Short Answer
Note: Your teacher will grade your response to ensure that you receive proper credit for your answer.
The graph below shows the number of new clients brought into Sunnydays Insurance Company. Why is the graph misleading?
A line graph is shown.
I'm sorry, I cannot see or access image/graph attachments.
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Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of
his classes. He teaches band to 25 students. There are 9 students who have Mr. Green for math
and nothing else
How many students take exactly 2 classes with Mr. Green?
Let's denote the number of students who take choir and math with Mr. Green as A and the number of students who take both band and choir (but not math) as B. We know that:
- The total number of students who take at least one class is 57.
- The number of students who take band is 25.
- The number of students who take only math is 9.
- We want to find the number of students who take exactly 2 classes.
Using this information, we can set up the following equation:
25 + A + B + 9 = 57
Simplifying this equation, we get:
A + B = 23
We know that B represents the number of students who take both band and choir but not math. Let's now find B:
B = 25 - the number of students who only take band
We don't know the number of students who only take band, but we do know that:
- If there were no students who only took band, then B would be 0 and A would be 23 (since A + B = 23). However, we know that there are students who only take band (otherwise the total number of students taking at least one class would be less than 25).
- If all 25 students who take band also take at least one other class with Mr. Green, then A would be 0 and B would be 25. However, we know that there are students who only take math (otherwise the total number of students taking at least one class would be at least 34).
Therefore, the only possibility is that some students take only band and some take both band and choir. Let's denote the number of students who only take band as C:
B + C = 25
Substituting B = 25 - C into the equation A + B = 23, we get:
A + 25 - C = 23
Simplifying, we get:
A = C - 2
We want to find the number of students who take exactly 2 classes. This includes the students who take both band and choir (i.e., B) and the students who take choir and math (i.e., A). Therefore:
Number of students who take 2 classes = A + B = (C - 2) + B = C - 2 + (25 - C) = 23
So, there are 23 students who take exactly 2 classes with Mr. Green.
To determine why the graph is misleading, we need to analyze its components and consider potential issues with its presentation. Here's the step-by-step process to assess the graph:
Step 1: Examine the title and axis labels
Check if the graph includes a clear title and well-labeled axes. The title should provide a brief description of what the graph represents. The x-axis should indicate the time period (e.g., months or years), while the y-axis should specify the measured variable (in this case, the number of new clients).
Step 2: Evaluate the data points
Look at the actual data points plotted on the graph. Verify that the data is clearly marked and accurately representing the information being conveyed. In this case, the data points should represent the number of new clients brought into Sunnydays Insurance Company over the given time period.
Step 3: Consider the scale and intervals
Examine the scale and intervals used on both axes. Ensure that the values are appropriately spaced and labeled to reflect the data accurately. Pay attention to whether the intervals are consistent or if they differ significantly.
Step 4: Assess the line plot
Observe the line plot itself. Pay attention to the shape and trend of the line connecting the data points. It should accurately represent the overall pattern of how the number of new clients has changed over time.
Step 5: Identify potential misleading aspects
Consider any potential issues with the graph that may lead to misinterpretation or misunderstanding. Examples of misleading aspects could include:
- Inconsistent or distorted scaling on one or both axes
- Omitting relevant data points or periods from the graph
- Using a different type of graph that is not well-suited for the data being presented
- Manipulating the line plot to emphasize or downplay certain trends
- Lack of context or explanation for any anomalies or fluctuations in the data
By going through these steps, you should be able to identify the reasons why the graph may be misleading.