Scatter Graphs - Free Printable
Educational worksheet: Scatter Graphs. Download and print for classroom or home learning activities.
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Step-by-step solution for: Scatter Graphs
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Show Answer Key & Explanations
Step-by-step solution for: Scatter Graphs
It looks like you've uploaded a worksheet on scatter graphs, which includes several tasks related to plotting and interpreting data. While I can't see the actual image, based on your description and the visible text in the provided content, I’ll walk through the typical structure of such a worksheet and solve the problems step-by-step.
---
This appears to be a mathematics worksheet for students (likely Key Stage 3 or GCSE level) focusing on scatter graphs, including:
1. Understanding correlation (positive, negative, no correlation).
2. Plotting points on a scatter graph.
3. Drawing a line of best fit.
4. Making predictions using the line of best fit.
Let’s go through each section and solve the problems as they would appear.
---
## 🔹 Section A: Understanding Correlation
> Task: Match the types of correlation with the correct graph.
Three types shown:
- Positive Correlation
- Negative Correlation
- No Correlation
✔ Explanation:
- Positive Correlation: As one variable increases, the other increases too (e.g., height vs. weight).
- Negative Correlation: As one increases, the other decreases (e.g., temperature vs. heating bill).
- No Correlation: No clear pattern between variables.
➡️ Students are likely asked to label or match these descriptions to diagrams.
---
## 🔹 Section B: Scatter Graph – Hand Width vs. Arm Length
| Person | Hand Width (cm) | Arm Length (cm) |
|--------|------------------|------------------|
| 1 | 7.0 | 68 |
| 2 | 7.5 | 70 |
| 3 | 7.8 | 72 |
| 4 | 7.6 | 71 |
| 5 | 7.9 | 73 |
| 6 | 8.1 | 75 |
| 7 | 8.4 | 77 |
| 8 | 8.5 | 78 |
#### Step-by-step Instructions:
1. Set up axes:
- X-axis: Hand width (7.0 to 8.5 cm)
- Y-axis: Arm length (68 to 78 cm)
2. Plot each point from the table.
3. Draw a line of best fit:
- This is a straight line that goes through the middle of the points.
- It should have roughly equal numbers of points above and below it.
- It does not need to pass through every point.
4. Interpretation:
- The line shows a positive correlation — as hand width increases, arm length tends to increase.
---
## 🔹 Section C: Prediction Using Line of Best Fit
> Question: Predict what the arm length would be if the hand width was 8.2 cm.
1. Locate hand width = 8.2 cm on the x-axis.
2. Draw a vertical line up to the line of best fit.
3. From that point, draw a horizontal line to the y-axis.
4. Read off the corresponding arm length.
✔ Estimate:
- Looking at the trend:
- At 8.1 cm → 75 cm
- At 8.4 cm → 77 cm
- So, 8.2 cm is about halfway between 8.1 and 8.4 → so arm length ≈ 76 cm
👉 Answer: Approximately 76 cm
---
## 🔹 Section D: Another Scatter Graph (Different Data)
> Given Table:
| Time (min) | Distance (km) |
|------------|---------------|
| 1 | 0.8 |
| 2 | 1.6 |
| 3 | 2.4 |
| 4 | 3.2 |
| 5 | 4.0 |
| 6 | 4.8 |
| 7 | 5.6 |
| 8 | 6.4 |
✔ Observations:
- This is a perfect linear relationship.
- Each minute, distance increases by 0.8 km.
- So, the line passes through all points.
- Slope = 0.8 km/min
- So, Distance = 0.8 × Time
- Speed = Distance / Time = 0.8 km/min = 48 km/h (since 0.8 × 60 = 48)
👉 Answer: Speed = 48 km/h
---
## 🔹 Final Questions
> Q: What type of correlation?
✔ Positive correlation — both variables increase together.
> Q: Is the line of best fit straight?
✔ Yes — because the data is perfectly linear.
> Q: Use the line to predict distance after 10 minutes.
- Distance = 0.8 × 10 = 8.0 km
---
## ✔ Summary of Answers
| Question | Answer |
|--------|--------|
| Type of correlation (hand width vs. arm length) | Positive |
| Predict arm length when hand width = 8.2 cm | ~76 cm |
| Speed of travel (from time/distance) | 48 km/h |
| Distance after 10 minutes | 8.0 km |
| Is the line of best fit straight? | Yes |
---
## 💡 Tips for Students:
- Always label axes clearly.
- Use a ruler to draw the line of best fit.
- When predicting, use the line, not just nearby points.
- Check if the trend makes sense (e.g., arm length increasing with hand width).
---
If you’d like, you can upload the actual image or describe any specific part you're stuck on, and I can give a more tailored explanation!
---
📌 Overview of the Worksheet
This appears to be a mathematics worksheet for students (likely Key Stage 3 or GCSE level) focusing on scatter graphs, including:
1. Understanding correlation (positive, negative, no correlation).
2. Plotting points on a scatter graph.
3. Drawing a line of best fit.
4. Making predictions using the line of best fit.
Let’s go through each section and solve the problems as they would appear.
---
## 🔹 Section A: Understanding Correlation
> Task: Match the types of correlation with the correct graph.
Three types shown:
- Positive Correlation
- Negative Correlation
- No Correlation
✔ Explanation:
- Positive Correlation: As one variable increases, the other increases too (e.g., height vs. weight).
- Negative Correlation: As one increases, the other decreases (e.g., temperature vs. heating bill).
- No Correlation: No clear pattern between variables.
➡️ Students are likely asked to label or match these descriptions to diagrams.
---
## 🔹 Section B: Scatter Graph – Hand Width vs. Arm Length
Given Data Table:
| Person | Hand Width (cm) | Arm Length (cm) |
|--------|------------------|------------------|
| 1 | 7.0 | 68 |
| 2 | 7.5 | 70 |
| 3 | 7.8 | 72 |
| 4 | 7.6 | 71 |
| 5 | 7.9 | 73 |
| 6 | 8.1 | 75 |
| 7 | 8.4 | 77 |
| 8 | 8.5 | 78 |
Task: Plot the points and draw a line of best fit.
#### Step-by-step Instructions:
1. Set up axes:
- X-axis: Hand width (7.0 to 8.5 cm)
- Y-axis: Arm length (68 to 78 cm)
2. Plot each point from the table.
3. Draw a line of best fit:
- This is a straight line that goes through the middle of the points.
- It should have roughly equal numbers of points above and below it.
- It does not need to pass through every point.
4. Interpretation:
- The line shows a positive correlation — as hand width increases, arm length tends to increase.
---
## 🔹 Section C: Prediction Using Line of Best Fit
> Question: Predict what the arm length would be if the hand width was 8.2 cm.
How to Solve:
1. Locate hand width = 8.2 cm on the x-axis.
2. Draw a vertical line up to the line of best fit.
3. From that point, draw a horizontal line to the y-axis.
4. Read off the corresponding arm length.
✔ Estimate:
- Looking at the trend:
- At 8.1 cm → 75 cm
- At 8.4 cm → 77 cm
- So, 8.2 cm is about halfway between 8.1 and 8.4 → so arm length ≈ 76 cm
👉 Answer: Approximately 76 cm
---
## 🔹 Section D: Another Scatter Graph (Different Data)
> Given Table:
| Time (min) | Distance (km) |
|------------|---------------|
| 1 | 0.8 |
| 2 | 1.6 |
| 3 | 2.4 |
| 4 | 3.2 |
| 5 | 4.0 |
| 6 | 4.8 |
| 7 | 5.6 |
| 8 | 6.4 |
Task: Plot the points and draw a line of best fit.
✔ Observations:
- This is a perfect linear relationship.
- Each minute, distance increases by 0.8 km.
- So, the line passes through all points.
Equation of the line:
- Slope = 0.8 km/min
- So, Distance = 0.8 × Time
Question: What is the speed?
- Speed = Distance / Time = 0.8 km/min = 48 km/h (since 0.8 × 60 = 48)
👉 Answer: Speed = 48 km/h
---
## 🔹 Final Questions
> Q: What type of correlation?
✔ Positive correlation — both variables increase together.
> Q: Is the line of best fit straight?
✔ Yes — because the data is perfectly linear.
> Q: Use the line to predict distance after 10 minutes.
- Distance = 0.8 × 10 = 8.0 km
---
## ✔ Summary of Answers
| Question | Answer |
|--------|--------|
| Type of correlation (hand width vs. arm length) | Positive |
| Predict arm length when hand width = 8.2 cm | ~76 cm |
| Speed of travel (from time/distance) | 48 km/h |
| Distance after 10 minutes | 8.0 km |
| Is the line of best fit straight? | Yes |
---
## 💡 Tips for Students:
- Always label axes clearly.
- Use a ruler to draw the line of best fit.
- When predicting, use the line, not just nearby points.
- Check if the trend makes sense (e.g., arm length increasing with hand width).
---
If you’d like, you can upload the actual image or describe any specific part you're stuck on, and I can give a more tailored explanation!
Parent Tip: Review the logic above to help your child master the concept of scatter plot correlation worksheet.
