Pre-TestUnit9:DescriptiveStatisticsKEY
You may use a calculator.
The following table shows how many text messages different students sent this week. Answer the following
questions using the table.
20
200 340 0
75
55
90
120 60
150 170 220 240 90
85
40
35
100 65
30
1. Construct a histogram for the above data set using appropriate scale for the -axis and appropriate -axis
intervals for the frequency. (8 pts; 2 pts for y-axis scale and label, 2 pts for -axis intervals and label, 4 pts for
correct frequencies)
6
5
4
3
2
0
100
200
300
400
300-349
250-299
200-249
150-199
100-149
50-99
1
0-49
Frequency
7
Text Messages Sent
2. Construct a box and whisker plot for the above data set in the blank space above. (8 pts; 2 pts for quartiles, 2
pts for end points, 2 pts for number line labels, 2 pts for box/whisker)
3. What are the mean and median of the above data set? (4 pts; 2 pts each)
Median = 87.5, Mean = 109.25
4. What are the range and interquartile range of the above data set? (4 pts; 2 pts each)
Range = 340, Interquartile Range = 112.5
5. What is the population standard deviation of the above data set? (4 pts; no partial credit)
84.473
6. What can you tell about a data set of test scores with a mean of 75%, median of 78%, range of 30%, and
population standard deviation of 7%? (4 pts; partial credit at teacher discretion)
Answers will vary: The data is tightly clumped in the middle. Even the end points of the data set are not far.
7. What could be a mean and median of a data set of test scores where a third of the class failed, but the rest of
the class scored above an 80%? Justify each choice in writing. (4 pts; partial credit at teacher discretion)
Answers will vary: Mean = 70 since most passed, Median = 85 middle would be above 80
1
Construct a scatter plot for the following data set using appropriate scale for both the - and -axis.
(8 pts; 1 pts for each axis scale/interval, 1 pt for deciding to break each axis or not, 2 pts for correct
independent/dependent axes, 2 pts for correctly plotted points)
8. This table shows the number of hours students slept the night before their math test and their scores.
100
Test
Score
8
7
8
6
5
8
8
9
7
6
95
90
85
75
65
90
80
95
80
70
80
70
Test Score
Hours
Slept
Anna
Bob
Carly
Damien
Esther
Franco
Georgia
Hank
Innya
Jacob
90
60
50
40
30
20
10
1
2
3
4
5
6
7
8
9
Hours of Sleep
Percent of Income Saved
Use the following scatter plot to answer each question. The scatter plot shows the monthly income of each
person in hundreds of dollars versus the percent of their income that they save each month. (4 pts; 2 pts for
correct answer with no explanation)
9. What patterns or associations do you see present in this
data? Why do you think so?
Positive linear association since the data is going up at a
Kory
generally steady pace.
10. Which person makes the most money per month? How
much do they make?
Paul makes $2800 per month
Rachel
Nancy Paul
Lexi
Tanya Mike
Quinn Stan
Oliver
Monthly Income in Thousands of Dollars
2
Draw an informal function of best for the given scatter plots. (3 pts; partial credit at teacher discretion)
12. This scatter plot shows the hours a cubic foot of
ice was exposed to sunlight versus the thickness of
ice that melted in inches.
Plant Growth
Ice Melted
Plant Growth in cm
10
8
6
4
2
0
0
2
4
6
8
Copper in Water in ppm
Thickness of Ice Melted in inches
11. This scatter plot shows the amount copper in
water in ppm versus plant growth in cm over three
months.
2
1.5
1
0.5
0
0
2
-0.5
4
6
8
10
Hours of Sunlight Exposure
Explain why the drawn line of best fit is accurate or why not. (3 pts; partial credit at teacher discretion)
13. This scatter plot shows the age in years versus
the height in inches of a group of children.
14. This scatter plot shows the hours of TV watched
per week versus the GPA on a 4.0 scale for a group
of students.
Height
GPA
4.0
60
3.5
50
3.0
40
2.5
30
2.0
1.5
20
1.0
10
Age
2
4
6
8
10
12
14
−10
Not accurate because there are too many points
below at the beginning of the line, and too many
above at the end of the line.
0.5
Hours Weekly TV
−4
−0.5
4
8
12
16
20
24
28
Accurate because there is a balance of how far away
the data points are from the line.
3
The scatter plot shows what people think the temperature “feels like” ( axis) as the humidity (
axis) varies
when the room is actually at 68° F. The equation of the line of best fit is . (4 pts; 2 pts for
equation answer, 2 pts for graph answer)
15. Predict what a person would say the temperature “feels like” when
the humidity is at 80% using both the equation and graph.
Feels Like Temp
70
Equation Work:
60
50
Graph Prediction:
68°
68°69°
40
30
20
10
% Humidity
−10
10 20 30 40 50 60 70 80 90 100
−10
Using the same scatter plot and equation of the line of best fit of , answer the following
questions. (2 pts; partial credit at teacher discretion)
16. What does the slope of this equation mean in terms of the given situation? In other words, explain what the
rise and run mean for this problem.
The “feels like” temperature will go up one degree for every 10% increase in humidity.
17. What does the -intercept of this equation mean in terms of the given situation? In other words, explain
what the -intercept means when considering the humidity and “feels like” temperature.
The y-intercept of 61 degrees means that with 0% humidity it will “feel like” 61 degrees instead of 68 degrees.
Answer the following questions. (4 pts; partial credit at teacher discretion)
18. A function of best fit has a correlation coefficient of 0.8557. What does that tell us?
It has a strong correlation.
19. Plot the two sets of residuals on number lines. (4 pts; 2 pts each)
1
2
3
4
5
Anne’s
0.5
1.5
-0.5
-1
-2
Bob’s
4
1
0
2
0.5
3
-0.5
4
0.5
5
1
20. Which person’s line of best fit works better and why do you think so? (4 pts; 2 pts for answer, 2 pts for
explanation)
Bob’s because his residuals are closer to the zero line.
Answer the following questions about two-way tables. (4 pts; partial credit at teacher discretion)
21. Construct a two-way table from the following data about whether people are democrats or republicans and
whether or not they support stricter gun control laws.
Democrat or
Republican?
Support Strict
Gun Control?
Support Gun
Control
Against Gun
Control
D R R R D D R D D D R D R R D R D D R R
Y N N N N Y N Y Y Y N Y N Y N N Y Y Y N
Republican
2
8
Democrat
8
2
22. Do you think there is a relationship between party affiliation and gun control laws? Based on the data, why or
why not? (no credit without explanation of why, partial credit at teacher discretion for explanation)
Yes. 80% of Republicans are against gun control while 80% of Democrats support gun control.
Answer the following questions using the given two-way table. (4 pts; no partial credit)
Students
Teachers
Support School
Uniforms
278
82
Do Not Support
School Uniforms
1726
23
23. How many students were surveyed?
2004
24. As a percent to the nearest hundredth (two decimal places) what is the relative frequency of students who
support school uniforms?
278
≈ 13.87%
2004
5
Unit 9 Homework Answer Key
Lesson 9.1
For each of the data sets below, create a histogram, dot plot, and box plot.
1. The following data lists the number of hours per week spent playing video games for each person.
Abraham
Betty
Carrie
Demarcus
Ely
Francis
Gretchen
Heather
Ingrid
Jackson
Kamir
Lamar
Marcus
Noel
Oji
Pat
Queen
Reed
Sage
Tiko
Ugo
Victor
Wim
Xavia
Yuma
Zachary
9
8
7
Frequency
Name
Hours
per
week
8
3
0
0
5
6
2
8
3
2
7
5
3
1
9
7
0
3
1
2
9
4
3
5
6
1
6
5
4
3
2
1
0
1 2
3 4 5 6
7 8
9
6
7
Hours per week
0
0
1
1
2
2
3
3
4
4
6
5
5
6
7
8
8
9
9
10
10
2. The following data lists the number of wins for pitchers in MLB in the 2013 season.
21-23
15-17
18-20
12-14
9-11
6-8
0-2
3-5
Frequency
Name
Wins
18
Sanchez
14
Colon
18
16
Iwakuma
14
14
Darvish
13
12
Scherzer
21
10
Hernandez
12
8
Sale
11
Shields
13
6
Santana
9
4
Jimenez
13
2
Kuroda
11
Price
10
Wilson
17
Holland
10
Number of Wins
Masterson
14
Verlander
13
Quintana
9
Lackey
10
Fister
13
Tillman
16
Pettitte
11
Lester
15
Gonzalez
11
Griffin
14
Parker
12
0
15
18
21
12
24
3
6
9
Guthrie
15
Buehrle
12
Correia
9
Norris
10
Dickey
14
Porcello
13
Doubront
11
Damster
8
Williams
9
Sabathia
14
Hellickson
12
Saunders
11
0
15
18
21
3
6
9
12
24
3. Using the plots, can you tell about where the average might be? What about the middle?
The average might be in the third quartile and the middle is the middle of the box and whisker plot.
4. Using the plots, is this data very spread out or closely packed?
This data is closely packed except in the fourth quartile.
7
27
30
27
30
5. The following data lists the number of full years in office for U. S. presidents.
18
16
14
12
10
8
6
4
10-11
12-13
8-9
6-7
4-5
2
0-1
2-3
Years in office
6
4
8
8
8
4
8
8
0
3
4
1
2
4
4
4
3
8
4
0
3
4
4
4
4
7
4
8
2
5
4
12
7
8
2
5
5
2
4
8
4
8
8
Frequency
Name
Washington
J. Adams
Jefferson
Madison
Monroe
J. Q. Adams
Jackson
Van Buren
Harrison
Tyler
Polk
Taylor
Fillmore
Pierce
Buchanan
Lincoln
Johnson
Grant
Hayes
Garfield
Arthur
Cleveland
Harrison
Cleveland
McKinley
Roosevelt
Taft
Wilson
Harding
Coolidge
Hoover
Roosevelt
Truman
Eisenhower
Kennedy
Johnson
Nixon
Ford
Carter
Reagan
G. H. W. Bush
Clinton
G. Bush
Years in office
0
14
16
18
20
0
10
12
14
2
4
6
8
6. Using the plots, can you tell about where the average might be? What about the middle?
16
18
20
2
4
6
8
10
12
The average will probably be in the third quartile between 4 and 8 and the middle is 4.
7. Using the plots, is this data very spread out or closely packed?
This data has clumps around 4 and 8 because of four year terms.
8
8. The following data lists the amount of allowance each person receives.
9
8
7
6
5
4
3
2
15-17
18-20
12-14
9-11
6-8
1
0-2
3-5
Robert
Mary
John
Dorothy
James
Helen
William
Betty
Charles
Margaret
George
Ruth
Joseph
Virginia
Richard
Doris
Edward
Mildred
Donald
Frances
Thomas
Elizabeth
Frank
Evelyn
Harold
Anna
Allowance
$
5
15
8
10
12
15
7
5
10
8
7
12
15
14
13
10
8
15
20
18
12
7
15
10
6
12
Frequency
Name
Allowance
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
9
Lesson 9.2
The following table shows the test scores for various classes. Answer the following questions using the table.
Period
Period
Period
Period
1
2
3
4
95
80
90
45
73
90
95
87
100
70
45
100
90
75
89
30
95
68
90
92
71
67
85
95
80
83
41
80
83
60
88
20
81
88
97
84
75
88
84
45
73
85
86
35
72
72
90
90
88
79
30
85
80
82
89
25
98
65
20
40
88
65
15
81
85
78
96
92
79
70
85
10
93
75
95
88
80
75
81
5
1. What are the mean, median, range, interquartile range, and population standard deviation for period 1?
Mean: 83.95, Median: 82, Range: 29, IQR: 14.5, SD: ≈ 8.84
2. What are the mean, median, range, interquartile range, and population standard deviation for period 2?
Mean: 75.75, Median: 75, Range: 30, IQR: 13.5, SD: ≈ 8.40
3. What are the mean, median, range, interquartile range, and population standard deviation for period 3?
Mean: 74.55, Median: 87, Range: 82, IQR: 27, SD: ≈ 26.55
4. What are the mean, median, range, interquartile range, and population standard deviation for period 4?
Mean: 61.45, Median: 80.5, Range: 95, IQR: 56.5, SD: ≈ 31.63
5. Compare and contrast Period 1 and Period 2 using the measures of center and spread you calculated.
Answers will vary: They have similar spreads, but period 1 seems to have done better on the test based on the center.
6. Compare and contrast Period 1 and Period 3 using the measures of center and spread you calculated.
Answers will vary: They have similar medians, but period 3 has a much wider spread meaning scores dipped lower. That
caused the mean to be lower in period 3.
7. Compare and contrast Period 3 and Period 4 using the measures of center and spread.
Answers will vary: Even though the medians are somewhat close, the means are further away which means the spread for
period 4 is larger as seen in the IQR and SD.
8. What sort of centers and spread would you expect from a class that all scored relatively near 75%?
Centers close to 75% and spread relatively low.
9. What sort of centers and spread would you expect from a class whose test scores were evenly spread out from
0% to 100%?
Centers close to 50%, IQR near 50, and SD near 25.
10
The following table shows the batting averages for baseball players from four different teams. Answer the
following questions using the table.
Team 1
Team 2
Team 3
Team 4
0.300
0.320
0.280
0.350
0.290
0.310
0.275
0.280
0.280
0.150
0.270
0.270
0.270
0.150
0.270
0.260
0.260
0.150
0.265
0.250
0.250
0.150
0.265
0.240
0.240
0.150
0.220
0.230
0.230
0.120
0.210
0.220
0.220
0.110
0.200
0.100
0.210
0.100
0.180
0.050
10. What are the mean, median, range, interquartile range, and population standard deviation for Team 1?
Mean: 0.255, Median: 0.255, Range: 0.09, IQR: 0.05, SD: ≈ 0.029
11. What are the mean, median, range, interquartile range, and population standard deviation for Team 2?
Mean: 0.171, Median: 0.15, Range: 0.22, IQR: 0.03, SD: ≈ 0.074
12. What are the mean, median, range, interquartile range, and population standard deviation for Team 3?
Mean: 0.2435, Median: 0.265, Range: 0.1, IQR: 0.06, SD: ≈ 0.035
13. What are the mean, median, range, interquartile range, and population standard deviation for Team 4?
Mean: 0.225, Median: 0.245, Range: 0.3, IQR: 0.05, SD: ≈ 0.083
14. Compare and contrast Team 1 and Team 2 using the measures of center and spread you calculated.
Answers will vary: Team 2 has much lower centers and is spread out farther apart.
15. Compare and contrast Team 1 and Team 3 using the measures of center and spread you calculated.
Answers will vary: The two teams are very similar, but Team 3 may have a few lower people pulling down their mean.
16. Compare and contrast Team 2 and Team 4 using the measures of center and spread.
Answers will vary: Team 4 has higher centers but a wider spread.
17. What sort of centers and spread would you expect from a team that all batted relatively near 0.250?
Centers close to 0.250 and spread relatively low.
18. What sort of centers and spread would you expect from a team whose batting averages were evenly spread
out from 0.100 to 0.300?
Centers close to 0.200, IQR near 0.100 and SD near 0.050.
11
Answer the following questions.
19. What happened in a class if test score percents had a mean of 75% and a median of 90%? What sort of
population standard deviation and interquartile range would you expect?
Answers will vary: Most of the class scored above 90%, but several probably failed dragging down the mean. This
would produce a larger SD and IQR.
20. Let’s say two classes had a mean test score of 70% and a median test score of 70%, but their population
standard deviations were 5% and 20% respectively. What could you conclude about the differences between the
two classes?
Answers will vary: The second class had a much wider spread of data, but evenly spaced to produce the same
centers.
21. Describe a data set where the mean and median are far apart.
Answers will vary: Test scores where two-thirds of the class scored an A but the other third failed. The median
would be an A, but the mean would be a C or lower.
22. Describe a data set where the interquartile range and population standard deviation are far apart.
Answers will vary: Test scores where the middle half of the class scored a D, a fourth scored an A, and the other
fourth scored a low F. The IQR would be low because of all the D’s while the SD would be more because of the
actual range being larger.
12
Lesson 9.3
Use the given data to answer the questions and construct the scatter plots.
Pathfinder Character Level vs. Total Experience Points
Level
2
3
6
9
10
XP
15
35
150
500
710
11
1050
14
2950
15
4250
17
8500
20
24000
24000
21600
19200
16800
XP
14400
12000
9600
7200
4800
2400
0
0 2 4 6 8 10 12 14 16 18 20
1. Which variable should be the independent
variable (-axis) and which should be the dependent
variable (-axis)?
Level should be , XP should be 2. Should you use a broken axis? Why or why not?
No broken axis, uses all space in range
3. What scale and interval should you use for the xaxis?
0 to 20 by ones
4. What scale and interval should you use for the yaxis?
0 to 24,000 by 1,200
5. Construct the scatter plot.
Level
Allowance
Age vs. Weekly Allowance
Age
12
12
Allowance 0
5
13
5
13
8
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
14
10
14
15
15
20
15
20
16
25
16
30
6. Which variable should be the independent variable (xaxis) and which should be the dependent variable (y-axis)?
Age should be x, Allowance should be y
7. Should you use a broken axis? Why or why not?
Broken axis for x since 0 to 11 not used
8. What scale and interval should you use for the x-axis?
12 to 16 by 0.25
9. What scale and interval should you use for the y-axis?
0 to 30 by 1.5 or 0 to 40 by twos
10. Construct the scatter plot.
11
12
13
14
15
16
Age
13
Age vs. Number of Baby Teeth
Age
5
6
7
Baby
20
19
17
Teeth
7
15
8
10
9
10
10
8
11
4
11
2
12
2
20
18
16
Baby Teeth
14
12
10
8
6
4
2
0
0
2
4
6
8 10 12 14 16 18 20
11. Which variable should be the independent
variable (x-axis) and which should be the dependent
variable (y-axis)?
Age should be x, Baby Teeth should be y
12. Should you use a broken axis? Why or why not?
No broken axis, range greater than gap beforehand
13. What scale and interval should you use for the xaxis?
0 to 20 by ones
14. What scale and interval should you use for the yaxis?
0 to 20 by ones
15. Construct the scatter plot.
Age
Mileage
Car Speed (in mph) vs. Gas Mileage (in mpg)
Speed
20
25
35
40
Mileage 25
27
28
30
32
31
30
29
28
27
26
25
24
23
22
21
0 10 20 30 40 50 60 70 80 90 100
45
31
55
32
65
30
80
29
90
25
100
22
16. Which variable should be the independent
variable (x-axis) and which should be the dependent
variable (y-axis)?
Speed should be x, Mileage should be y
17. Should you use a broken axis? Why or why not?
Broken axis for y since 0 to 22 not used
18. What scale and interval should you use for the xaxis?
0 to 100 by fives
19. What scale and interval should you use for the yaxis?
22 to 32 by ones (or by halves)
20. Construct the scatter plot.
Speed
14
Lesson 9.4
Use the given scatter plots to answer the questions.
1. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Positive, going up from left to right
Daily Study Time
Daily Study Time (minutes)
80
70
2. Is there an outlier in this data set? If so,
approximately how old is the outlier and about how
many minutes does he or she study per day?
12 years old and 75 minutes
60
50
40
30
3. Is this association linear or non-linear? Explain
why.
Linear, increases by about the same amount each
year
20
10
0
0
5
10
15
20
4. What can you say about the relationship between
your age and the amount that you study?
The older you are, the more you study
Age
5. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Negative, going down from left to right
Daily Family Time
350
Daily Family Time
300
6. Is there an outlier in this data set? If so,
approximately how old is the outlier and about how
many minutes does he or she spend with family per
day?
No outlier in this data set
250
200
150
100
7. Is this association linear or non-linear? Explain
why.
Non-linear, it curves down
50
0
0
5
10
Age
15
20
8. What can you say about the relationship between
your age and the amount of time that you spend with
family?
As you get older, you spend much less time with
family each day
15
9. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Negative, going down from left to right
Math Grade
Math Grade
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
10. Is there an outlier in this data set? If so,
approximately how much does that person watch TV
daily and what is his or her approximate math grade?
About 5.5 hours of TV and 95% math grade
11. Is this association linear or non-linear? Explain
why.
Linear, grade goes down by the same amount for each
hour of TV
0
2
4
6
12. What can you say about the relationship between
the amount of time you watch TV and your math
grade?
Watching more TV correlates with lower math grades
Daily TV Time (hours)
13. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Positive, math grade goes up from left to right
Math Grade
Math Grade
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
14. Is there an outlier(s) in this data set? If so,
approximately how much time does that person(s)
spend with his or her family daily and what is his or
her approximate math grade?
40 minutes with 92% and 100 minutes with 96%
15. Is this association linear or non-linear? Explain
why.
Questionable, could go either way
0
100
200
300
Daily Family Time (minutes)
400
16. What can you say about the relationship between
the amount of time that you spend with your family
and your math grade?
More time with family correlates with higher math
grades
17. Are there any other patterns that you notice in this data?
Clumping around 280 minutes and also around 140 minutes
16
18. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Negative, going down from left to right
Number of Pets
14
Number of Pets
12
19. Is there an outlier(s) in this data set? If so,
approximately how many pets does that person(s)
have?
No outlier
10
8
6
20. Is this association linear or non-linear? Explain
why.
Linear, going down the same amount each time
4
2
0
0
10
20
30
First Letter of Last Name (A = 1 and Z = 26)
21. What can you say about the relationship between
your last name and the number of pets you have?
Earlier in the alphabet has more pets
22. Are there other patterns that you notice about people’s last names and how many pets they have?
Clumping, early alphabet between 8 and 13 pets, middle alphabet between 4 and 6, later alphabet
between 0 and 2 pets
23. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
No association, no clear pattern
Last Name
First Letter of Last Name
(A = 1 and Z = 26)
30
24. Is there an outlier(s) in this data set? If so,
approximately how old is that person?
No outlier
25
20
15
25. Is this association linear or non-linear? Explain
why.
Neither since there is no association
10
5
0
0
5
10
Age
15
20
26. What can you say about the relationship between
your last name and your age?
There is no relationship
17
27. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Positive, going up from left to right
Weekly Allowance ($)
Weekly Allowance ($)
30
28. Is there an outlier(s) in this data set? If so,
approximately how tall is that person and how much
does he or she make in allowance each week?
72 inches with $0 allowance
25
20
15
10
29. Is this association linear or non-linear? Explain
why.
Non-linear, it curves up
5
0
0
20
40
60
80
Height (inches)
30. What can you say about the relationship between
your height and your allowance?
As height increases, allowance increases
31. Do you think that being taller means that you will get more allowance? In other words, do you
think this relationship is a causation or a correlation?
This is a correlation, not a causation because being tall doesn’t cause more allowance
32. Does this scatter plot show a positive association,
negative association, or no association? Explain why.
Positive, going up from left to right
Weekly Allowance ($)
Weekly Allowance ($)
30
33. Is there an outlier(s) in this data set? If so,
approximately how old is that person and how much
does he or she make in allowance each week?
16 years old with $0 allowance
25
20
15
34. Is this association linear or non-linear? Explain
why.
Non-linear, it curves up
10
5
0
0
5
10
Age
15
20
35. What can you say about the relationship between
your age and your allowance?
As age increases, allowance increases
36. Do you think that being older means that you will get more allowance? In other words, do think
this relationship is a causation or a correlation?
This is probably a causation since being older means you generally spend more money and therefore
need more allowance
18
Lesson 9.5
Draw an informal function of best fit on the given scatter plot and explain why you chose that type of function.
A real function of best fit is the thick line in red.
1.
2.
Math Grade
80
100%
70
95%
60
90%
Math Grade
Daily Study Time (minutes)
Daily Study Time
50
40
30
85%
80%
75%
20
70%
10
65%
0
60%
0
5
10
15
20
0
2
Age
4
6
Daily TV Time (hours)
3.
4.
Total Worth in Millions
How Well Can We See Stars?
100
80
15.00
Visibility %
Millions of Dollars after 50 Years
20.00
10.00
5.00
0.00
0
-5.00
200
400
600
800
60
40
20
0
1000
0
-20
Monthly Payment at 10% Return
19
2
4
6
8
Distance from Earth in AUs
10
5.
6.
$20,000 at 10% per Year
Age vs. Sleep
14
2.50
12
Daily Sleep (hours)
Total Worth in Millions of $
3.00
2.00
1.50
1.00
0.50
10
8
6
4
2
0.00
0
0
20
-0.50
40
60
0
5
Years Invested
10
15
20
Age (years)
7.
8.
Ultrasonic Response of Metal
Detectors
200
180
160
140
120
100
80
60
40
20
0
Ultrasonic Response (as %)
Weight (pounds)
Age vs. Weight
0
5
10
15
20
100
90
80
70
60
50
40
30
20
10
0
0
Age (years)
2
4
6
8
Distance from Metal (in meters)
20
10
Determine whether the drawn function of best fit is accurate or not. Explain why you think your position is true.
A real function of best fit is the thick line in red.
9.
10.
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
0
10
20
30
11.
0
10
20
30
0
10
20
30
12.
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
0
10
20
30
21
13.
14.
350
350
300
300
250
250
200
200
150
150
100
100
50
50
0
0
0
5
10
15
20
25
0
15.
16.
8
8
6
6
4
4
2
2
0
5
10
15
20
25
0
0
2
4
6
8
10
12
0
-2
-2
-4
-4
-6
-6
-8
-8
22
2
4
6
8
10
12
Use the given graph of the line of best fit or equation of the line of best fit to answer the following questions.
!
The equation of the line of best fit is: − .
17. Using the graph only, about how much would you
expect an 18 year old to weigh?
185 – 190 lbs
Weight (pounds)
Age vs. Weight
200
180
160
140
120
100
80
60
40
20
0
18. Using the equation only, about how much would you
expect a 4 year old to weigh?
185.5 lbs
19. Using the graph only, if a person weighed 80 pounds,
how old would you expect them to be?
8 years old
0
5
10
15
20
Age (years)
20. Using the equation only, if a person weighed 80
pounds, how old would you expect them to be?
8 years old
21. What is the rate of change (slope) of the line of best fit? What does the slope represent in this context and
"
does that make sense?
#$#%#&'%ℎ)*+&,-%$##+./+0&
22. What is the initial value (-intercept) of the line of best fit? What does it represent in this context and does
1
that make sense?
− #$#%#&'%)#0/ℎ'+'-0'ℎ, 3#%&4 '*+5#%#&%#'ℎ+6#&#/+'06#)#0/ℎ'
23
Use the given graph of the function of best fit or equation of the function of best fit to answer the
following questions. The equation of the line of best fit is: 7(9) −;. <9 + ;=9.
23. Using the graph only, about how high would you expect
the baseball to be after 5 seconds?
104*#'#%
Baseball Height w/ Upward
Velocity of 45 Meters/Sec
120
24. Using the equation only, about how high would you
expect the baseball to be after 5 seconds?
102.5*#'#%
Height in Meters
100
80
60
40
25. Using the graph only, how long had the ball been in the
air if it were 100 meters high?
≈ 3.6+&35.4%#>&3%
20
0
0
2
4
6
Time in Seconds
8
10
26. Using the equation only, how long had the ball been in
the air if it were 100 meters high?
≈ 3.8+&35.4%#>&3%
27. What does the > value in the quadratic equation represent in this situation?
It represents the height at which the ball was at time zero or the height at which the person who threw the ball
was standing, which is 0 meters above ground.
28. What does the - value in the quadratic equation represent in this situation?
It represents the speed at which the ball was thrown into the air, which is 45 meters per second.
29. What does the + value in the quadratic equation represent in this situation?
It represents the force of gravity pulling the ball back down to the ground.
24
The following data about weekly allowances at various ages was used to create the given scatterplot. Four
students estimated the line of best fit for this data. Plot the given residuals calculated from each student’s line
of best fit and determine which student had the best line of best fit.
Age
10
Allowance 2
10
5
11
0
11
5
12
10
12
5
Allowance by Age
13
10
13
15
14
15
14
20
15
20
15
25
Abby’s LOBF:
4.1 − 41
30
Bennett’s LOBF:
25
Allowance
= 4.5 − 41
20
Courtney’s LOBF:
15
= 4 − 43
10
Drew’s LOBF:
5
= 5 − 45
0
0
5
10
15
20
Age
30. Abby’s Residuals from LOBF = 4.1 − 41
Age ()
10
10
11
11
12
Abby’s
Residuals
-2
-5
4.1
-0.9
-1.8
Correlation Coefficient: ≈ 0.860
12
13
13
14
14
15
15
3.2
0.5
-4.5
2.3
-2.7
Abby's Residuals
10
8
6
4
2
0
-2 10
-4
-6
-8
-10
11
12
13
14
25
15
1.4
-3.6
31. Bennett’s Residuals from LOBF 4.5 − 41
Age ()
10
10
11
11
12
Bennett’s
Residuals
2
-1
8.5
3.5
3
Correlation Coefficient: ≈ 0.742
13
13
14
14
12
8
7.5
2.5
7
2
15
15
6.5
1.5
15
15
-3
-8
Bennett's Residuals
10
8
6
4
2
0
-2 10
-4
-6
-8
-10
11
12
13
14
15
Correlation Coefficient: ≈ 0.758
12
13
13
14
14
32. Courtney’s Residuals from LOBF = 4 − 43
Age ()
10
10
11
11
12
Courtney’s
Residuals
-5
-8
1
-4
-5
0
-1
-6
Courtney's Residuals
10
8
6
4
2
0
-2 10
-4
-6
-8
-10
11
12
13
14
26
15
-2
-7
33. Drew’s Residuals from LOBF 5 − 45
Age ()
10
10
11
11
12
Drew’s
Residuals
3
0
10
5
5
Correlation Coefficient: ≈ 0.643
12
13
13
14
14
10
10
5
10
5
15
15
10
5
Drew's Residuals
10
8
6
4
2
0
-2 10
-4
-6
-8
-10
11
12
13
14
15
34. Which person’s line of best fit do you think is the best based off your residual plots and their
corresponding correlation coefficients? Explain why you think so.
Abby’s LOBF is the best because her residuals are closely centered around zero and her line also has the highest
correlation coefficient.
35. Using technology (Excel), calculate the correlation coefficient ( ) of the line of best fit for the original
data set. What does that mean?
≈ 0.8557 which means that a linear function is a good choice for a function of best fit.
36. If a function of best fit had a correlation coefficient of ≈ 0.02, what would that mean?
The choice of function does not fit the data hardly at all. Either this is a terrible choice for a function of best fit or
there is little correlation between the variables.
37. If a function of best fit had a correlation coefficient of ≈ 0.92, what would that mean?
The choice of function fits the data extremely well. There appears to be a strong correlation between the
variables in the data set.
38. If a function of best fit had a correlation coefficient of ≈ 0.41, what would that mean?
The choice of function fits the data moderately. There may be better choices for a function of best fit or there is
not as strong of a correlation between the variables.
27
Lesson 9.6
Use the data set to answer the following questions. For this data set a class of middle school students was
asked what they thought was most important in school: good grades or popularity.
Boy or
Girl
Grades or
Popularity
B
B
G
G
G
B
G
B
B
G
G
B
G
B
G
B
B
G
G
B
P
G
G
P
G
P
G
G
P
G
G
P
G
P
P
P
G
G
G
P
Boy or
Girl
Grades or
Popularity
B
B
G
G
G
B
G
B
B
G
G
B
G
B
G
B
B
G
G
B
P
G
P
G
G
P
G
P
P
G
G
G
G
P
P
P
G
P
G
G
1. Construct a two-way table of the data.
Boys
Girls
Grades
7
15
Popularity
13
5
2. What is the frequency of students who believe grades are more important?
22
3. What is the relative frequency of students who believe grades are more important?
22
= 55%
40
4. What is the frequency of students who believe popularity is more important?
18
5. What is the relative frequency of students who believe popularity is more important?
18
= 45%
40
6. What is the frequency of girls who believe grades are more important?
15
7. What is the relative frequency of girls who believe grades are more important?
15
= 75%
20
8. What is the frequency of boys who believe popularity is more important?
13
9. What is the relative frequency of boys who believe popularity is more important?
13
= 65%
20
10. Based on this data, do you feel there is relationship between a student’s gender and what they think is most
important in school? What is that relationship and what evidence do you have that it exists?
Based on the relative frequencies, girls typically believe that grades are more important, while boys believe
popularity is more important.
28
Use the data set to answer the following questions. For this data set a class of middle school students was
asked what hand was their dominant hand.
Boy or
Girl
Right or
Left
B
B
G
G
G
B
G
B
B
G
G
B
G
B
G
B
B
G
G
B
L
R
R
L
R
L
R
R
R
R
L
R
R
R
R
R
L
R
L
R
Boy or
Girl
Right or
Left
B
B
G
G
G
B
G
B
B
G
G
B
G
B
G
B
B
G
G
B
R
R
L
R
R
R
L
R
L
R
R
R
L
R
R
L
R
R
L
L
11. Construct a two-way table of the data.
Boys
Girls
Right-handed
14
13
Left-handed
6
7
12. What is the frequency of students who are right-handed?
27
13. What is the relative frequency of students who are right-handed?
27
= 67.5%
40
14. What is the frequency of students who are left-handed?
13
15. What is the relative frequency of students who are left-handed?
13
= 32.5%
40
16. What is the frequency of girls who are right-handed?
13
17. What is the relative frequency of girls who are right-handed?
13
= 65%
20
18. What is the frequency of boys who are right-handed?
14
19. What is the relative frequency of boys who are right-handed?
14
= 70%
20
20. Based on this data, do you feel there is relationship between a student’s gender and whether or not they are
right-handed? What is that relationship and what evidence do you have that it exists?
Based on the relative frequencies it appears that boys and girls have the same chances of being left- or righthanded and that being right-handed is much more likely than being left-handed.
29
Use the two-way tables representing surveys middle school students took to answer the following questions.
Survey 1:
Boys
Girls
Prefer Spicy
Salsa
255
68
Prefer Mild
Salsa
45
132
Survey 2:
Right-handed
Left-handed
Prefer Spicy
Salsa
280
43
Prefer Mild
Salsa
170
7
21. How many students were surveyed?
500
22. What is the relative frequency of students who prefer spicy salsa? Is it the same on both two-way tables?
323
= 64.6%
500
23. How many boys were surveyed?
300
24. How many girls were surveyed?
200
25. What is the relative frequency of boys who prefer spicy salsa?
255
= 85%
300
26. What is the relative frequency of girls who prefer spicy salsa?
68
= 34%
200
27. Do you think there is a relationship between gender and salsa preference? What is that relationship and
what evidence do you have that it exists?
Based on the relative frequencies, it appears that boys prefer spicy salsa more than girls.
28. How many right-handed students were surveyed?
450
29. How many left-handed students were surveyed?
50
30. What is the relative frequency of right-handed students who prefer mild salsa?
170
= 37. 7?%
450
31. What is the relative frequency of left-handed students who prefer mild salsa?
7
= 14%
50
32. Do you think there is a relationship between a student’s dominant hand and salsa preference? What is that
relationship and what evidence do you have that it exits?
Based on the relative frequencies, it appears that that right-handed students are between two and three times as
likely to prefer mild salsa.
30
ReviewUnit9:DescriptiveStatisticsKEY
You may use a calculator.
The following table shows the fall MAP scores for students. Answer the following questions using the table.
210 225 208 245 232 219 253 228 218 230 234 241 240 221 235 218 227 261
1. Construct a histogram for the above data set using appropriate scale for the y-axis and appropriate x-axis
intervals for the frequency.
9
8
208-210
211-213
214-216
217-219
220-222
223-225
226-228
229-231
232-234
235-237
238-240
241-243
244-246
247-249
250-252
253-255
256-258
259-261
262-264
265-267
268-270
6
5
4
3
2
256-261
250-255
244-249
238-243
232-237
226-231
220-225
214-219
1
208-213
Frequency
7
208 214 220
226 232 238 244 250
256 262 268
MAP scores
2. Construct a dot plot for the above data set in the space above.
3. Construct a box and whisker plot for the above data set in the space above.
4. What are the mean and median of the above data set?
Mean: 230.28; Median: 229
5. What are the range and interquartile range of the above data set?
Range: 53; Interquartile range: 21
6. What is the population standard deviation of the above data set?
13.73
7. What can you tell about a data set of test scores with a mean of 228 median of 230, range of 35, and
population standard deviation of 4?
The data is pretty closely packed around 228; the end points are not far off as well. Data is evenly distributed due
to mean and median being close together.
8. What could be a mean and median of a data set of test scores where a third of the class scored above 250, but
the rest of the class scored around 225? Justify each choice in writing.
Median would be around 225 since more than half of the data was around 225. The mean would be above 225
but probably below 250 since a third of the data is above 250.
31
The following table shows the free throw percentages from two different teams. Answer the following
questions using the table.
Team 1
Team 2
.714
.819
.807 .671
.721 .672
.817 .676
.694 .750
.733 .730 .750
.623 .619 .636
.710
.875
.794 .615 .500
.500 .900 .710
.500 .815
.650 .450
.790 .735
.500 .621
9. What are the mean, median, range, interquartile range, and population standard deviation for Team 1?
Mean: 0.71, Median: 0.732, Range: 0.317, Interquartile Range: 0.119, Standard Deviation: 0.096
10. What are the mean, median, range, interquartile range, and population standard deviation for Team 2?
Mean: 0.671, Median: 0.661, Range: 0.45, Interquartile Range: 0.116, Standard Deviation: 0.123
11. Compare and contrast Team 1 and Team 2 using the measures of center and spread you calculated.
The center for team 2 is slightly lower. The spreads are very similar.
12. What sort of centers and spread would you expect from a team that all shot relatively near 0.750?
Centers will be around 0.75 and the spread will be low
13. What sort of centers and spread would you expect from a team whose free throw percentages were evenly
spread out from 0.600 to 0.800?
Centers near 0.700 and interquartile range near 0.1 and standard deviation near 0.07.
Construct a scatter plot for the following data set using appropriate scale for both the x- and y-axis.
14. This table shows the age of students slept and their scores on the MAP test.
8
10
11
12
9
15
13
14
13
14
180
200
215
220
195
235
230
235
225
225
230
220
MAP Score
Anna
Bob
Carly
Damien
Esther
Franco
Georgia
Hank
Innya
Jacob
240
MAP
Score
Age
250
210
200
190
180
170
160
150
0
2
4
6
8 10 12 14 16 18 20
Age
32
Use the following scatter plot to answer each question. The scatter plot shows the number of years each person
invested ten thousand dollars versus the end value of that investment in thousands of dollars.
15. Does this scatter plot represent a
positive association, negative association,
or no association? Why?
Negative, going down over time.
Remaining Student Loan Debt
on a $30,000 Loan
35000
Mike
Remaining Debt
30000
Jazmin
Gonzo
Eloise Amanda
Fifi
25000
20000
16. Which person paid off their debt?
About how long did it take?
Brady, 30 years.
Donna
Katy
Leonard
15000
Chuck
Hannah
Isildor
10000
5000
0
0
5
10
15
20
25
30
17. Does this appear to a linear or nonlinear association? Why?
Non-linear, curves down.
Brady
35
Years Since Graduating College
18. Which person is the outlier in this data
set? Why?
Mike, has more debt after many years.
Draw an informal line of best for the given scatter plots.
20. This scatter plot shows the hours of TV watched
per week versus the GPA on a 4.0 scale for a group
of students.
80
4
70
3.5
60
3
50
2.5
GPA
Height in Inches
19. This scatter plot shows the age in years versus
the height in inches of a group of children.
40
2
30
1.5
20
1
10
0.5
0
0
0
5
10
15
20
0
Age
5
10
Hours of TV Watched per Week
33
15
Explain why the drawn line of best fit is accurate or why not.
22. This scatter plot shows the hours a cubic foot of
ice was exposed to sunlight versus the amount of ice
that melted in cubic inches.
Inaccurate, not the right slope.
21. This scatter plot shows the amount copper in
water in ppm versus plant growth in cm over three
months.
Inaccurate, does not split data in half.
10
9
9
Ice Melted in Cubic Inches
10
Plant Growth in cm
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
0
0
0
20
40
60
0
2
Cu in Water (ppm)
4
6
8
Hours of Sunlight
The scatter plot shows the price of a gallon of milk from 2001 to 2012. The equation of the line of best fit is
approximately = = + . @.
23. Predict what price of a gallon of milk would have been in 2005
using both the equation and the graph.
$4.50
$4.00
Equation Work:
Avg Price of Milk
$3.50
$3.00
=
$2.50
Graph Prediction:
21
85: + 2.68 = $3.10
250
$3.10
$2.00
$1.50
$1.00
$0.50
$0.00
0
5
10
Years since 2000
15
24. Predict what year it would have been when a gallon of milk cost
approximately $3.00 using both the equation and the graph.
"
Equation Work: 3 = BC + 2.68
1.32 =
21
250
≈ 3.8 meaning about 2004
34
Graph Prediction:
2004
Using the same scatter plot and equation of the line of best fit of = = + . @, answer the following
questions.
25. What does the slope of this equation mean in terms of the given situation? In other words, explain what the
rise and run mean for this problem.
The price goes up $21 every 250 years.
26. What does the -intercept of this equation mean in terms of the given situation? In other words, explain
what the -intercept means when considering the price of a gallon of milk and the year.
In the year 2000, the price of a gallon of milk was $2.68.
Answer the following questions.
27. A function of best fit has a correlation coefficient of ≈ 0.901. What does that tell us?
Negative relationship that is close to linear
28. A function of best fit has a correlation coefficient of ≈ 0.029. What does that tell us?
Positive relationship that is not linear
29. Plot the two sets of residuals on the number lines.
Nate’s
1
-1
2
-0.5
3
2
4
1
Nancy’s
5
2
1
0
2
0.5
3
-1
4
0.5
5
1
30. Which person’s line of best fit works better and why do you think so?
Nancy’s LOBF is the best because her residuals are closely centered near zero and only exceed 1 or -1 in a couple
of instances. The other residuals are lopsided and exceed 1 or -1 more often.
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Answer the following questions about two-way tables.
31. Construct a two-way table from the following data about whether or not students own an iPhone and
whether or not they own an iPad.
Own an
iPhone?
Own a iPad?
Y N Y Y N Y N N Y Y Y N N Y N N Y N Y N
Y N Y N N Y Y N Y N Y Y N Y N N Y Y N N
Owns iPhone
Owns iPad
Does Not Own iPad
7
3
Does Not Own
iPhone
3
7
32. Do you think there is a relationship between owning a iPhone and owning an iPad? Based on the data, why or
why not? Yes, there is a relationship. Owners of iPhones are more likely to own iPads. 70% of iPhone owners
also own an iPad and 70% of those who do not own an iPhone also do not own an iPad.
Answer the following questions using the given two-way table.
Students
Teachers
Support Year-Round
School
250
80
Do Not Support YearRound School
2150
70
33. How many teachers were surveyed? 150
34. How many students were surveyed? 2400
35. How many people support year-round school? 330
36. How many teachers do not support year-round school? 70
37. How many students do not support year-round school? 2150
38. As a percent to the nearest hundredth (two decimal places) what is the relative frequency of the teachers
"BC
compared to all those surveyed? BBC ≈ 5.88%
39. As a percent to the nearest hundredth (two decimal places) what is the relative frequency of the students
BC
who support year-round school compared to all students? DCC ≈ 10.42%
40. As a percent to the nearest hundredth (two decimal places) what is the relative frequency of the teachers
1C
who do not support year-round school compared to all teachers? "BC ≈ 46.67%
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