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Answer :
- Calculate the percentage of respondents from the 46-55 age group who rated the film excellent.
- Use the formula: $\frac{\text{Number of respondents from 46-55 age group who rated the film excellent}}{\text{Total number of respondents}} \times 100$.
- Substitute the values: $\frac{25}{446} \times 100$.
- The percentage is approximately: $\boxed{5.61}\%$.
### Explanation
1. Understand the problem and provided data
We need to find the percentage of respondents from the 46-55 age group who rated the film excellent, out of the total respondents. From the table, we see that 25 respondents from the 46-55 age group rated the film excellent. The total number of respondents is 446.
2. State the formula
To find the percentage, we use the formula: $$ \text{Percentage} = \frac{\text{Number of respondents from 46-55 age group who rated the film excellent}}{\text{Total number of respondents}} \times 100 $$
3. Substitute the values
Substitute the values into the formula: $$ \text{Percentage} = \frac{25}{446} \times 100 $$
4. Calculate the result
Calculate the percentage: $$ \text{Percentage} = \frac{25}{446} \times 100 \approx 5.60538116591704 \approx 5.61 $$ Rounded to two decimal places, the percentage is 5.61%.
5. State the final answer
Therefore, the percentage of respondents from the 46-55 age group who rated the film excellent is approximately 5.61%.
### Examples
Understanding audience preferences through surveys is crucial in the movie industry. For example, a producer can use this percentage to gauge the film's appeal to a specific age group and tailor marketing strategies accordingly. If a particular age group shows a strong liking for the movie, the marketing team might focus on advertising channels popular among that demographic. This targeted approach can significantly improve the film's box office success.
- Use the formula: $\frac{\text{Number of respondents from 46-55 age group who rated the film excellent}}{\text{Total number of respondents}} \times 100$.
- Substitute the values: $\frac{25}{446} \times 100$.
- The percentage is approximately: $\boxed{5.61}\%$.
### Explanation
1. Understand the problem and provided data
We need to find the percentage of respondents from the 46-55 age group who rated the film excellent, out of the total respondents. From the table, we see that 25 respondents from the 46-55 age group rated the film excellent. The total number of respondents is 446.
2. State the formula
To find the percentage, we use the formula: $$ \text{Percentage} = \frac{\text{Number of respondents from 46-55 age group who rated the film excellent}}{\text{Total number of respondents}} \times 100 $$
3. Substitute the values
Substitute the values into the formula: $$ \text{Percentage} = \frac{25}{446} \times 100 $$
4. Calculate the result
Calculate the percentage: $$ \text{Percentage} = \frac{25}{446} \times 100 \approx 5.60538116591704 \approx 5.61 $$ Rounded to two decimal places, the percentage is 5.61%.
5. State the final answer
Therefore, the percentage of respondents from the 46-55 age group who rated the film excellent is approximately 5.61%.
### Examples
Understanding audience preferences through surveys is crucial in the movie industry. For example, a producer can use this percentage to gauge the film's appeal to a specific age group and tailor marketing strategies accordingly. If a particular age group shows a strong liking for the movie, the marketing team might focus on advertising channels popular among that demographic. This targeted approach can significantly improve the film's box office success.
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