Understanding Graphing Worksheet featuring a bar graph of cereal calories and a line graph of student enrollment trends in science subjects.
Bar graph comparing calories in four brands of cereal (Korn Krispies, Sugar Circles, Oat Boats, Honey Hunks) and line graph showing student enrollment in physical science and chemistry at North High School from 1984 to 1988.
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Show Answer Key & Explanations
Step-by-step solution for: Solved Understanding Graphing Worksheet Graphs appear not | Chegg.com
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Show Answer Key & Explanations
Step-by-step solution for: Solved Understanding Graphing Worksheet Graphs appear not | Chegg.com
Let's go through each question on the Understanding Graphing Worksheet and solve them step by step with clear explanations.
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Answer:
The current vertical axis ranges from 100 to 130 calories, in increments of 10. If we changed it to 100, 150, 200, and 300, the scale would be much larger and spaced further apart.
- This would make the differences between the calorie values appear smaller visually.
- The bars would look shorter and less distinct because the same data is now compressed into a much larger range.
- For example, Honey Hunks has about 130 calories — this would only reach halfway up the first interval (100–150), making the bar seem very small compared to its actual value.
✔ Conclusion: The graph would distort the perception of differences between cereals, making small differences seem even smaller.
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Answer:
If the vertical axis starts at 0 and increases by 10s (0, 10, 20, ..., 130):
- The bars would become much taller relative to the graph space.
- The differences in height between bars would be more visually exaggerated.
- For example, the difference between Korn Krispies (~110) and Honey Hunks (~130) would be twice as tall on the chart compared to the original scale.
⚠️ Note: Starting at zero is generally better for accurate comparisons unless you're focusing on small changes within a narrow range. But here, since all values are above 100, starting at 0 would make the graph larger and possibly misleading due to excessive white space.
✔ Conclusion: The graph would show greater visual contrast between the values but might be less efficient in space usage.
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Answer:
Looking at the line graph:
- Physical Science (solid black squares):
- Starts at 59 students in 1984
- Drops slightly to 56 in 1985
- Rises steadily: 66 (1986), 68 (1987), 70 in 1988
→ Overall upward trend
- Chemistry (diamonds):
- Starts at 55 in 1984
- Increases to 60 in 1985
- Then drops: 57 (1986), 55 (1987), rises slightly to 58 in 1988
→ No strong trend; fluctuates around 55–60
✔ Comparison:
- Physical science increased consistently after 1985.
- Chemistry peaked early and then declined or stabilized.
- In 1984, chemistry had fewer students than physical science.
- By 1988, physical science had significantly more students.
✔ Trend Summary:
- Physical science shows a clear increasing trend.
- Chemistry shows no clear trend, with minor fluctuations.
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Answer:
The legend identifies which line represents which subject:
- Diamonds = Chemistry
- Squares = Physical Science
Without the legend, viewers wouldn't know which line corresponds to which class.
✔ Purpose of the Legend:
- To clarify data when multiple lines are plotted.
- Helps readers interpret the graph correctly.
- Essential for comparing two variables (here, enrollment in two different subjects) over time.
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Data given:
- School A: 850
- School B: 600
- School C: 1200
- School D: 900
- School E: 350
We’re comparing number of students across different schools.
✔ Independent Variable: The school name (A, B, C, D, E).
These are categories chosen by the observer, not changing based on other factors.
➡️ Plotted on the horizontal (x) axis.
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✔ Dependent Variable: The number of students enrolled in each school.
This depends on which school you're looking at.
➡️ Plotted on the vertical (y) axis.
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| Question | Answer |
|--------|--------|
| 1 | The bars would appear shorter and differences less noticeable because the scale is stretched. |
| 2 | The bars would be much taller and differences more exaggerated; starting at 0 makes the graph less compact. |
| 3 | Physical science enrollment increased steadily; chemistry fluctuated with no clear trend. Physical science grew faster and ended higher. |
| 4 | The legend distinguishes between the two subjects (Chemistry vs. Physical Science) so viewers can interpret the data correctly. |
| 5 | Independent variable: School name → plotted on the x-axis. |
| 6 | Dependent variable: Number of students → plotted on the y-axis. |
Let me know if you'd like a visual sketch or explanation of how to draw the bar graph for question 5!
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1. Look at the numbers used on the vertical axis. What would happen to the bars on the graph if these numbers were changed to 100, 150, 200, and 300?
Answer:
The current vertical axis ranges from 100 to 130 calories, in increments of 10. If we changed it to 100, 150, 200, and 300, the scale would be much larger and spaced further apart.
- This would make the differences between the calorie values appear smaller visually.
- The bars would look shorter and less distinct because the same data is now compressed into a much larger range.
- For example, Honey Hunks has about 130 calories — this would only reach halfway up the first interval (100–150), making the bar seem very small compared to its actual value.
✔ Conclusion: The graph would distort the perception of differences between cereals, making small differences seem even smaller.
---
2. How would the graph change if the numbers on the vertical axis started with 0 and increased in increments of 10?
Answer:
If the vertical axis starts at 0 and increases by 10s (0, 10, 20, ..., 130):
- The bars would become much taller relative to the graph space.
- The differences in height between bars would be more visually exaggerated.
- For example, the difference between Korn Krispies (~110) and Honey Hunks (~130) would be twice as tall on the chart compared to the original scale.
⚠️ Note: Starting at zero is generally better for accurate comparisons unless you're focusing on small changes within a narrow range. But here, since all values are above 100, starting at 0 would make the graph larger and possibly misleading due to excessive white space.
✔ Conclusion: The graph would show greater visual contrast between the values but might be less efficient in space usage.
---
3. How does the enrollment in physical science compare with that in chemistry over the years? Do you see any trends?
Answer:
Looking at the line graph:
- Physical Science (solid black squares):
- Starts at 59 students in 1984
- Drops slightly to 56 in 1985
- Rises steadily: 66 (1986), 68 (1987), 70 in 1988
→ Overall upward trend
- Chemistry (diamonds):
- Starts at 55 in 1984
- Increases to 60 in 1985
- Then drops: 57 (1986), 55 (1987), rises slightly to 58 in 1988
→ No strong trend; fluctuates around 55–60
✔ Comparison:
- Physical science increased consistently after 1985.
- Chemistry peaked early and then declined or stabilized.
- In 1984, chemistry had fewer students than physical science.
- By 1988, physical science had significantly more students.
✔ Trend Summary:
- Physical science shows a clear increasing trend.
- Chemistry shows no clear trend, with minor fluctuations.
---
4. Why does this graph include a legend?
Answer:
The legend identifies which line represents which subject:
- Diamonds = Chemistry
- Squares = Physical Science
Without the legend, viewers wouldn't know which line corresponds to which class.
✔ Purpose of the Legend:
- To clarify data when multiple lines are plotted.
- Helps readers interpret the graph correctly.
- Essential for comparing two variables (here, enrollment in two different subjects) over time.
---
5. In a bar graph of these data, what would be the independent variable and on which axis would it be plotted?
Data given:
- School A: 850
- School B: 600
- School C: 1200
- School D: 900
- School E: 350
We’re comparing number of students across different schools.
✔ Independent Variable: The school name (A, B, C, D, E).
These are categories chosen by the observer, not changing based on other factors.
➡️ Plotted on the horizontal (x) axis.
---
6. What would be the dependent variable and on which axis would it be plotted?
✔ Dependent Variable: The number of students enrolled in each school.
This depends on which school you're looking at.
➡️ Plotted on the vertical (y) axis.
---
✔ Final Answers Summary:
| Question | Answer |
|--------|--------|
| 1 | The bars would appear shorter and differences less noticeable because the scale is stretched. |
| 2 | The bars would be much taller and differences more exaggerated; starting at 0 makes the graph less compact. |
| 3 | Physical science enrollment increased steadily; chemistry fluctuated with no clear trend. Physical science grew faster and ended higher. |
| 4 | The legend distinguishes between the two subjects (Chemistry vs. Physical Science) so viewers can interpret the data correctly. |
| 5 | Independent variable: School name → plotted on the x-axis. |
| 6 | Dependent variable: Number of students → plotted on the y-axis. |
Let me know if you'd like a visual sketch or explanation of how to draw the bar graph for question 5!
Parent Tip: Review the logic above to help your child master the concept of understanding graphs worksheet.
