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Sagot :
Sure, let's plot the points step-by-step and then describe what the scatterplot would look like based on the given data.
Here is the table of values:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of years collecting stamps} & \text{Number of stamps} \\ \hline 2 & 100 \\ 5 & 175 \\ 4 & 150 \\ 3 & 125 \\ 4\pi & 175 \\ 3 & 100 \\ \hline \end{array} \][/tex]
First, let's list and organize the data points that will be plotted on the scatterplot:
1. (2, 100)
2. (5, 175)
3. (4, 150)
4. (3, 125)
5. (4\pi, 175) (Note: This translates to approximately 12.57 since [tex]\(\pi \approx 3.14\)[/tex])
6. (3, 100)
Steps to make the scatterplot:
1. Draw a horizontal axis (x-axis) and a vertical axis (y-axis).
- The x-axis represents "Number of years collecting stamps."
- The y-axis represents "Number of stamps."
2. Label the axes:
- On the x-axis, mark intervals that cover the range of years, e.g., from 0 to around 13 (since [tex]\(4\pi\)[/tex] is approximately 12.57).
- On the y-axis, mark intervals that cover the range of stamps, e.g., from 0 to 200.
3. Plot each of the points:
- (2, 100): Go 2 units along the x-axis and then move up to 100 units on the y-axis.
- (5, 175): Go 5 units along the x-axis and then move up to 175 units on the y-axis.
- (4, 150): Go 4 units along the x-axis and then move up to 150 units on the y-axis.
- (3, 125): Go 3 units along the x-axis and then move up to 125 units on the y-axis. Also, plot another point at (3, 100).
- (4\pi, 175): Go approximately 12.57 units along the x-axis and then move up to 175 units on the y-axis.
- (3, 100): Go 3 units along the x-axis and then move up to 100 units on the y-axis.
4. Add a title to your graph: "Years Collecting Stamps vs. Stamps in Collection".
The scatterplot will have the following characteristics:
1. A cluster of points between x-values of 2 and 5.
2. One point on x-axis value at around 12.57.
3. Two points with the same y-value of 175, one at x=5 and another at [tex]\(x \approx 12.57\)[/tex].
4. Two points at x=3 but different y-values (125 and 100).
To visualize, here is a rough sketch of the coordinates:
[tex]\[ \begin{array}{l|l|l} \text{x-axis} & \text{y-axis} & \text{Points} \\ 0 & 0 & \\ 2 & 100 & (2, 100) \\ 3 & 100 & (3, 100) \\ 3 & 125 & (3, 125) \\ 4 & 150 & (4, 150) \\ 5 & 175 & (5, 175) \\ 4\pi (\approx 12.57) & 175 & (12.57, 175) \\ \end{array} \][/tex]
This explains how each point corresponds to the table of values given, and by plotting these steps you should be able to correctly represent the scatterplot.
Here is the table of values:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of years collecting stamps} & \text{Number of stamps} \\ \hline 2 & 100 \\ 5 & 175 \\ 4 & 150 \\ 3 & 125 \\ 4\pi & 175 \\ 3 & 100 \\ \hline \end{array} \][/tex]
First, let's list and organize the data points that will be plotted on the scatterplot:
1. (2, 100)
2. (5, 175)
3. (4, 150)
4. (3, 125)
5. (4\pi, 175) (Note: This translates to approximately 12.57 since [tex]\(\pi \approx 3.14\)[/tex])
6. (3, 100)
Steps to make the scatterplot:
1. Draw a horizontal axis (x-axis) and a vertical axis (y-axis).
- The x-axis represents "Number of years collecting stamps."
- The y-axis represents "Number of stamps."
2. Label the axes:
- On the x-axis, mark intervals that cover the range of years, e.g., from 0 to around 13 (since [tex]\(4\pi\)[/tex] is approximately 12.57).
- On the y-axis, mark intervals that cover the range of stamps, e.g., from 0 to 200.
3. Plot each of the points:
- (2, 100): Go 2 units along the x-axis and then move up to 100 units on the y-axis.
- (5, 175): Go 5 units along the x-axis and then move up to 175 units on the y-axis.
- (4, 150): Go 4 units along the x-axis and then move up to 150 units on the y-axis.
- (3, 125): Go 3 units along the x-axis and then move up to 125 units on the y-axis. Also, plot another point at (3, 100).
- (4\pi, 175): Go approximately 12.57 units along the x-axis and then move up to 175 units on the y-axis.
- (3, 100): Go 3 units along the x-axis and then move up to 100 units on the y-axis.
4. Add a title to your graph: "Years Collecting Stamps vs. Stamps in Collection".
The scatterplot will have the following characteristics:
1. A cluster of points between x-values of 2 and 5.
2. One point on x-axis value at around 12.57.
3. Two points with the same y-value of 175, one at x=5 and another at [tex]\(x \approx 12.57\)[/tex].
4. Two points at x=3 but different y-values (125 and 100).
To visualize, here is a rough sketch of the coordinates:
[tex]\[ \begin{array}{l|l|l} \text{x-axis} & \text{y-axis} & \text{Points} \\ 0 & 0 & \\ 2 & 100 & (2, 100) \\ 3 & 100 & (3, 100) \\ 3 & 125 & (3, 125) \\ 4 & 150 & (4, 150) \\ 5 & 175 & (5, 175) \\ 4\pi (\approx 12.57) & 175 & (12.57, 175) \\ \end{array} \][/tex]
This explains how each point corresponds to the table of values given, and by plotting these steps you should be able to correctly represent the scatterplot.
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