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The problem shown in the image involves calculating the best estimate for the mean exam score based on a grouped frequency distribution. Here's the frequency table from the image:

| Scores (Class Intervals) | Frequency (Freq) |
|--------------------------|------------------|
| 50 ≤ x < 60              | 9                |
| 60 ≤ x < 70              | 11               |
| 70 ≤ x < 80              | 9                |
| 80 ≤ x < 90              | 16               |
| 90 ≤ x < 100             | 5                |

### Steps to calculate the mean:
1. **Determine class midpoints** for each interval:
   - For the class 50 ≤ x < 60, midpoint = \((50 + 59) / 2 = 54.5\)
   - For the class 60 ≤ x < 70, midpoint = \((60 + 69) / 2 = 64.5\)
   - For the class 70 ≤ x < 80, midpoint = \((70 + 79) / 2 = 74.5\)
   - For the class 80 ≤ x < 90, midpoint = \((80 + 89) / 2 = 84.5\)
   - For the class 90 ≤ x < 100, midpoint = \((90 + 99) / 2 = 94.5\)

2. **Multiply each midpoint by its corresponding frequency** to calculate the total for each class:
   - \(54.5 \times 9 = 490.5\)
   - \(64.5 \times 11 = 709.5\)
   - \(74.5 \times 9 = 670.5\)
   - \(84.5 \times 16 = 1352\)
   - \(94.5 \times 5 = 472.5\)

3. **Find the total of the frequencies** and the sum of the products from step 2:
   - Total frequency = \(9 + 11 + 9 + 16 + 5 = 50\)
   - Sum of products = \(490.5 + 709.5 + 670.5 + 1352 + 472.5 = 3695\)

4. **Calculate the mean** by dividing the sum of the products by the total frequency:
   \[
   \text{Mean} = \frac{3695}{50} = 73.9
   \]

Thus, the best estimate for the mean exam score is **73.9**.

Let me know if you need more details or further clarification.

Here are 5 related questions:
1. How would the mean change if a frequency were adjusted in one of the intervals?
2. Can you calculate the median score from this grouped frequency distribution?
3. How would you determine the mode of this data set?
4. How does the range of exam scores impact the mean in grouped data?
5. What is the standard deviation for this dataset?

**Tip:** Always check if the sum of the frequencies matches the total number of observations to avoid miscalculations.

What is the best estimate we can get for the mean exam score of these students? Round your answer correct to one decimal place.

Learn how to calculate the mean exam score from a grouped frequency distribution with detailed steps. This problem includes calculating midpoints, multiplying by frequencies, and finding the mean using the formula. Suitable for high school students in Grades 10-12.

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