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(a) Construct a relative frequency bar graph for the data. Round your answers to two decimal places.



To construct a relative frequency bar graph, we first need to extract the relevant data from the pie chart. I will analyze the image and then proceed to calculate and describe how to plot the bar graph.

### Data Extraction from the Pie Chart:
The pie chart includes different segments with percentages that likely represent the frequency distribution of different categories. Here's what the image reveals:

- **Category 1 (75%):** Dark Blue section
- **Category 2 (50%):** Light Blue section
- **Category 3 (25%):** Pink section
- **Category 4 (0%):** Yellow section

### Step-by-Step Calculation:
1. **Convert Percentages to Relative Frequencies:**
   - Category 1: \( \frac{75}{100} = 0.75 \)
   - Category 2: \( \frac{50}{100} = 0.50 \)
   - Category 3: \( \frac{25}{100} = 0.25 \)
   - Category 4: \( \frac{0}{100} = 0.00 \)

2. **Round to Two Decimal Places:**
   - Category 1: 0.75
   - Category 2: 0.50
   - Category 3: 0.25
   - Category 4: 0.00

### Constructing the Bar Graph:
- The x-axis will have the categories (e.g., Category 1, Category 2, etc.).
- The y-axis will represent the relative frequencies (ranging from 0.00 to 0.75).
- Each bar's height will correspond to the relative frequency of each category.

### Visualization:
If you would like, I can describe how to plot this bar graph or provide further analysis on this data. 

Would you like any further details, such as instructions on how to create the bar graph in software, or do you have any other questions?

### Relative Questions:
1. How would you interpret the relative frequencies in this context?
2. How do relative frequency bar graphs differ from regular frequency bar graphs?
3. What insights can be drawn from a relative frequency bar graph compared to a pie chart?
4. What software would you use to create the bar graph, and why?
5. How can you use relative frequencies in decision-making processes?

**Tip:** When constructing a bar graph, ensure that the bars are equally spaced, and the y-axis is properly labeled for clarity and accuracy in data representation.

Learn how to construct a relative frequency bar graph from pie chart data, rounded to two decimal places. Understand the steps involved in converting percentages to relative frequencies and plotting them on a bar graph. Suitable for high school students and anyone interested in data visualization and statistics.

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