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The problem presents a frequency distribution table with data about scores obtained by 63 players. It also asks for the calculation of some characteristic value, likely the mean (average) score based on the options provided. Here’s the frequency distribution table:

| **Points Interval** | **Fa (Frequency)** |
|---------------------|-------------------|
| 701 ⟶ 744           | 7                 |
| 744 ⟶ 787           | 9                 |
| 787 ⟶ 830           | 13                |
| 830 ⟶ 873           | 7                 |
| 873 ⟶ 916           | 11                |
| 916 ⟶ 959           | 7                 |
| 959 ⟶ 1002          | 9                 |
| **Total**            | **63**            |

### To calculate the mean score, we follow these steps:
1. **Find the midpoint** of each interval. This is done by averaging the lower and upper bounds of each interval.
2. **Multiply the midpoint by its corresponding frequency** (Fa).
3. **Sum all these products**.
4. **Divide the total sum by the number of players** (63) to get the mean.

Let me calculate the mean score based on these steps.The mean score of the 63 players is **851.5**, which does not directly match any of the options provided in the list.

It seems the closest option might involve some rounding or slightly different interpretations of the data. However, the calculation of the mean score based on the given intervals and frequencies results in **851.5**.

Let me know if you'd like more details or have any questions!

Here are five follow-up questions:
1. How do you calculate the midpoint of a class interval?
2. What role does the frequency (Fa) play in calculating the mean?
3. Could the choice of rounding rules affect the final answer?
4. What is the difference between mean, median, and mode in a frequency distribution?
5. How would you calculate the median score from this data?

**Tip:** When working with grouped data, using midpoints to estimate the mean can simplify calculations and provide a reasonable approximation.

A group of 63 players gathered to try a newly released game. Each player had one round, and the scores are shown in the table. What is the correct calculated score from the options below?

Learn how to calculate the mean score for a frequency distribution table of 63 players in a game. The process involves finding midpoints, multiplying by frequencies, and calculating the average. This tutorial is suitable for high school statistics students.

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