Multiple Choice
Using the frequency table below, find how many students received a score of 70 or better on a mathematics test.
Score Interval
Frequency
50 – 59
2
60 – 69
5
70 – 79
5
80 – 89
7
90 – 99
2
A. 19
B. 12
C. 17
D. 14
C. 17
Researchers at Jackson Hospital asked 40 randomly selected patients about their sleep habits. Sixteen reported sleeping 8 hours or more each night. If there are 700 patients in the hospital, estimate the number of patients who sleep 8 hours or more each night.
A. 140
B. 160
C. 180
D. 280
B. 160
To estimate the number of patients who sleep 8 hours or more each night, we can use proportion:
16/40 = x/700
Solving for x:
x = (16/40) * 700
x = 280/2 = 140
We can estimate that about 140 patients out of the 700 in the hospital sleep 8 hours or more each night.
A newspaper reporter wants to know how popular the hobby of bird watching is in the city. He asked people at the local bird refuge if they watched birds as a hobby. Which of the following best explains whether the reporter's data is valid or not?
A. The data is valid for the entire city because the bird refuge is located in the city.
B. The data is not valid for the entire city because people can have more than one hobby.
C. The data is not valid for the entire city because bird watchers are more likely to visit a bird refuge.
D. The data is valid for the entire city because a bird refuge is a good place to find people who like to watch birds.
C. The data is not valid for the entire city because bird watchers are more likely to visit a bird refuge.
The data collected by the reporter may not be valid for the entire city because people who visit a bird refuge are more likely to be interested in bird watching as a hobby than the general population. Furthermore, people who are not interested in bird watching would have no reason to visit a bird refuge. As a result, the sample may not be representative of the population as a whole, and the data may be biased. Therefore, option C is the best explanation.
Which of the following types of information is suited for display on a double line graph?
A. average wages paid to men and to women over 5 years
B. average heights of basketball players in five schools
C. average ages of people entering the pubic library in five locations
D. average prices of two car models at five dealerships
D. Average prices of two car models at five dealerships.
Double line graphs are typically used to show the relationship between two variables over time or some other shared interval. For example, a double line graph could be used to show how the average price of two car models changes over time. Option D is the only answer that includes data that can be compared on a shared interval (i.e. the same set of dealerships).
Option A is better suited for a side-by-side bar graph, whereas Option B and Option C may be better suited for a grouped bar graph.
The stem and leaf plot below shows the number of points scored in each basketball game a team played during a season. In how many games were more than 40 points scored?
Stem
Leaf
6
1 6 7
5
2 2 8
4
4 5 8 9
3
0 2 6 6 6
2
0 8
A. 4
B. 6
C. 7
D. 10
C. 7
To find out in how many games were more than 40 points scored, we need to look at the numbers in the stem and leaf plot that are greater than 4 (since the stem for 40 is 4).
We can see from the plot that there are 3 games with a score of 51, 1 game with a score of 52, 1 game with a score of 54, and 2 games with a score of 69.
Therefore, the answer is 3 + 1 + 1 + 2 = 7.
The stem-and-leaf plot shows the height, in inches, of the players on two different basketball teams. How many players on each team are less than 70 inches tall?
Heights of Players
In inches
Austin College Barton College
Leaf
Stem
Leaf
6 7 8 8 9
6
4 6 8
1 1 2 6
7
1 1 1 3 4 5
1
8
2
A. Austin College, 4; Barton College, 6
B. Austin College, 5; Barton College, 7
C. Austin College, 5; Barton College, 3
D. Austin College, 9; Barton College, 9
A. Austin College, 4; Barton College, 6.
To find the number of players on each team that are less than 70 inches tall, we need to look at the numbers in the stem-and-leaf plot that are less than 7 (since 70 inches is equivalent to a height of 7 feet).
We can see from the plot that on the Austin College team, there are 4 players with a height less than 70 inches (the numbers in the 6th row). On the Barton College team, there are 6 players with a height less than 70 inches (the numbers in the 4th and 6th rows).
Therefore, the answer is Austin College, 4; Barton College, 6.
Which survey question is biased?
A. “Should the President of the United States serve a six-year term?”
B. “Which meal—breakfast, lunch, or dinner—is your favorite meal of the day?”
C. “During which month do you prefer to go on vacation?”
D. “Do you prefer white bread or healthy, whole-wheat bread?”
D. “Do you prefer white bread or healthy, whole-wheat bread?”
This survey question is biased because it is leading the respondent towards choosing the "healthy, whole-wheat bread" option. The term "healthy" implies that the whole-wheat bread is a better choice than white bread, and this could influence the respondent's answer.
The other survey questions are neutral and do not contain any leading or biased language.
Game wardens use experiments to help determine the number of squirrels in a specific area. Suppose 150 squirrels are caught, tagged, and released back into the wild. Six weeks later, 300 squirrels are caught with 12 found to have tags. Using this information, estimate the number of squirrels in the area.
A. 375
B. 500
C. 3,750
D. 5,000
B. 500
This is an application of the capture-mark-recapture method for estimating population size. The basic idea is that if some individuals are captured, marked (or tagged), and then released, and a second sample is collected later, the proportion of marked individuals in the second sample can be used to make an estimate of the total population size.
Let N = the population size, and let M = the number of marked individuals in the first sample. We can use the formula:
(N * M) / n = R
where n = the size of the second sample, and R = the number of marked individuals in the second sample.
In this case, we have:
N = unknown
M = 150 (the number of squirrels tagged in the first sample)
n = 300 (the number of squirrels in the second sample)
R = 12 (the number of tagged squirrels in the second sample)
Plugging in the numbers:
(N * 150) / 300 = 12
N = (12 * 300) / 150 = 24
Thus, the estimated population size is N = 500. Note that this is just an estimate, and there may be some variability or bias associated with this method.
The table shows the relationship between the number of roller coasters ridden at the fair and the amount spent at the fair. Graph the data in a scatter plot and describe the trend shown by the graph.
# of Roller Coasters Total Cost
0 8.75
2 10
5 12.75
7 14.25
8 15
9 16
A. A scatter plot of the price of riding roller coasters is shown.The x-axis is labeled # of Roller Coasters and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Total Cost and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 9 right-parenthesis, left-parenthesis 2 comma 10 right-parenthesis, left-parenthesis 5 comma 12.5 right-parenthesis, left-parenthesis 7 comma 15 right-parenthesis, left-parenthesis 8 comma 15 right-parenthesis, and left-parenthesis 9 comma 16 right-parenthesis.
The scatter plot shows a negative trend. As the number of roller coasters increases, the total cost decreases.
B. A scatter plot of the price of riding roller coasters is shown. The x-axis is labeled # of Roller Coasters and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Total Cost and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 9 right-parenthesis, left-parenthesis 2 comma 12 right-parenthesis, left-parenthesis 5 comma 14 right-parenthesis, left-parenthesis 7 comma 15 right-parenthesis, left-parenthesis 8 comma 17.5 right-parenthesis, and left-parenthesis 9 comma 20 right-parenthesis.
The scatter plot shows a negative trend. As the number of roller coasters increases, the total cost decreases.
C. A scatter plot of the price of riding roller coasters is shown.The x-axis is labeled # of Roller Coasters and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Total Cost and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 9 right-parenthesis, left-parenthesis 2 comma 10 right-parenthesis, left-parenthesis 5 comma 12.5 right-parenthesis, left-parenthesis 7 comma 15 right-parenthesis, left-parenthesis 8 comma 15 right-parenthesis, and left-parenthesis 9 comma 16 right-parenthesis.
The scatter plot shows a positive trend. As the number of roller coasters increases, the total cost increases.
D. A scatter plot of the price of riding roller coasters is shown. The x-axis is labeled # of Roller Coasters and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Total Cost and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 9 right-parenthesis, left-parenthesis 2 comma 12 right-parenthesis, left-parenthesis 5 comma 14 right-parenthesis, left-parenthesis 7 comma 15 right-parenthesis, left-parenthesis 8 comma 17.5 right-parenthesis, and left-parenthesis 9 comma 20 right-parenthesis.
The scatter plot shows a positive trend. As the number of roller coasters increases, the total cost increases.
B. A scatter plot of the price of riding roller coasters is shown. The x-axis is labeled # of Roller Coasters and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Total Cost and has numbers from 0 to 20 with a step size of 5. The scatter plot shows these approximate points: left-parenthesis 0 comma 9 right-parenthesis, left-parenthesis 2 comma 12 right-parenthesis, left-parenthesis 5 comma 14 right-parenthesis, left-parenthesis 7 comma 15 right-parenthesis, left-parenthesis 8 comma 17.5 right-parenthesis, and left-parenthesis 9 comma 20 right-parenthesis.
The scatter plot shows a positive trend. As the number of roller coasters increases, the total cost increases.
Jared drew a scatter plot comparing the number of hours worked and the amount of money earned over the course of a week. He graphed the ordered pairs (number of hours, amount paid) for each day worked. Which of the three scatter plots below most likely represents the data?
A. A graph shows six points. The points begin at the upper left and continue down and to the right in a nearly linear pattern.
B. A graph shows six points. The points begin at the lower left and continue up and to the right in a nearly linear pattern.
C. A graph shows six points. The points begin at the upper left and continue primarily down and to the right in a somewhat random pattern.
D. None of these
A. A graph shows six points. The points begin at the upper left and continue down and to the right in a nearly linear pattern.
Since Jared is comparing the number of hours worked and the amount of money earned, it makes sense that as the number of hours worked increases, the amount of money earned would also increase. This would result in a positive association between the two variables, which would be best represented by a scatter plot that begins at the lower left and continues up and to the right in a nearly linear pattern. Option A is the only choice that describes this pattern, so it is the correct answer.
The list shows the final exam grades for Ms. Gold’s math class. Make a stem-and-leaf plot for the data.
66, 98, 92, 91, 69, 55, 53, 90, 67, 74, 57, 58, 60, 59, 86, 92, 63, 55, 51, 84
A.
stem-and-leaf plot
The step-and-leaf plot consists of five rows of numbers. A single vertical line separates the first and second columns. The numbers in row 1 are, from left to right, 5, 1, 3, 5, 5, 7, and 8. The numbers in row 2 are, from left to right, 6, 0, 3, 6, 7, 9, and 9. The numbers in row 3 are, from left to right, 7 and 4. The numbers in row 4 are, from left to right, 8, 4, and 6. The numbers in row 5 are, from left to right, 9, 0. 1. 2, 2, and 8.
B.
stem-and-leaf plot
The step-and-leaf plot consists of five rows of numbers. A single vertical line separates the first and second columns. The numbers in row 1 are, from left to right, 5, 1, 3, 5, 5, 7, 8, and 9. The numbers in row 2 are, from left to right, 6, 0, 3, 6, 7, and 9. The numbers in row 3 are, from left to right, 7 and 4. The numbers in row 4 are, from left to right, 8, 4, and 6. The numbers in row 5 are, from left to right, 9, 0. 1. 2, 2, and 8.
C.
stem-and-leaf plot
The step-and-leaf plot consists of five rows of numbers. A single vertical line separates the first and second columns. The numbers in row 1 are, from left to right, 5, 1, 3, 5, 5, 7, and 8. The numbers in row 2 are, from left to right, 6, 0, 3, 6, 7, and 9. The numbers in row 3 are, from left to right, 7, 4, and 9. The numbers in row 4 are, from left to right, 8, 4, and 8. The numbers in row 5 are, from left to right, 9, 0. 1. 2, and 2.
D.
stem-and-leaf plot
The step-and-leaf plot consists of five rows of numbers. A single vertical line separates the first and second columns. The numbers in row 1 are, from left to right, 5, 1, 3, 5, 5, 7, 8, and 9. The numbers in row 2 are, from left to right, 6, 0, 3, 6, 7, and 9. The numbers in row 3 are, from left to right, 7, 4, and 4. The numbers in row 4 are, from left to right, 8 and 4. The numbers in row 5 are, from left to right, 9, 0. 1. 2, 2, and 8.
A. Stem-and-leaf plot:
5 | 1 3 5 5 7 8 9
6 | 0 3 6 7 9 9
7 | 4 7
8 | 4 6 8
9 | 0 1 2 2 8
Note: The vertical line separates the stems (left-hand side) from the leaves (right-hand side). For example, the first row shows that there are two students who scored in the 50s (stem 5