The stem-and-leaf plot shows scores on a recent math quiz for two classes. How many students in each class scored 85?
Quiz Scores
Mrs. James’s Class
Mr. Cleveland’s Class
Leaf
Stem
Leaf
8
6
7
7 6 4 3
7
5 5 7 9
9 7 5 5 3 1
8
2 4 4 5 8
3 1 0
9
2 5
Key: 8|6 means 68%
Key: 6|7 means 67%
A. Mrs. James’s class, two; Mr. Cleveland’s class, one
B. Mrs. James’s class, one; Mr. Cleveland’s class, two
C. Mrs. James’s class, two; Mr. Cleveland’s class, two
D. none of these
B. Mrs. James’s class, one; Mr. Cleveland’s class, two.
Which survey question is biased?
A. Which – fall, winter, spring, or summer – is your favorite season?
B. Which sport is your favorite: baseball, basketball, football, or tennis?
C. Which do you like better, television or video games?
D. Which do you like better, coffee or fresh, tasty water
D. Which do you like better, coffee or fresh, tasty water?
This question is biased because it presents coffee as not being fresh or tasty, and implies that water is the better option. It also assumes that the respondent is interested in both coffee and water as beverage choices.
Game wardens use experiments to help determine the number of fish in a lake. Suppose 80 fish are caught, tagged, and released back into the lake. Two weeks later 120 fish are caught, 3 of which are found to have tags. Using this information, estimate the number of fish in the lake.
A. 3,200
B. 600
C. 120
D. 280
We can use a proportion to estimate the number of fish in the lake:
tagged fish in sample 1 / total number of fish in lake = tagged fish in sample 2 / total number of fish in sample 2
We know that 80 fish were tagged in sample 1, and 3 of those were caught in sample 2. We also know that the total number of fish caught in sample 2 was 120. So:
80 / x = 3 / 120
Cross-multiplying gives:
80 * 120 = 3 * x
x = (80 * 120) / 3 = 3200
Therefore, the estimated number of fish in the lake is 3,200.
Answer: A. 3,200
The table shows the relationship between the number of days an ice cream shop is open
and the number of ice cream cones sold. Graph the data in a scatter plot and describe the trend shown by the graph.
Number of Days
Number of Cones Sold
1
38
2
68
3
70
4
86
5
89
6
93
7
97
A. A scatter plot of the number of cones sold for 7 days is shown. The x-axis is labeled Number of Days and has numbers from 0 to 7 with a step size of 1. The y-axis is labeled Number of Cones Sold and has numbers from 0 to 100 with a step size of 25. The scatter plots shows these approximate points: left-parenthesis 1 comma 42 right-parenthesis, left-parenthesis 2 comma 66 right-parenthesis, left-parenthesis 3 comma 70 right-parenthesis, left-parenthesis 4 comma 81 right-parenthesis, left-parenthesis 5 comma 87 right-parenthesis, left-parenthesis 6 comma 92 right-parenthesis, and left-parenthesis 7 comma 99 right-parenthesis.
The scatter plot shows a positive trend. As the number of days increases, the number of cones sold increases.
B. A scatter plot of the number of cones sold for 7 days is shown. The x-axis is labeled Number of Days and has numbers from 0 to 7 with a step size of 1. The y-axis is labeled Number of Cones Sold and has numbers from 0 to 100 with a step size of 25. The scatter plots shows these approximate points: left-parenthesis 1 comma 42 right-parenthesis, left-parenthesis 2 comma 66 right-parenthesis, left-parenthesis 3 comma 70 right-parenthesis, left-parenthesis 4 comma 81 right-parenthesis, left-parenthesis 5 comma 87 right-parenthesis, left-parenthesis 6 comma 92 right-parenthesis, and left-parenthesis 7 comma 99 right-parenthesis.
The scatter plot shows a negative trend. As the number of days increases, the number of cones sold decreases.
C. A scatter plot of the number of cones sold for 7 days is shown. The x-axis is labeled Number of Days and has numbers from 0 to 7 with a step size of 1. The y-axis is labeled Number of Cones Sold and has numbers from 0 to 100 with a step size of 25. The scatter plots shows these approximate points: left-parenthesis 1 comma 36 right-parenthesis, left-parenthesis 2 comma 46 right-parenthesis, left-parenthesis 3 comma 57 right-parenthesis, left-parenthesis 4 comma 68 right-parenthesis, left-parenthesis 5 comma 79 right-parenthesis, left-parenthesis 6 comma 89 right-parenthesis, and left-parenthesis 7 comma 100 right-parenthesis.
The scatter plot shows a positive trend. As the number of days increases, the number of cones sold increases.
D. A scatter plot of the number of cones sold for 7 days is shown. The x-axis is labeled Number of Days and has numbers from 0 to 7 with a step size of 1. The y-axis is labeled Number of Cones Sold and has numbers from 0 to 100 with a step size of 25. The scatter plots shows these approximate points: left-parenthesis 1 comma 36 right-parenthesis, left-parenthesis 2 comma 46 right-parenthesis, left-parenthesis 3 comma 57 right-parenthesis, left-parenthesis 4 comma 68 right-parenthesis, left-parenthesis 5 comma 79 right-parenthesis, left-parenthesis 6 comma 89 right-parenthesis, and left-parenthesis 7 comma 100 right-parenthesis.
The scatter plot shows a negative trend. As the number of days increases, the number of cones sold decreases.2
B. A scatter plot of the number of cones sold for 7 days is shown. The x-axis is labeled Number of Days and has numbers from 0 to 7 with a step size of 1. The y-axis is labeled Number of Cones Sold and has numbers from 0 to 100 with a step size of 25. The scatter plot shows these approximate points: (1,38), (2,68), (3,70), (4,86), (5,89), (6,93), and (7,97).
The scatter plot shows a positive trend. As the number of days increases, the number of cones sold 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
The scatter plot most likely represents a positive correlation between the number of hours worked and the amount of money earned. Option A shows a nearly linear pattern that starts at the upper left and continues down and to the right. This direction and pattern is consistent with a positive correlation.
Answer: 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.
To determine how many students in each class scored 85, we need to examine the stem-and-leaf plot. In the plot for Mrs. James's class, we see a stem of 8 with a leaf of 5. This means there is one student in Mrs. James's class who scored 85.
In the plot for Mr. Cleveland's class, we see a stem of 8 with a leaf of 7. This means there is one student in Mr. Cleveland's class who scored 85.
Therefore, the correct answer is:
B. Mrs. James’s class, one; Mr. Cleveland’s class, two