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
It is impossible to determine the correct answer without seeing the actual scatter plot created by Jared.
Which of the following types of information is suited for display on a double line graph?
A. annual changes in Melody’s height and weight from 5 to 10 years old
B. number of Democrats and Republicans in the Senate during the past decade
C. monthly sales of two different types of cars during a one-year period
D. all of these answers
C. monthly sales of two different types of cars during a one-year period is suited for display on a double line graph. A double line graph is used to compare two sets of data over time. Monthly sales of two different types of cars over one year can be effectively compared using this type of graph. Annual changes in height and weight and the number of Democrats and Republicans in the Senate do not have a clear relationship that can be shown on a double line graph.
Short Answer
Note: Your teacher will grade your responses to questions 18 and 19 to ensure that you receive proper credit for your answers.
You are surveying students to find out their opinion of the quality of food served in the school cafeteria. You decide to poll only those students who buy hot lunch on a particular day. Is your sample random? Explain.
No, the sample is not random. Random sampling requires that every member of the population has an equal chance of being selected for the sample. By choosing only students who buy hot lunch on a particular day, the sample is limited to a specific group and does not represent the entire population of students. It is possible that students who do not buy hot lunch have different opinions about the quality of the food, so the results of the survey may not be representative of the entire student body.
The table shows the rainfall, in inches, in the month of July for the years 2006 through 2011.
Year
2006
2007
2008
2009
2010
2011
Rainfall
4.5
4.4
4.1
4.2
3.9
4.0
Alex used the data to make the graph below.
A line graph representing the data in the table is shown.A line graph is titled July Rainfall.
The horizontal axis is labeled Year and is equally spaced. The axis scale starts at 2006 increases by 1 until ending at 2011.
The vertical axis is labeled Rainfall in inches and is equally spaced. The axis scale starts at 3.6 and increases by 0.1 until ending at 4.6.
The data points represented in the tabled are connected by line segments from left to right.
a) In what way could the graph be misleading?
b) How could you redraw the graph so that it is less misleading?
a) The graph could be misleading in a couple of ways. First, the vertical axis is drawn with too much detail. The axis scale starts at 3.6 inches, which makes the differences between the data points difficult to see. Second, the line connecting the data points suggests a smooth trend in the data, even though the differences between the rainfall amounts from year to year are relatively small. Finally, the use of a line graph implies that the rainfall amounts are continuous and that intermediate values can be estimated, which may not be the case.
b) To redraw the graph so that it is less misleading, the vertical axis could be redrawn with a larger scale that includes only the possible values of rainfall given in the table (e.g. 3.5 to 4.5 inches with intervals of 0.5 inches). This would make it easier to see the differences between the years and avoid overemphasizing small changes. Additionally, a bar graph could be used instead of a line graph to show the discrete nature of the data. Each bar could represent the rainfall for a particular year, and the heights of the bars would correspond to the rainfall values in inches.
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
Incorrect answer A. 4
Incorrect answer B. 6
Incorrect answer C. 7
Correct answer D. 10
D. 10. We can count the number of games with more than 40 points by looking at the stem and leaf plot. There are two numbers in the 5 stem (52 and 58), three numbers in the 4 stem (44, 45, and 48), and five numbers in the 3 stem (56, 66, 63, 62, and 60). Adding these up, we get a total of 10 games with more than 40 points scored.
To determine which scatter plot most likely represents the data, we need to think about the relationship between the number of hours worked and the amount of money earned.
Typically, as the number of hours worked increases, the amount of money earned also tends to increase. So, the scatter plot that shows a rising trend from the lower left to the upper right would be the most likely representation of the data.
Based on the given options:
A. A graph that shows a nearly linear pattern from the upper left to the lower right does not match the expected relationship.
B. A graph that shows a nearly linear pattern from the lower left to the upper right matches the expected relationship and is the most likely representation of the data.
C. A graph that shows a somewhat random pattern does not match the expected relationship.
D. None of these options match.
Therefore, option B, which shows a rising trend from the lower left to the upper right, is the most likely representation of the data.