Unit 1 | Spring 2011
Statistics Review
Tues
1/4
Vocabulary Review
p. 2-3
Wed
1/5
Types of Categorical Graphs
(Pie chart, Bar graph, Pareto)
p. 4
Thurs
1/6
Types of Quantitative Graphing
(Histogram, Boxplots, Double-line graph,
Scatterplot, Stem-and-leaf)
p. 6-8
Fri
1/7
Quiz
(Pep Rally)
Mon
1/10
Making Quantitative Graphs
(Scatterplots)
p. 9-10
Tues
1/11
Histograms
p. 12
Wed
1/12
Histograms
p. 13
Thurs
1/13
Interpreting Quantitative Graphs
Worksheet 1
Fri
1/14
Interpreting Quantitative Graphs
Worksheet 2
Mon
1/17
No School!!!
Tues
1/18
Quiz over Quantitative Graphs
Wed
1/19
Venn Diagrams (2 Groups)
p.14-15
Thurs
1/20
Venn Diagrams (3 Groups)
p. 16-18
Fri
1/21
Vocabulary of Venn Diagrams
(And, Or, Only, Not, None, All of the above)
Mon
1/24
Review
Tues
1/25
Test
Statistics Unit 1-Spring 2011
Review Worksheet
Page 1
Statistics
Spring 2011
Name: _________________________________
Fill in the blank, there is a word bank on the next page.
1. _______________________________________________ occurs when some groups in the population are
left out of the process of choosing the sample.
2. A _______________________________________________ consists of people who choose themselves by
responding to a general appeal.
3. A _______________________________________________ is the part of the population that we actually
examine in order to gather information.
4. When a population that is divided into strata from which separate simple random samples are collected and then
combined to make one simple random sample, this sample is called
_______________________________________________.
5. _______________________________________________ is when a study systematically favors certain
outcomes.
6. A _______________________________________________ gives each member of the population a known
chance (greater than zero) to be selected.
7. _______________________________________________ is when neither the subjects nor personnel know
who receives which treatment.
8. _______________________________________________ is the use of chance to divide experimental
units into groups.
9. When those being studied are people, they are referred to as ____________________________________.
10. When the effects of an explanatory variable or lurking variable cannot be distinguished from each other, this
is called
_______________________________________________.
11. _______________________________________________ observes individuals and measures variables of
interest but does not attempt to influence responses.
12. _______________________________________________ is a random assignment of similar experimental
units to treatments carried out separately within each group.
13. An observed effect so large that it would rarely occur by chance is called
Statistics Unit 1-Spring 2011
Page 2
_______________________________________________.
14. _______________________________________________ is when an individual cannot be contacted or
refuses to cooperate.
15. A specific experiment condition that is applied to experimental units is called
_______________________________________________.
16. _______________________________________________ are individuals on which the experiment is done.
17. A(n) _______________________________________________ deliberately imposes some treatment on
individuals in order to observe their responses.
18. _______________________________________________ is a long string of digits 0-9 that are equally
likely and independent from each other.
19. _______________________________________________ is the entire group of individuals that we want
information about.
20. _______________________________________________ of size “n” consists of “n” individuals from the
population chosen in such a way that every set of “n” individuals has an equal chance to be the sample actually
selected.
WORD BANK
individuals
correlation
Randomization
variable
Probability Sample
Observational Study
categorical variable
Stratified Random Sample
Experiment
quantitative variable
Undercoverage
Confounding
outliers
Nonresponse
Population
mean
Experimental Units
Sample
median
Subjects
Voluntary Response Sample
mode
Treatment
Bias
response variable
Statistically Significant
Simple Random Sample (SRS)
explanatory variable
Double Blind
Random Digits
scatter plot
Block Design
Statistics Unit 1-Spring 2011
Page 3
All of these types of graphs describe distribution of categorical variables.
Bar Graphs - the categories are represented by bars, where the height of each bar is frequency.
• bars can be vertical or horizontal
• bars are all same width and same space between
• bars represent frequency
Pie Chart/Circle Graph - the categories are represented by slices of a pie (circle). The size of each slice is
proportional to the frequency.
• must include all categories that make up the WHOLE!
• usually read as a %
Pareto Chart - A bar graph with the categories arranged by height in descending order from left to right (highest
bar first).
• used primarily in quality management
• bars represent frequency AND are arranged by height, tallest on left/top
Make a bar graph, pie chart and Pareto chart for each question.
1. The following is data of American adults’ favorite pizza toppings(out of a survey of 200 people): 43% chose
pepperoni, 19% chose sausage, 14% chose mushrooms, 13% chose vegetables, 7% chose other and 4%
chose onions.
2. The results from a recent survey, how much time do you spend talking on the phone after 5 p.m., of 500
people are as follows: less than half an hour: 296 people, half an hour to one hour: 83 people, more than
one hour: 121 people.
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All of these graphs describe quantitative variables
Double Line Graph: Graphs can show two sets of data, used in stock patterns.
Number of Miles
Time Plot of Distance Jogged in 30
4
Minutes
3
Tom
Bob
2
1
0
Sun Mon Tues Wed Thurs Fri
Sat
Days of the Week
Histogram: show overall pattern: shape, center, spread, and any major deviations: outliers.
Scatterplots: Shows the relationship between two quantitative variables measure on the same individual.
Box Plots - used for side-by-side comparisons of more than one distribution.
EX: Mark McGwire’s home run counts: 9, 9, 22, 32, 33, 39, 39, 42, 49, 52, 58, 70.
M = 39
Q1 = 27
Q3 = 50.5
Babe Ruth’s home run counts: 22, 25, 34, 35, 41, 41, 46, 46, 46, 47, 49, 54, 54, 59
M = 46
Q1 = 35
Q3 = 54
Ruth is more consistent than McGwire because his home run counts are less spread out.
Statistics Unit 1-Spring 2011
Page 5
Stem-and-Leaf Plot:
1. Writing the data in numerical order may help to organize the data, but is NOT a required step. Ordering can be
done later.
Data: 35, 36, 38, 40, 42, 42, 44, 45, 45, 47, 48, 49, 50, 50, 50
2. Separate each number into a stem and leaf. Since these are two digit numbers, the tens digit is the “stem” and the
units digit is the “leaf.”
The number 38 would be represented as:
STEM LEAF
3
8
3. Group the numbers with the same stems List the stems in numerical order. If your leaf values are not in
increasing order, order them now. Title the graph.
4. Prepare an appropriate legend.
(key) for the graph.
Legend: 3 6 means 36
1. More and more people take fitness walks before or after work or during their lunch hour. The want comfortable
walking shoes. Periodically, Consumer Reports rates walking shoes and includes the prices as well. In one issue, the
rated men’s and women’s walking shoes and gave the prices. For a random sample of 19 of the rated walking
shoes, the prices were:
59
65
109
70
70
60
76
110
55
50
55
69
58
59
40
46
62
52
55
Seven years later an issue of Consumer Reports again rated men’s and women’s walking shoes. The prices were:
90
70
70
68
70
65
70
40
75
65
70
70
65
68
60
74
70
95
75
a) Make a stem-and-leaf diagram for the prices of walking shoes 7 years ago.
b) Make a stem-and-leaf diagram for recent prices of walking shoes.
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2. Make a double line graph. Below is a table that shows the stock prices for two competing airlines. The table
shows their stock prices over the last 6 months.
January
February
March
April
May
June
Delta
$12.50/share
$15.50/share
$8.00/share
$7.00/share
$7.50/share
$5.50/share
AirTran
$10.00/share
$9.50/share
$5.00/share
$4.50/share
$5.00/share
$8.00/share
4. You found the following prices of 24 different brands of backpacks:
a) Find the 5 number summary.
$15
$25
$50
$42
$29
b) Draw a box plot of the data.
$50
$33
$27
$35
$32
$40
$35
$28
$40
$40
$35
$35
$75
$40
$40
$25
$50
$25
$50
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5. Which version of The Landry News receives the most views?
6. In which month do the printed and online versions receive the same amount of votes?
7. About how many more copies of the printed version are viewed versus the online version in February?
8.Interpret the data during the summer months of June and July. Why do you think the online views are so high an
d the printed version is so low?
9. For the first three months of the year, about how many views are there of the online version of the paper?
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Scatterplots:
Shows the relationship between two quantitative variables measure on the same individual.
Example: Where x is the height of the class and y is the shoe size.
1. Create and label a scatter plot of the data. Mary’s parents are concerned that she seems short for her age. Their
doctor has the following record of Mary’s height:
Age
36
(months)
Height
35
(inches)
40
45
48
51
54
57
60
66
36.5
37
38
40
41
42
43
45
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2. In one of the Boston city parks there has been a problem with muggings in the summer months. A police cadet
took a random sample of 10 days (out of the 90 day summer) and compiled the following data. For each day, x
represents the number of police officers on duty in the park and y represents the number of reported muggings on
that day. Construct and label a scatterplot to display this data.
x
10
15
16
1
4
6
18
12
14
7
y
5
2
1
9
7
8
1
5
3
6
3. These are the prices and weights of bicycles. Make a scatter plot of the data.
price
weight
1000
940
1100
1100
700
600
440
450
550
340
180
140
Statistics Unit 1-Spring 2011
32
34
30
31
29
28
29
29
30
33
34
37
Page 10
Histogram:
Step 1: Divide the range of the data into classes of equal width (number of classes will be given) by subtracting
smallest from the largest and dividing by number of classes. (make a whole # if not).
Step 2: Count the number of observations in each class (total number in data set)
Step 3: Draw histogram:
•Mark scale for the variable on the horizontal axis
•Vertical axis contains total number in the data set
•Each bar represents a class
•No space between bars unless there is a bar with the frequency of 0.
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1. Make a histogram for the following data. How hot does it get in Fairbanks, Alaska, in January? The record
maximum temperature (F  ) for each day in January can be found on the web at <http://www.gi.alaska.edu/>. The
results (in F  ) for January 1 to 31 are as follows:
41
35
29
39
34
43
39
46
45
*Use six classes
40
50
39
33
42
39
34
43
42
33
38
35
40
42
38
40
45
42
40
47
37
37
2. “Readability Levels of Magazine Ads,” by F. K. Shuptrine and D.D. McVicker is an article in the Journal of
Advertising Research (see Web site <http://lib.stat.cmu.edu/DASL/>. Look in Data Subjects under Consumer and
then Magazine Ads Readability file). The following is a list of the number of three-syllable (or longer) words in
advertising copy of randomly selected magazine advertisements.
34
21
37
17
3
10
5
2
9
15
3
8
11
12
13
*Use eight classes
31
6
3
16
1
Statistics Unit 1-Spring 2011
10
5
0
9
9
24
6
4
10
43
39
6
29
3
13
10
13
26
12
14
17
22
5
10
32
18
25
5
10
24
32
3
24
10
15
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1. Recreational skiing is big business in some of the western and New England states. Many recreational skiers
are beyond the beginning level and want intermediate or “more difficult” terrain (but not the most difficult).
Snow Country described the 35 top-rated ski areas and gave the percentage of skiing terrain that was at the
more difficult level. The percentages follow:
36
57
58
54
51
43
51
40
59
49
40
49
30
45
55
43
40
30
40
60
33
46
20
60
35
25
30
40
50
46
52
40
65
28
65
*Use five classes
2. Franchise and Business Opportunities Annual Report contains information about franchise opportunities in
the United States and Canada. A franchise fee is one of the expenses associated with owning a franchise. There
are other expenses, such as startup, advertising, royalties, and so on. A large category of franchises is the fastfood business, which includes franchises such as baked goods, donuts, hamburgers chicken and hot dogs.
Franchise fees (in thousands of dollars) for the fast-food category are as follows:
21
28
20
15
25
8
25
30
15
35
40
25
25
25
10
24
15
10
18
25
20
40
25
8
44
25
25
15
15
20
20
25
25
20
75
25
25
10
13
35
33
20
15
25
30
5
23
30
19
25
15
30
30
24
20
28
30
10
10
20
15
15
15
*Use five classes.
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Venn Diagrams
Draw a venn diagram for each problem.
1. In a class of 50 students, 18 take orchestra, 26 take band, and 2 take both orchestra and band.
2. In a school of 320 students, 103 students are in clubs, 198 are on sports teams, and 60 students participate in
both activities.
3. On the football team, there are 75 players. There are 30 players on the baseball team. 21 of the players play both
football and baseball.
4. Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both
classes, how many students are in neither class? How many are in either class?
5. Of 178 ninth grade students, 83 are on a sports team, 111 are in a club, and 48 are involved in both sports and a
club. How many ninth grade students are involved in neither sports nor a club?
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6. Stephen asked 100 coffee drinkers whether they like cream or sugar in their coffee. According to the Venn
diagram below, how many like cream? Sugar?
7. Sugar but not cream? Cream but not sugar?
8. Cream and sugar? Cream or sugar?
9. A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four
have dogs and cats, 3 have dogs and fish, and one has a cat and a fish. No one has all three kinds of pets.
10. A guidance counselor is planning schedules for 30 students. Sixteen students say they want to take French, 16
want to take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3
wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish.
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3 part Venn diagrams
Draw and label the Venn Diagram that would represent this data.
1. Restaurant
100 people seated at different tables in a Mexican restaurant were asked if their party had ordered any of the
following items: tacos, chili con queso, or quesadillas
23 people had ordered none of these items.
11 people had ordered all three of these items.
29 people had ordered chili con queso or quesadillas but did not order tacos.
41 people had ordered quesadillas.
46 people had ordered at least two of these items.
13 people had ordered tacos and quesadillas but had not ordered chili con queso.
26 people had ordered tacos and chili con queso.
2. Cartoons
A study was made of 200 students to determine what TV shows they watch.
22 students don't watch these cartoons.
73 students watch only Tiny Toons.
136 students watch Tiny Toons.
14 students watch only Animaniacs and Pinky & the Brain.
31 students watch only Tiny Toons and Pinky & the Brain.
63 students watch Animaniacs.
135 students do not watch Pinky & the Brain.
3. Concert
150 people at a Van Halen concert were asked if they knew how to play piano, drums or guitar.
18 people could play none of these instruments.
10 people could play all three of these instruments.
77 people could play drums or guitar but could not play piano.
73 people could play guitar.
49 people could play at least two of these instruments.
13 people could play piano and guitar but could not play drums.
21 people could play piano and drums.
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4. Star Trek
A study was made of 200 students to determine what TV shows they watch.
73 students watch only The Next Generation (TNG).
31 students watch only TNG and VOY.
136 students watch TNG.
22 students hated all Star Trek shows.
14 students watch only Deep Space 9 (DS9) and Voyager (VOY).
135 students do not watch VOY.
63 students watch DS9.
5. Mythology
100 people were asked if they knew who any of the following are: Loki, Hermes, and Ra.
25 people did not know any of these.
3 people knew all three.
48 people knew who Hermes or Ra were but did not know who Loki was.
40 people knew who Ra was.
21 people knew who at least two of these were.
7 people knew who Loki and Ra were but did not know who Hermes was.
8 people knew who Loki and Hermes were.
6. Pollutants
A study was made of 1000 rivers to determine what pollutants were in them.
177 rivers were clean
101 rivers were polluted only with crude oil
439 rivers were polluted with phosphates.
72 rivers were polluted with sulfur compound and crude oil, but not with phosphates.
289 rivers were polluted with phosphates, but not with crude oil.
463 rivers were polluted with sulfur compounds.
137 rivers were polluted with only phosphates.
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7. Tennis
200 tennis players were asked which of these strokes they considered their weakest stroke(s): the serve, the
backhand, the forehand.
20 players said none of these were their weakest stroke.
30 players said all three of these were their weakest stroke.
40 players said their serve and forehand were their weakest strokes.
40 players said that only their serve and backhand were their weakest strokes.
15 players said that their forehand but not their backhand was their weakest stroke.
52 players said that only their backhand was their weakest stroke.
115 players said their serve was their weakest stroke.
8. Tennis Tournaments
200 people were asked which of these grand slam tournaments that they have attended. The tournaments inquired
about were: US Open, Wimbledon, or Australian Open.
30 people have not attended any of these tournaments.
10 people have been to all three tournaments.
25 people have been to Wimbledon and the Australian Open.
20 people have been to the US Open and the Australian Open but not to Wimbledon.
65 people have been to exactly two of the tournaments.
165 people have been to the US Open or to Wimbledon.
120 people have been to Wimbledon or to the Australian Open.
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