year  number of cases  

row 1  1941  222,202 
row 2  1950  120,718 
row 3  1945  133,792 
row 4  1942  191,383 
row 5  1953  37,129 
row 6  1939  103,188 
row 7  1951  68,687 
row 8  1948  74,715 
row 9  1955  62,786 
row 10  1952  45,030 
row 11  1940  183,866 
row 12  1954  60,866 
row 13  1944  109,873 
row 14  1946  109,860 
row 15  1943  191,890 
row 16  1949  69,479 
row 17  1947  156,517 
Unit 6: Practice Problem Sets
Lesson 1
Problem 1
Here is data on the number of cases of whooping cough from 1939 to 1955.
 Make a new table that orders the data by year.
 Which years in this period of time had fewer than 100,000 cases of whooping cough?
 Based on this data, would you expect 1956 to have closer to 50,000 cases or closer to 100,000 cases?
Problem 2
In volleyball statistics, a block is recorded when a player deflects the ball hit from the opposing team. Additionally, scorekeepers often keep track of the average number of blocks a player records in a game. Here is part of a table that records the number of blocks and blocks per game for each player in a women’s volleyball tournament. A scatter plot that goes with the table follows.
blocks  blocks per game  

row 1  13  1.18 
row 2  1  0.17 
row 3  5  0.42 
row 4  0  0 
row 5  0  0 
row 6  7  0.64 
Label the axes of the scatter plot with the necessary information.
Problem 3 (from Unit 5, Lesson 18)
A cylinder has a radius of 4 cm and a height of 5 cm.
 What is the volume of the cylinder?
 What is the volume of the cylinder when its radius is tripled?
 What is the volume of the cylinder when its radius is halved?
Lesson 2
Problem 1
In hockey, a player gets credited with a “point” in their statistics when they get an assist or goal. The table shows the number of assists and number of points for 15 hockey players after a season.
assists  points  

row 1  22  28 
row 2  16  18 
row 3  46  72 
row 4  19  29 
row 5  13  26 
row 6  9  13 
row 7  16  22 
row 8  8  18 
row 9  12  13 
row 10  12  17 
row 11  37  50 
row 12  7  12 
row 13  17  34 
row 14  27  58 
row 15  18  34 
Problem 2
Select all the representations that are appropriate for comparing bite strength to weight for different carnivores.
 Histogram
 Scatter plot
 Dot plot
 Table
 Box plot
Problem 3
When is it better to use a table? When is it better to use a scatter plot?
Problem 4 (from Unit 5, Lesson 17)
There are many cylinders with radius 6 meters. Let $h$ represent the height in meters and $V$ represent the volume in cubic meters.

Write an equation that represents the volume $V$ as a function of the height $h$.

Sketch the graph of the function, using 3.14 as an approximation for $\pi$.

If you double the height of a cylinder, what happens to the volume? Explain this using the equation.

If you multiply the height of a cylinder by $\frac 1 3$, what happens to the volume? Explain this using the graph.
Lesson 3
Problem 1
Here is a table and a scatter plot that compares points per game to free throw attempts for a basketball team during a tournament.
player  free throw attempts  points 

player A  5.5  28.3 
player B  2.1  18.6 
player C  4.1  13.7 
player D  1.6  10.6 
player E  3.1  10.4 
player F  1  5 
player G  1.2  5 
player H  0.7  4.7 
player I  1.5  3.7 
player J  1.5  3.5 
player K  1.2  3.1 
player L  0  1 
player M  0  0.8 
player N  0  0.6 
 Circle the point that represents the data for Player E.
 What does the point $(2.1,18.6)$ represent?
 In that same tournament, Player O on another team scored 14.3 points per game with 4.8 free throw attempts per game. Plot a point on the graph that shows this information.
Problem 2 (from Unit 6, Lesson 2)
Select all the representations that are appropriate for comparing exam score to number of hours of sleep the night before the exam.
 Histogram
 Scatter plot
 Dot plot
 Table
 Box plot
Problem 3 (from Unit 5, Lesson 17)
A cone has a volume of $36\pi$ cm^{3} and height $h$. Complete this table for volume of cylinders with the same radius but different heights.
height (cm)  volume (cm^{3})  

row 1  $h$  $36\pi$ 
row 2  $2h$  
row 3  $5h$  
row 4  $\frac h2$  
row 5  $\frac h5$ 
Lesson 4
Problem 1
The scatter plot shows the number of hits and home runs for 20 baseball players who had at least 10 hits last season. The table shows the values for 15 of those players.
The model, represented by $y = 0.15x  1.5$, is graphed with a scatter plot.
Use the graph and the table to answer the questions.
 Player A had 154 hits in 2015. How many home runs did he have? How many was he predicted to have?
 Player B was the player who most outperformed the prediction. How many hits did Player B have last season?
 What would you expect to see in the graph for a player who hit many fewer home runs than the model predicted?
hits  home runs  predicted home runs  

row 1  12  2  0.3 
row 2  22  1  1.8 
row 3  154  26  21.6 
row 4  145  11  20.3 
row 5  110  16  15 
row 6  57  3  7.1 
row 7  149  17  20.9 
row 8  29  2  2.9 
row 9  13  1  0.5 
row 10  18  1  1.2 
row 11  86  15  11.4 
row 12  163  31  23 
row 13  115  13  15.8 
row 14  57  16  7.1 
row 15  96  10  12.9 
Problem 2
Here is a scatter plot that compares points per game to free throw attempts per game for basketball players in a tournament. The model, represented by $y = 4.413x + 0.377$, is graphed with the scatter plot. Here, $x$ represents free throw attempts per game, and $y$ represents points per game.
 Circle any data points that appear to be outliers.
 What does it mean for a point to be far above the line in this situation?
 Based on the model, how many points per game would you expect a player who attempts 4.5 free throws per game to have? Round your answer to the nearest tenth of a point per game.
 One of the players scored 13.7 points per game with 4.1 free throw attempts per game. How does this compare to what the model predicts for this player?
Lesson 5
Problem 1
 Draw a line that you think is a good fit for this data. For this data, the inputs are the horizontal values, and the outputs are the vertical values.
 Use your line of fit to estimate what you would expect the output value to be when the input is 10.
Problem 2 (from Unit 6, Lesson 3)
Here is a scatter plot that shows the most popular videos in a 10year span.
 Use the scatter plot to estimate the number of views for the most popular video in this 10year span.
 Estimate when the 4th most popular video was released.
Problem 3 (from Unit 5, Lesson 8)
A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour.

Name two quantities in this situation that are in a functional relationship.

Write an equation that represents the function.

Draw the graph of the function. Label at least two points with inputoutput pairs.
Lesson 6
Problem 1
Which of these statements is true about the data in the scatter plot?
 As $x$ increases, $y$ tends to increase.
 As $x$ increases, $y$ tends to decrease.
 As $x$ increases, $y$ tends to stay unchanged.
 $x$ and $y$ are unrelated.
Problem 2
Here is a scatter plot that compares hits to at bats for players on a baseball team.
Problem 3
The linear model for some butterfly data is given by the equation $y = 0.238x + 4.642$. Which of the following best describes the slope of the model?
 For every 1 mm the wingspan increases, the length of the butterfly increases 0.238 mm.
 For every 1 mm the wingspan increases, the length of the butterfly increases 4.642 mm.
 For every 1 mm the length of the butterfly increases, the wingspan increases 0.238 mm.
 For every 1 mm the length of the butterfly increases, the wingspan increases 4.642 mm.
Problem 4 (from Unit 6, Lesson 4)
Nonstop, oneway flight times from O’Hare Airport in Chicago and prices of a oneway ticket are shown in the scatter plot.
 Circle any data that appear to be outliers.
 Use the graph to estimate the difference between any outliers and their predicted values.
Problem 5 (from Unit 4, Lesson 14)
Solve: \(\begin{cases} y=\text3x+13 \\ y=\text2x+1 \\ \end{cases}\)
Lesson 7
Problem 1
Literacy rate and population for the 12 countries with more than 100 million people are shown in the scatter plot. Circle any clusters in the data.
Problem 2
Here is a scatter plot:
Select all the following that describe the association in the scatter plot:
 Linear association
 Nonlinear association
 Positive association
 Negative association
 No association
Problem 3 (from Unit 6, Lesson 5)
For the same data, two different models are graphed. Which model more closely matches the data? Explain your reasoning.
Problem 4 (from Unit 6, Lesson 3)
Here is a scatter plot of data for some of the tallest mountains on Earth.
The heights in meters and year of first recorded ascent is shown. Mount Everest is the tallest mountain in this set of data.
 Estimate the height of Mount Everest.
 Estimate the year of the first recorded ascent of Mount Everest.
Problem 5 (from Unit 5, Lesson 18)
A cone has a volume $V$, radius $r$, and a height of 12 cm.
 A cone has the same height and $\frac13$ of the radius of the original cone. Write an expression for its volume.
 A cone has the same height and 3 times the radius of the original cone. Write an expression for its volume.
Lesson 8
Problem 1
Different stores across the country sell a book for different prices. The table shows the price of the book in dollars and the number of books sold at that price.
price in dollars  number sold  

row 1  11.25  53 
row 2  10.50  60 
row 3  12.10  30 
row 4  8.45  81 
row 5  9.25  70 
row 6  9.75  80 
row 7  7.25  120 
row 8  12  37 
row 9  9.99  130 
row 10  7.99  100 
row 11  8.75  90 
 Draw a scatter plot of this data. Label the axes.
 Are there any outliers? Explain your reasoning.
 If there is a relationship between the variables, explain what it is.
 Remove any outliers, and draw a line that you think is a good fit for the data.
Problem 2 (from Unit 6, Lesson 7)
Here is a scatter plot:
Select all the following that describe the association in the scatter plot:
 Linear association
 Nonlinear association
 Positive association
 Negative association
 No association
Problem 3 (from Unit 6, Lesson 6)
Using the data in the scatter plot, what can you tell about the slope of a good model?
 The slope is positive.
 The slope is zero.
 The slope is negative.
 There is no association.
Lesson 9
Problem 1
A scientist wants to know if the color of the water affects how much animals drink. The average amount of water each animal drinks was recorded in milliliters for a week and then graphed. Is there evidence to suggest an association between water color and animal?
cat intake (ml)  dog intake (ml)  total (ml)  

blue water  210  1200  1410 
green water  200  1100  1300 
total  410  2300  2710 
Problem 2
A farmer brings his produce to the farmer’s market and records whether people buy lettuce, apples, both, or something else.
bought apples  did not buy apples  

bought lettuce  14  58 
did not buy lettuce  8  29 
Problem 3
Researchers at a media company want to study newsreading habits among different age groups. They tracked print and online subscription data and made a 2way table.
internet articles  print articles  

18–25 year olds  151  28 
26–45 year olds  132  72 
45–65 year olds  48  165 
 Create a segmented bar graph using one bar for each row of the table.
 Is there an association between age groups and the method they use to read articles? Explain your reasoning.
Problem 4 (from Unit 6, Lesson 6)
Using the data in the scatter plot, what is a reasonable slope of a model that fits this data?
 2.5
 1
 1
 2.5
Lesson 10
Problem 1
An ecologist is studying a forest with a mixture of tree types. Since the average tree height in the area is 40 feet, he measures the height of the tree against that. He also records the type of tree. The results are shown in the table and segmented bar graph. Is there evidence of an association between tree height and tree type? Explain your reasoning.
under 40 feet  40 feet or taller  total  

deciduous  45  30  75 
evergreen  14  10  24 
total  59  40  99 
Problem 2
Workers at an advertising agency are interested in people’s TV viewing habits. They take a survey of people in two cities to try to find patterns in the types of shows they watch. The results are recorded in a table and shown in a segmented bar graph. Is there evidence of different viewing habits? If so, explain.
reality  news  comedy  drama  

Chicago  50  40  90  20 
Topeka  45  70  40  45 
Problem 3
A scientist is interested in whether certain species of butterflies like certain types of local flowers. The scientist captures butterflies in two zones with different flower types and records the number caught. Do these data show an association between butterfly type and zone? Explain your reasoning.
zone 1  zone 2  

eastern tiger swallowtail  16  34 
monarch  24  46 
Lesson 11
No practice problems for this lesson.