blue gills in a small lake, a biologist captured and
carefully tagged 85 of the fish. She then released them. One week later she caught 122
blue gills, of which 18 were tagged. About how many blue gills are in the lake?
2.
In 1988 it was estimated that about 6.5 million Ghanaians could read English. If the
literacy rate was about 45% estimate the population of Ghana in 1988.
3.
A group of people were trying to estimate the number of Great Northern beans in a one
pound bag. They withdrew 50 beans and replaced them with pinto beans. They mixed
the beans well. They withdrew 120 beans of which 4 were pinto beans. About how
many Great Northern beans were in the original one-pound bag?
Homework pg 7-9
5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 19, 21-24
Lesson 1-2
Tables and Graphs
FST - Notes
Name:________________________
Date:_________________________
Objectives
Read and interpret bar graphs, circle graphs, coordinate graphs, stemplots, boxplots, and
histograms.
Draw graphs to display data.
Notes
Bar graphs
Pie Charts (Circle Graphs)
What are some things to consider when looking at representations (eg. graphs, charts) of data?
1.
2.
3.
Can data always be trusted? Why/why not?
How would you display the following data? Create a display that you think best represents these
data.
Examples
Reading Graphs
In 1-4, use the
following graph.
1.
What was the total median family income for
all regions in 1988?
2.
How did the total family income compare with
that for families in the South in 1988?
3.
How did the median income for families with one
or two earners compare with the median income for
families with three or more earners in 1988?
4.
True or False: Family income tended to be higher in
households with more than one earner.
In 5-7, use a pie chart at the right
from The Statistical Abstract of the
United Stated 1990.
5.
What group suffered the most
deaths from AIDS from 1982
to 1988?
6.
What age group had the least number of deaths
from AIDS from 1982 to 1988?
7.
About how many people under the age of 30 died
from AIDS from 1982 to 1998?
Drawing Graphs
8.
Advertising-Estimated Expenditures, by Selected Media (in Millions of Dollars)
Newspapers
Television
Radio
Direct Mail
1970
5704
3596
1308
2766
1980
14,794
11,469
3702
7596
1988
31,197
25,686
7798
21,115
Source: Statistical Abstract of the United States 1990, table no. 934
Draw a bar graph to display the total amount spent on advertising in these media in 1970,
1980, and 1988.
9.
The data below show how teenagers spend their money
Boys
Food, Snacks
Clothing
Entertainment
Music
Grooming
Spending
per Week
$10.10
$6.19
$4.35
$1.55
$1.10
Girls
Clothing
Food, Snacks
Entertainment
Grooming
Music
Spending
per Week
$10.65
$6.50
$3.45
$3.35
$1.80
Source: Rand Youth Poll, Summer/Fall 1990.
Draw a circle graph to show how boys spend their money.
Homework pg 13-16: 1-5, 7, 10,11, 12a(bar graph) b(circle graph), 14, 16, 17, 19-21
Review
1.
From several locations on an island, a naturalist catches 96 rabbits, tags them, and
releases them. Ten days later 120 rabbits are caught and 36 have tags. Estimate the
number of rabbits on the island.
2.
In order to learn the TV Habits of all Carlton students, those students entering the north
entrance of the school between 7:30 a.m. and 7:45 a.m. are asked which TV programs
they watched last night. Identify the population, the sample, and the variable of interest.
Lesson 1-3
Other Displays
FST - Notes
Name:________________________
Date:_________________________
Objectives
Read and interpret bar graphs, circle graphs, coordinate graphs, stemplots, boxplots, and
histograms.
Draw graphs to display data.
Definitions and terms
Scatterplot
Line Graph
Average Rate of Change
(Include Formula)
Increasing Interval
Decreasing Interval
Constant Interval
Stem-and-leaf diagram (Stemplot)
Maximum
Minimum
Range of data
Outliers
Back-to-Back Stemplot
Univariate Data vs. Bivariate Data
Examples
For 1-4 use the stemplot below
3rd Period
6th Period
1.
2 5
3 7 9
0 4
6 3 0 5 5 5 6
9 6 0 1 2 2
2 1 0 0 7 0 1 1 3 4 5
6 4 2 1 1 0 8 3 4 7 7
9 8 5 5 4 3 9 1 6
0 0 10
Identify the a. minimum, b. maximum, and c. range for both periods.
2.
How many students in each class took the test?
3.
How many students in each class scored in the 70’s?
4.
Which scores (if any) appear to be outliers in each class?
In 5-8 use the graph below of a science experiment. Acrylic acid was frozen in a test tube
containing a thermometer. Later the test tube was placed in a beaker of warm water in which a
second thermometer had been placed. Temperature readings were taken on both thermometers
over a period of time. These data were plotted on the graph.
5.
At what time was the water temperature 30oC?
6.
What was the initial temperature of the acrylic acid?
7.
What was the range of temperature for the water?
8.
Calculate the average rate of change of the water temperature over the first 40 minutes.
Why is the result negative?
9.
Use the data below for monthly normal temperatures in degrees Fahrenheit for Nashville,
TN and Seattle, WA. Draw a line graph.
Nashville
Seattle
Jan. Feb. Mar. Apr. May June
37
40
49
60
68
76
39
43
44
49
55
60
Source: The World Almanac and Book of Facts 1989
10.
Theresa Chair gave her FST classes a test on Chapter 1. the 4th period scores were
68 86 65 88 76 86 43 91
42 86 79 82 85 72 20 100
The 8th period scores were:
78 96 89 85 86 86 52 90
53 97 100 89 89 97 85
Make a back-to-back stemplot of these data.
Review
In Pepin county 5% of the residents (at least 10 years old) are illiterate. There are 85,450 people
who can read in the county. What is the population of Pepin county.
Homework pg 20-23:
1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20
Lesson 1-4
Measures of Center
FST - Notes
Name:________________________
Date:_________________________
Objectives
 Calculate the measures of center and measures of spread for a data set.
 Use ∑-notation to represent a sum, mean, variance, and standard deviation.
 Use statistics to describe and compare data sets.
Terms and Definitions
Summation Notation
Index Subscript
Measures of Center (Central Tendency)
Mean (Include notation and formula)
Median (Include a comparison when there is an even number of data versus an odd
number)
Mode
Class Notes
Examples
1.
Of the central measures, which one(s) can be numbers that are not in the data set?
When calculating measures of central tendency, which one(s) can have:
no answer?
more than one answer?
Do the mean, median, and mode have units?
Which central measure(s) of typical data require the data to be in numerical order from
smallest to largest?
2.
Use the stemplot
at the right. Find
a. the mean, b. the
median, and c. the
mode.
Mathematics Class Enrollment
0 9
1 2 4 4 5 7 8 9
2 0 4 6 6 7 7 7 8 9 9
3 2 3 3 6
3.
Jerry Attic was a dedicated golfer. His scores over a two month period were 93, 85, 85,
103, 97, 87, 88, 86, 94, 99, 101, 85, and 89. What would Jerry have to shoot in his next
game to lower his mean score to 90?
4.
In an algebra class of 24 students the mean grade on a test was 82; in another algebra
class with 30 students the mean was 74. What was the combined mean of the two
classes?
Suppose that xi equals the number of loaves of bread sold in the ith day by the corner grocery
store.
x1 = 15, x2 = 30, x3 = 29, x4 = 24, x5 = 31, x6 = 12
5
5.
Find
x
i2
i
6.
Write an expression using sigma (summation notation) which indicates the total number
of loaves of bread.
7.
Write an expression using summation notation which indicates the mean number of
loaves of bread sold daily.
8.
Calculate the following
15
a.
w
w6
6
b.
 3s
s2
4
c.
x
i 1
2
i
9.
The weekly salaries of workers in a small factory are $250, $250, $375, $400, $400,
$400, $400, $425, $500, and $900. If the top salary is increased to $1000, how will that
affect the
a.
mean?
b.
median?
10.
If data values are bunched close together, then ________________________ is probably
the best measure of center. Outliers will have less effect on ______________________
or the middle data.
Homework pg 27-30: 5, 6, 9-12,14, 16-18, 21, 22, 24
Lesson 1-5
Quartiles, Percentiles, and Box Plots
FST - Notes
Name:________________________
Date:_________________________
Book Notes
Rank-Ordered
Quartiles
Second Quartile (Middle)
First Quartile (Lower)
Third Quartile (upper)
Interquartile Range / IQR
Five Number Summary
Box Plot
Percentile
Class Notes
Suppose that we measure the heights in inches of the players on a baseball team.
There heights in inches are
86
70
68
71
61
63
62
60
64
Below is the data of heights of children in a small elementary class.
The units are in centimeters
63, 79, 84, 84, 87, 88, 90, 95, 97, 102
The child with the height of 95 cm is at what percentile?
The child with the height of 84 cm is at what percentile?
Which child is at the 40th percentile?
Which child that is at least at the 75th percentile?
Examples
1.
Consider the following data concerning mathematics class enrollment at one school
Mathematics Class Enrollment
0 9
1 2 4 4 5 7 8 9
2 0 4 6 6 7 7 7
3 2 3 3 6
a.
Find the median
b.
Find the first quartile
c.
Find the third quartile
d.
Find the interquartile range
9
7
7
8
8
9
2.
Draw the box-plot that represents the data.
3.
Determine if there are any outliers and adjust your plot according to your findings.
4.
What is the class enrollment at the
a.
12th percntile?
b.
80th percentile?
5.
At what percentile is the class with 33 students?
6.
Name a situation when you would like to be above the 90th percentile?
7.
Name a situation where you would like to be lower than the 10th percentile?
8.
Below is a list of years and hits for Tony Gwynn’s major league career. Make a box plot
using Tony’s hits per year.
1982 - 55
1987 - 218
1992 - 165
1997 - 220
1983 - 94
1988 - 163
1993 - 175
1998 - 148
1984 - 213
1989 - 203
1994 - 165
1999 - 139
1985 - 197
1990 - 177
1995 - 197
2000 - 41
1986 - 211
1991 - 168
1996 - 159
2001 - 33
Homework pg 35-37: 1-12, 15, 16
Lesson 1-6
Histograms
FST - Notes
Name:________________________
Date:_________________________
Objectives

Read and interpret bar graphs, circle graphs, coordinate graphs, stemplots, boxplots, and
histograms.

Draw graphs to display data.

Use statistics to describe and compare data sets.
Understand the difference between bar graphs and histograms.
Terms and Definitions
Histogram
Frequency
Frequency Distribution
Relative Frequency Distribution
Frequency Table
Class Notes
Consider the frequency table displaying the number of absences after 1 month of Mr. Witte’s
class last year.
# of days absent
0
1
2
3
4
5
6
7
8
9
# of students
1
2
1
4
7
3
4
0
0
1
How many students are there?
How many total absences?
What is the average number of absences?
What is the median number of absences?
Examples
1.
The table at the right gives the relative frequency of arrests
by age group in the U.S.
in 1988.
Relative
Frequency
.05
.21
.21
.18
.14
.09
.05
.03
.02
.03
Age
Under 15
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55 and over
a. About __________% of those arrested are
between the ages of 15 and 54.
b. The “55 and over” group accounted for _______% less
arrests than “30-39” group.
Source: Information Please
Almanac Atlas and Yearbook 1990
2.
Below are the 1950 and the projected 2075 distributions of the population in the U.S.
2075
40
1950
30
Population (in millions)
25
20
15
10
5
35
30
25
20
15
10
5
Age group (years)
4.
100-109
90-99
80-89
70-79
60-69
50-59
40-49
30-39
20-29
0-9
100-109
90-99
80-89
70-79
60-69
50-59
40-49
30-39
20-29
10-19
0
0-9
0
10-19
Population (in millions)
35
Age group (years)
a.
The total population in 1950 was about 151.1 million. In what age group was the
median age?
b.
How does the relative number of children (ages 0-9) in 1950 compare with the
relative number of children projected in 2075?
c.
In what ways are the distributions different?
The following table gives the number of
deaths due to heart disease and cancer in
the U.S. in 1986.
a.
Draw a histogram for the Cancer
column.
b.
Which measure of center most
accurately represents the data?
Homework: pg 41-45
1-4, 6, 10-13, 19
Age
15-24
25-34
35-44
45-54
55-64
65-74
75-84
Number of Deaths (in 1000s) Due to
Heart Disease
Cancer
1.1
2.1
3.7
5.6
12.4
15.0
33.0
37.8
94.3
98.9
180.8
146.8
238.0
116.6
Source: Statistical Abstract of the United States 1990
Lesson 1-8
Name:________________________
Variance and Standard Deviation
FST - Notes
Date:_________________________
Objectives

Calculate the measures of center and measures of spread for a data set.

Describe the relationship between measures of center and measures of spread.

Use ∑-notation to represent a sum, mean, variance, and standard deviation.
Use statistics to describe and compare data sets.
Terms and Definitions
Measures of Spread
Deviation
Standard Deviation (Include Formula with Notation)
Variance (Include Formula with Notation)
How are standard deviation and variance related?
Class Notes
Consider the following situation.
One physics class was testing the elasticity of rubber bands. As a measure of strength and durability they stretched a
rubber band out 8 inches and "let 'r fly." They then measured the distance it flew. Two groups used two different
rubber bands and performed this experiment 7 times. Their data are recorded below.
Group A distance (cm):
Group B distance (cm):
{182, 186, 182, 184, 185, 184, 185}
{152, 194, 166, 216, 200, 176, 184}
What statistics can we use to compare this data?
Examples
1.
Central tendencies include ___________________, ____________________, and
_________________.
2.
Measures of spread include ___________________, ___________________,
_________________, and _________________
3.
Suppose the data set was the wing span of the common housefly. Which would be a
reasonable deviation from the mean?
3’ 5”
.2 cm
4.
Now suppose that the data set was the cost of a new motor cycle. Which would be a
“reasonable” measure of spread?
$0.25
5.
6 cm
$1.00
$1500.00
$30,000.00
Which of the following is a correct formula for finding the
standard deviation on the data set a1, a2, a3, …, a20?
20
 (a
a.
i 1
i
 a20 )
2
19
20
b.
20
 (a  a )
 ( ai  a 2 )
c.
2
i 1
19
 20

  ( ai  a ) 
 i 1

19
d.
i 1
i
19
2
2
6.
Find the standard deviation of each data set.
a.
43, 47, 50, 56, 60, 64, 65, 72, 75, 87
b.
5, 5, 6, 7, 9, 10, 10, 12.
c.
If we are allowed to changed the data, how could we make a set using 5, 6, 7, 9,
10, and 12 has the same mean but a smaller standard deviation?
7.
If y is the variance of a set of n numbers, which of these is
the standard deviation of the set?
y
y
a.
b.
c. y
d. y 2
n
n 1
8.
If the standard deviation of a data set is 4.9, what is the variance?
9.
The average monthly precipitation, in inches, for Juneau is given below.
3.7
3.7
3.3
2.9
3.4
3.0
4.1
5.0
6.4
7.7
5.2
4.7
a.
Find the mean and standard deviation of these data.
b.
How many of these data are within one standard deviation of the mean?
Homework: pg 55-58
1, 2, 4, 5(No Calc & Calc), 8-11, 13, 16, 17