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The data in the table below represents the percentage of a country's population aged 25 years or older who do not have a high school diploma. Complete parts (a) through (c) below.

\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\text{Age, } a & 30 & 40 & 50 & 60 & 70 & 80 \\
\hline
\text{Percentage without a H.S. Diploma, } P & 13.4 & 11.6 & 9.9 & 13.9 & 23.1 & 31.4 \\
\hline
\end{tabular}
\]

(a) Using a graphing utility, draw a scatter diagram of the data, treating age as the independent variable. What type of relation appears to exist between age and percentage of the population without a high school diploma?

Which graph below is a scatter diagram of the data?

A.
B.
C.
D.

Use the graph to determine which sentence below best describes the relation between age and percentage of the population without a high school diploma.

A. There appears to be a quadratic relation between age and percentage.
B. There appears to be a linear relation between age and percentage.
C. There does not appear to be any relation between age and percentage.

Answer :

To address the given question and determine the relationship between age and the percentage of the population without a high school diploma, we can follow a few steps to understand and graph the data. We can then use that graph to determine the type of relationship.

### Given Data:
The table shows the percentage of people without a high school diploma across different age groups:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Age (a) & 30 & 40 & 50 & 60 & 70 & 80 \\
\hline
Percentage (P) & 13.4 & 11.6 & 9.9 & 13.9 & 23.1 & 31.4 \\
\hline
\end{tabular}
\][/tex]

### Steps to Address the Question:

#### Step 1: Plot the Data
Plotting the data on a scatter plot can help us visualize the relationship. We'll plot 'Age' on the x-axis and 'Percentage without a high school diploma' on the y-axis.

#### Step 2: Visual Inspection of the Relationship
By observing the plotted points, we can determine the type of relationship:
- If the points approximately form a straight line, it suggests a linear relationship.
- If the points form a parabolic shape (a U or an inverted U), it suggests a quadratic relationship.
- If the points appear random without any discernible pattern, there may be no clear relationship.

### Analysis:
- At age 30: 13.4%
- At age 40: 11.6%
- At age 50: 9.9%
- At age 60: 13.9%
- At age 70: 23.1%
- At age 80: 31.4%

#### Plotting this data:
1. Age vs Percentage scatter plot would help us visualize these datapoints.

### Conclusion:
After plotting, you would see the following patterns:
- The percentages gradually decrease from age 30 to age 50.
- They begin to increase again from age 60 upward.

This pattern suggests a quadratic relationship because the data points form a parabola-like shape (decreasing and then increasing).

Thus, the best answer is:
A. There appears to be a quadratic relation between age and percentage.

This conclusion is based on the visual inspection of the expected scatter plot. By seeing how the data points create a curve that changes direction, it indicates the quadratic nature of the relationship.

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Rewritten by : Barada