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Answer :
To determine the height of the purple bar in a relative frequency bar graph, follow these steps:
1. Understand the Problem: We are tasked with converting the frequency of a specific color pattern, "Purple," into a percentage of the total number of responses. This will give us the relative frequency, which corresponds to the height of the bar in a relative frequency bar graph marked off in percentages.
2. Frequency Details: From the frequency table:
- Total number of responses = 50 (from the sample size given).
- The frequency for the "Purple" pattern = 11.
3. Calculate Relative Frequency:
- The relative frequency is calculated by taking the frequency of the color pattern of interest (purple in this case) and dividing it by the total number of responses.
- [tex]\( \text{Relative Frequency of Purple} = \frac{\text{Frequency of Purple}}{\text{Total Number of Responses}} \times 100 \)[/tex].
4. Substitute the Values:
- [tex]\( \text{Relative Frequency of Purple} = \frac{11}{50} \times 100 \)[/tex].
5. Perform the Calculation:
- Calculate the division: [tex]\( \frac{11}{50} = 0.22 \)[/tex].
- Convert to a percentage: [tex]\( 0.22 \times 100 = 22\%\)[/tex].
6. Conclusion: The height of the purple bar in the relative frequency bar graph, marked off in percentages, will be 22.
Therefore, the correct option for the height of the purple bar in the graph is C. 22.
1. Understand the Problem: We are tasked with converting the frequency of a specific color pattern, "Purple," into a percentage of the total number of responses. This will give us the relative frequency, which corresponds to the height of the bar in a relative frequency bar graph marked off in percentages.
2. Frequency Details: From the frequency table:
- Total number of responses = 50 (from the sample size given).
- The frequency for the "Purple" pattern = 11.
3. Calculate Relative Frequency:
- The relative frequency is calculated by taking the frequency of the color pattern of interest (purple in this case) and dividing it by the total number of responses.
- [tex]\( \text{Relative Frequency of Purple} = \frac{\text{Frequency of Purple}}{\text{Total Number of Responses}} \times 100 \)[/tex].
4. Substitute the Values:
- [tex]\( \text{Relative Frequency of Purple} = \frac{11}{50} \times 100 \)[/tex].
5. Perform the Calculation:
- Calculate the division: [tex]\( \frac{11}{50} = 0.22 \)[/tex].
- Convert to a percentage: [tex]\( 0.22 \times 100 = 22\%\)[/tex].
6. Conclusion: The height of the purple bar in the relative frequency bar graph, marked off in percentages, will be 22.
Therefore, the correct option for the height of the purple bar in the graph is C. 22.
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