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:

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.