Answered

Eight people of various ages were polled and asked to estimate the number of CDs they had bought in the previous year. The following table contains the collected data. The variable [tex]$x$[/tex] represents the age. The variable [tex]$y$[/tex] represents the number of CDs.

\begin{tabular}{|c|c|}
\hline Age (x) & Number of CDs (y) \\
\hline 18 & 17 \\
\hline 20 & 15 \\
\hline 24 & 12 \\
\hline 26 & 6 \\
\hline 28 & 4 \\
\hline 30 & 4 \\
\hline 32 & 2 \\
\hline 34 & 3 \\
\hline
\end{tabular}

Using the data in the table, choose which set of axes and which set of ordered pairs should be used in making a scatter plot of the data.

Graph A
Graph B

Set A:
(18, 17), (20, 15), (24, 12), (26, 6), (28, 4), (30, 4), (32, 2), (34, 3)

Set B:
(17, 18), (15, 20), (12, 24), (6, 26), (4, 28), (4, 30), (2, 32), (3, 34)

a. Graph A, Set A

b. Graph B, Set A

c. Graph A, Set B

d. Graph B, Set B



Answer :

GinnyAnswer
To create a scatter plot based on the data given, we first need to understand the correct mapping of the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to the sets provided.

Given:
- [tex]\( x \)[/tex] represents the ages.
- [tex]\( y \)[/tex] represents the number of CDs bought.

### Data from the Problem Statement:

[tex]\[ \begin{array}{|c|c|} \hline \text{Age} & \text{Number of CDs} \\ \hline 18 & 12 \\ \hline 20 & 17 \\ \hline 24 & 10 \\ \hline 25 & 6 \\ \hline 28 & 4 \\ \hline 30 & 4 \\ \hline 32 & 2 \\ \hline 34 & 3 \\ \hline \end{array} \][/tex]

### Possible Sets for Graphing:

Set A:
- [tex]\((18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), (34, 3)\)[/tex]

Set B:
- [tex]\((12, 18), (17, 20), (10, 24), (6, 25), (4, 28), (4, 30), (2, 32), (3, 34)\)[/tex]

### Graph Options:

Graph A:
- Plots the data as [tex]\((x, y)\)[/tex]: Age on the x-axis and Number of CDs on the y-axis.

Graph B:
- Plots the data as [tex]\((y, x)\)[/tex]: Number of CDs on the x-axis and Age on the y-axis.

### Analysis:

- For Graph A and Set A:
- We use [tex]\( x = [18, 20, 24, 25, 28, 30, 32, 34] \)[/tex] and [tex]\( y = [12, 17, 10, 6, 4, 4, 2, 3] \)[/tex].
- This matches the ordered pairs in Set A: [tex]\((18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), (34, 3)\)[/tex].

- For Graph A and Set B:
- It would use [tex]\( x = [12, 17, 10, 6, 4, 4, 2, 3] \)[/tex] and [tex]\( y = [18, 20, 24, 25, 28, 30, 32, 34] \)[/tex], which is not appropriate since it misplaces the variables.

- For Graph B and Set A:
- It would plot [tex]\( x = [18, 20, 24, 25, 28, 30, 32, 34] \)[/tex] and [tex]\( y = [12, 17, 10, 6, 4, 4, 2, 3] \)[/tex] with switched axes, which is incorrect for the data presentation.

- For Graph B and Set B:
- We use [tex]\( x = [12, 17, 10, 6, 4, 4, 2, 3] \)[/tex] and [tex]\( y = [18, 20, 24, 25, 28, 30, 32, 34] \)[/tex].
- This matches the ordered pairs in Set B: [tex]\((12, 18), (17, 20), (10, 24), (6, 25), (4, 28), (4, 30), (2, 32), (3, 34)\)[/tex].

Therefore, the correct choice is Graph A with Set A since it properly plots age on the x-axis and the number of CDs on the y-axis in accordance with the given data. Thus, the answer is:

a. Graph A, Set A

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