Answer :
To draw a scatter plot that visualizes the relationship between a college student's monthly income and the amount they spend on recreation, follow these steps:
### Step-by-Step Solution:
1. Understand the Data:
- We have two sets of data points:
- Monthly income ([tex]\(x\)[/tex]) in dollars.
- Amount spent on recreation ([tex]\(y\)[/tex]) in dollars.
The data is represented in tabular form as follows:
| Monthly income (\[tex]$x) | 1069 | 785 | 1369 | 1127 | 965 | 1098 | 1000 | |-----------------------|------|-----|------|------|-----|------|------| | Amount (\$[/tex]y) | 265 | 164 | 365 | 285 | 232 | 273 | 239 |
2. Identify the Axes:
- The horizontal axis (x-axis) will represent the monthly income.
- The vertical axis (y-axis) will represent the amount spent on recreation.
3. Label the Axes:
- The x-axis should be labeled as "Monthly Income (\[tex]$)". - The y-axis should be labeled as "Amount Spent on Recreation (\$[/tex])".
4. Plot the Data:
- Each pair of values ([tex]\(x\)[/tex], [tex]\(y\)[/tex]) will form a point on the graph.
- For example, the first data point [tex]\( (1069, 265) \)[/tex] represents a monthly income of \[tex]$1069 and an amount spent of \$[/tex]265.
5. Scatter Plot:
- Draw a graph with the x-axis ranging from the lowest to the highest income value (approx. 750 to 1400).
- Draw the y-axis ranging from the lowest to the highest amount spent (approx. 150 to 400).
- Mark each pair of ([tex]\(x\)[/tex], [tex]\(y\)[/tex]) values on the graph.
### Creating the Scatter Plot:
1. Create the Axes:
- Draw the x-axis and y-axis on a graph paper or a plotting tool.
2. Mark the Scale:
- Decide on the appropriate scale for both axes.
- For example, you might increment the x-axis by 100 dollars and the y-axis by 20 dollars.
3. Plot Data Points:
- (1069, 265): Locate 1069 on the x-axis and move vertically to 265 on the y-axis.
- (785, 164): Locate 785 on the x-axis and move vertically to 164 on the y-axis.
- (1369, 365): Locate 1369 on the x-axis and move vertically to 365 on the y-axis.
- (1127, 285): Locate 1127 on the x-axis and move vertically to 285 on the y-axis.
- (965, 232): Locate 965 on the x-axis and move vertically to 232 on the y-axis.
- (1098, 273): Locate 1098 on the x-axis and move vertically to 273 on the y-axis.
- (1000, 239): Locate 1000 on the x-axis and move vertically to 239 on the y-axis.
4. Label the Plot:
- Provide a title for the scatter plot, such as "Scatter Plot of Amount Spent on Recreation vs. Monthly Income".
- Ensure each axis has the appropriate label.
### Example of Scatter Plot (Manually Drawn):
- X-Axis (Monthly Income [tex]\( \)[/tex]): Mark from 750 to 1400 in increments of 100.
- Y-Axis (Amount Spent [tex]\( \)[/tex]): Mark from 150 to 400 in increments of 20.
Then, mark each data point as specified above on the graph.
By following these steps, you should have a scatter plot that visually represents the relationship between monthly income and the amount spent on recreation for the data provided. This visual representation can help interpret whether there seems to be any correlation between the two variables.
### Step-by-Step Solution:
1. Understand the Data:
- We have two sets of data points:
- Monthly income ([tex]\(x\)[/tex]) in dollars.
- Amount spent on recreation ([tex]\(y\)[/tex]) in dollars.
The data is represented in tabular form as follows:
| Monthly income (\[tex]$x) | 1069 | 785 | 1369 | 1127 | 965 | 1098 | 1000 | |-----------------------|------|-----|------|------|-----|------|------| | Amount (\$[/tex]y) | 265 | 164 | 365 | 285 | 232 | 273 | 239 |
2. Identify the Axes:
- The horizontal axis (x-axis) will represent the monthly income.
- The vertical axis (y-axis) will represent the amount spent on recreation.
3. Label the Axes:
- The x-axis should be labeled as "Monthly Income (\[tex]$)". - The y-axis should be labeled as "Amount Spent on Recreation (\$[/tex])".
4. Plot the Data:
- Each pair of values ([tex]\(x\)[/tex], [tex]\(y\)[/tex]) will form a point on the graph.
- For example, the first data point [tex]\( (1069, 265) \)[/tex] represents a monthly income of \[tex]$1069 and an amount spent of \$[/tex]265.
5. Scatter Plot:
- Draw a graph with the x-axis ranging from the lowest to the highest income value (approx. 750 to 1400).
- Draw the y-axis ranging from the lowest to the highest amount spent (approx. 150 to 400).
- Mark each pair of ([tex]\(x\)[/tex], [tex]\(y\)[/tex]) values on the graph.
### Creating the Scatter Plot:
1. Create the Axes:
- Draw the x-axis and y-axis on a graph paper or a plotting tool.
2. Mark the Scale:
- Decide on the appropriate scale for both axes.
- For example, you might increment the x-axis by 100 dollars and the y-axis by 20 dollars.
3. Plot Data Points:
- (1069, 265): Locate 1069 on the x-axis and move vertically to 265 on the y-axis.
- (785, 164): Locate 785 on the x-axis and move vertically to 164 on the y-axis.
- (1369, 365): Locate 1369 on the x-axis and move vertically to 365 on the y-axis.
- (1127, 285): Locate 1127 on the x-axis and move vertically to 285 on the y-axis.
- (965, 232): Locate 965 on the x-axis and move vertically to 232 on the y-axis.
- (1098, 273): Locate 1098 on the x-axis and move vertically to 273 on the y-axis.
- (1000, 239): Locate 1000 on the x-axis and move vertically to 239 on the y-axis.
4. Label the Plot:
- Provide a title for the scatter plot, such as "Scatter Plot of Amount Spent on Recreation vs. Monthly Income".
- Ensure each axis has the appropriate label.
### Example of Scatter Plot (Manually Drawn):
- X-Axis (Monthly Income [tex]\( \)[/tex]): Mark from 750 to 1400 in increments of 100.
- Y-Axis (Amount Spent [tex]\( \)[/tex]): Mark from 150 to 400 in increments of 20.
Then, mark each data point as specified above on the graph.
By following these steps, you should have a scatter plot that visually represents the relationship between monthly income and the amount spent on recreation for the data provided. This visual representation can help interpret whether there seems to be any correlation between the two variables.
