Question

plot to display the data shown in the table available below. the data represent the numbers of hours and hourly wages (in dollars) of 12 production workers. describe any patterns.

hours worked and hourly wage data
\

$$\begin{tabular}{|c|c|} \\hline hours & hourly wage \\\\ \\hline 31 & 17.16 \\\\ \\hline 37 & 14.66 \\\\ \\hline 34 & 15.79 \\\\ \\hline 40 & 16.71 \\\\ \\hline 34 & 16.80 \\\\ \\hline 33 & 16.82 \\\\ \\hline 40 & 18.65 \\\\ \\hline 32 & 17.05 \\\\ \\hline 28 & 15.54 \\\\ \\hline 45 & 16.62 \\\\ \\hline 39 & 16.57 \\\\ \\hline 28 & 14.45 \\\\ \\hline \\end{tabular}$$

which plot below displays the data?

Explanation:

Identify key data points to distinguish the plots

We examine specific coordinates \((x, y) = (\text{Hours}, \text{Hourly wage})\) from the data table:

• Point 1: \((31, 17.16)\)
• Point 2: \((37, 14.66)\)
• Point 3: \((34, 15.79)\)
• Point 4: \((40, 16.71)\)
• Point 5: \((34, 16.80)\)
• Point 6: \((33, 16.82)\)
• Point 7: \((40, 18.65)\)
• Point 8: \((32, 17.05)\)
• Point 9: \((28, 15.54)\)
• Point 10: \((45, 16.62)\)
• Point 11: \((39, 16.57)\)
• Point 12: \((28, 14.45)\)

Check coordinates on the candidate plots

• For \(x = 28\), we must have two points at \(y = 14.45\) and \(y = 15.54\).
• For \(x = 40\), we must have two points at \(y = 16.71\) and \(y = 18.65\).
• For \(x = 45\), we must have one point at \(y = 16.62\).

Compare with the options

• Option A: At \(x = 40\), there is a point near \(y = 18.65\) and another near \(y = 16.71\). At \(x = 45\), there is a point near \(y = 16.62\). At \(x = 28\), there are points at \(y \approx 14.45\) and \(y \approx 15.54\).
• Option B: Shows a downward trend where higher hours have lower wages (e.g., \(x = 45\) is near \(y = 14.7\)), which does not match the data.
• Option C: At \(x = 45\), the point is plotted near \(y = 18.65\), which is incorrect.
• Option D: At \(x = 28\), the points are plotted near \(y = 14.7\) and \(y = 17.2\), which does not match the data.

Answer:

• (A) Scatter plot with points matching the coordinates: (28, 14.45), (28, 15.54), (31, 17.16), (32, 17.05), (33, 16.82), (34, 15.79), (34, 16.80), (37, 14.66), (39, 16.57), (40, 16.71), (40, 18.65), (45, 16.62) (Correct answer)
• (B) Scatter plot showing a downward trend
• (C) Scatter plot with incorrect high values at 45 hours
• (D) Scatter plot with incorrect values at 28 hours