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The data in the table below represents the percentage of a country's population aged 25 years or older, whose age is [tex]$x$[/tex], who do not have a high school diploma. Complete parts (a) through (c) below.

[tex]
\[
\begin{array}{|l|cccccc|}
\hline
\text{Age, } a & 30 & 40 & 50 & 60 & 70 & 80 \\
\hline
\text{Percentage without a H. S. Diploma, } P & 13.9 & 11.2 & 9.9 & 13.3 & 21.8 & 29.2 \\
\hline
\end{array}
\]
[/tex]

(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 the percentage of the population without a high school diploma?

Which graph below is a scatter diagram of the data?
A.
B.
C.
D.

Answer :

To solve this problem, we're examining the relationship between age and the percentage of the population without a high school diploma. Here's how to approach it step-by-step:

### Step 1: Understand the Variables
- Independent Variable: Age (denoted as [tex]\( a \)[/tex]).
- Dependent Variable: Percentage without a high school diploma (denoted as [tex]\( P \)[/tex]).

### Step 2: Analyze the Data
The data provided is as follows:

| Age (years) | Percentage without H.S. Diploma (%) |
|-------------|-------------------------------------|
| 30 | 13.9 |
| 40 | 11.2 |
| 50 | 9.9 |
| 60 | 13.3 |
| 70 | 21.8 |
| 80 | 29.2 |

### Step 3: Draw a Scatter Diagram (Conceptually)
A scatter diagram is a graph that visually represents the relationship between two variables. Plotting this data on a cartesian plane with 'Age' on the x-axis and 'Percentage without H.S. Diploma' on the y-axis will help identify any patterns or trends.

### Step 4: Interpret the Scatter Diagram
- Observation of Trend:
By plotting the data, you can observe how the percentage of the population without a high school diploma changes with age. At younger ages (30-50), the percentage appears relatively lower and fluctuates slightly. However, as age increases (60 and over), there is a noticeable increase in the percentage.

- Potential Relationship:
From the data, it can be inferred that there might be a non-linear relationship. The percentages are lower at middle ages and increase with older age groups, which might suggest a possible trend where earlier generations had less access to high school education.

### Step 5: Choose the Correct Graph
If provided with multiple graphing options (labeled A, B, C, D), you would look for the one that correctly reflects the plotted points corresponding to the above data:

- At age 30, the percentage is 13.9%.
- At age 40, the percentage is 11.2%.
- At age 50, the percentage is 9.9%.
- At age 60, the percentage is 13.3%.
- At age 70, the percentage is 21.8%.
- At age 80, the percentage is 29.2%.

Find the scatter diagram among the given options that accurately places these points based on the coordinates. The correct graph will align with these values.

This step-by-step analysis helps to determine the apparent relationship between age and the percentage of people without a high school diploma, showcasing how to interpret such data visually.

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Rewritten by : Barada