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.
