extension questions
model 4 – sat scores
graph f (bar graph: average sat of incoming freshmen, x - axis college (a, b, c, d), y - axis sat score 0 - 2500)
graph g (bar graph: average sat of incoming freshmen, x - axis college (a, b, c, d), y - axis sat score 1600 - 2400)

19. describe the independent and dependent variables for the data that is displayed in graphs f and g in model 4.

20. when you look at graph f, what message is communicated by the relative lengths of the bars to prospective students about college d’s average sat scores compared to the other three schools?

21. when you look at graph g, what message is communicated by the relative lengths of the bars to prospective students about college d’s average sat scores compared to the other three schools?

22. for each of the graphs in model 4, estimate the average score for each college represented by the height of the bar. is the data being displayed in the two graphs the same or different? support your answer with evidence from the graph.

23. a student takes a quick look at graph g and says “based on the size of these bars, it looks to me as though college d had entering freshman with sat scores nearly four times higher than college a.” explain to this student what mistake he has made in processing the information presented in graph g.

Question

extension questions
model 4 – sat scores
graph f (bar graph: average sat of incoming freshmen, x - axis college (a, b, c, d), y - axis sat score 0 - 2500)
graph g (bar graph: average sat of incoming freshmen, x - axis college (a, b, c, d), y - axis sat score 1600 - 2400)

19. describe the independent and dependent variables for the data that is displayed in graphs f and g in model 4.

20. when you look at graph f, what message is communicated by the relative lengths of the bars to prospective students about college d’s average sat scores compared to the other three schools?

21. when you look at graph g, what message is communicated by the relative lengths of the bars to prospective students about college d’s average sat scores compared to the other three schools?

22. for each of the graphs in model 4, estimate the average score for each college represented by the height of the bar. is the data being displayed in the two graphs the same or different? support your answer with evidence from the graph.

23. a student takes a quick look at graph g and says “based on the size of these bars, it looks to me as though college d had entering freshman with sat scores nearly four times higher than college a.” explain to this student what mistake he has made in processing the information presented in graph g.

Accepted Answer

### Question 19
# Brief Explanations:
In bar graphs, the independent variable is the one on the x - axis (the category), and the dependent variable is the one on the y - axis (the quantity being measured). For Graphs F and G, the x - axis has different colleges (A, B, C, D), so the independent variable is the college (type of college or college name). The y - axis measures the average SAT score of incoming freshmen, so the dependent variable is the average SAT score of incoming freshmen.
# Answer:
Independent variable: College (the different colleges A, B, C, D). Dependent variable: Average SAT score of incoming freshmen.

### Question 20
# Brief Explanations:
In Graph F, we compare the heights of the bars for each college. The bar for College D is the tallest among the four colleges (A, B, C, D). This means that when prospective students look at Graph F, the message is that College D has a significantly higher average SAT score of incoming freshmen compared to Colleges A, B, and C. The difference in bar heights makes it seem like College D's average SAT score is much higher than the other three.
# Answer:
The relative lengths of the bars in Graph F show that College D's average SAT score of incoming freshmen is much higher than the average SAT scores of incoming freshmen at Colleges A, B, and C. The bar for College D is the tallest, indicating a higher average SAT score compared to the other three schools.

### Question 21
# Brief Explanations:
In Graph G, we look at the heights of the bars for each college. The bar for College D is taller than the bars for A, B, and C, but the difference in height is not as dramatic as in Graph F when we consider the scale. However, it still shows that College D's average SAT score of incoming freshmen is higher than that of Colleges A, B, and C. The bar for D is the highest among the four, so it communicates that College D has a higher average SAT score than the other three schools, but the visual impact of the difference is less exaggerated compared to Graph F (due to the scale of the y - axis).
# Answer:
The relative lengths of the bars in Graph G show that College D's average SAT score of incoming freshmen is higher than the average SAT scores of incoming freshmen at Colleges A, B, and C. The bar for College D is the tallest among the four, indicating a higher average SAT score, but the difference in height between College D and the other colleges appears less extreme than in Graph F (because of the y - axis scale).

### Question 22
# Explanation:
## Step 1: Estimate scores for Graph F
- College A: The bar reaches up to around 1900 (since it's between 1500 and 2000, closer to 2000? Wait, looking at Graph F's y - axis (0 - 2500 with intervals of 500). Let's re - estimate. The y - axis has 0, 500, 1000, 1500, 2000, 2500. College A's bar is at 1900? Wait, no, maybe: College A: ~1900, College B: ~2100, College C: ~2300, College D: ~2500? Wait, no, the first graph (Graph F) has y - axis from 0 to 2500. Let's see the height: College A: about 1900 (since it's below 2000), College B: about 2100, College C: about 2300, College D: about 2500? Wait, maybe better to look at the second graph (Graph G) which has y - axis from 1600 to 2400. Wait, no, the problem says "for each of the graphs". Let's do Graph F first:
    - Graph F:
        - College A: The bar is at 1900 (since it's between 1500 and 2000, let's say 1900)
        - College B: Between 2000 and 2500, let's say 2100
        - College C: Between 2000 and 2500, closer to 2300
        - College D: Close to 2500, say 2450
    - Graph G:
        - College A: Around 1750 (since it's between 1600 and 1800)
        - College B: Around 2000 (between 1800 and 2200)
        - College C: Around 2200 (between 2000 and 2400)
        - College D: Around 2400 (close to 2400)
## Step 2: Compare data
Now, let's check if the data is the same. For College A: In Graph F, we estimated ~1900, in Graph G ~1750? Wait, no, maybe I made a mistake. Wait, actually, the data should be the same because both graphs are about the average SAT scores of incoming freshmen for the same colleges. The difference is in the scale of the y - axis. Let's re - estimate correctly. Let's look at the y - axis of Graph F: 0, 500, 1000, 1500, 2000, 2500. Graph G: 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400. Wait, maybe the actual values are: College A: 1750 (Graph G) which is 1750, in Graph F, if we consider the scale, 1750 is between 1500 and 2000. College B: 2000 (Graph G) which is 2000, in Graph F, 2000 is a mark. College C: 2200 (Graph G) which is 2200, in Graph F, between 2000 and 2500. College D: 2400 (Graph G) which is 2400, in Graph F, close to 2500. So the data is the same because the relative differences between the colleges' scores are consistent. For example, College D has the highest score, College A the lowest, and the order (D > C > B > A) is the same in both graphs. The only difference is the scale of the y - axis (Graph F has a wider range from 0, Graph G starts at 1600), but the actual scores (the data) are the same.
# Answer:
### Estimates:
- **Graph F**:
    - College A: ~1900
    - College B: ~2100
    - College C: ~2300
    - College D: ~2450
- **Graph G**:
    - College A: ~1750
    - College B: ~2000
    - College C: ~2200
    - College D: ~2400

### Data Comparison:
The data being displayed in the two graphs is the same. Evidence: The relative order of average SAT scores (College D > College C > College B > College A) is consistent in both graphs. The difference in the appearance of the bars is due to the different scales of the y - axes (Graph F has a y - axis starting at 0, Graph G starts at 1600), but the actual scores (the underlying data) for each college are the same.

### Question 23
# Brief Explanations:
The student made a mistake in not considering the scale of the y - axis. In Graph G, the y - axis starts at 1600, not 0. So the height of the bar for College D is not four times the height of the bar for College A in terms of actual SAT scores. To find the actual ratio, we need to look at the values on the y - axis. Let's say College A's score is around 1750 and College D's is around 2400. The difference is about 650, not three times (2400/1750≈1.37, not 4). The student only looked at the visual height of the bars without considering the scale (the starting point of the y - axis), which led to an incorrect estimation of the ratio of the SAT scores.
# Answer:
The student made the mistake of not considering the scale of the y - axis. Graph G's y - axis starts at 1600, not 0. So the visual height of the bars (which the student used to estimate the ratio) is misleading because the y - axis does not start at 0. To determine the actual ratio of SAT scores, one must use the values on the y - axis (e.g., if College A's score is ~1750 and College D's is ~2400, the ratio is ~1.37, not 4). The student incorrectly assumed the y - axis starts at 0 when comparing the bar heights.

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