Let's solve both problems step by step:

Problem 1: Compute the mean, median, and mode of each section (A, B, C).

We are given the scores for 10 students in three sections, A, B, and C.

Section A:

Scores: 25, 24, 24, 20, 20, 20, 16, 12, 10, 7

• Mean:
  $\text{Mean} = \frac{\text{Sum of Scores}}{\text{Number of Scores}} = \frac{25 + 24 + 24 + 20 + 20 + 20 + 16 + 12 + 10 + 7}{10} = \frac{178}{10} = 17.8$

• Median: Arrange scores in ascending order: 7, 10, 12, 16, 20, 20, 20, 24, 24, 25. The median is the average of the 5th and 6th terms (20 and 20), so: $\text{Median} = 20$

• Mode: The most frequent score is 20 (it appears 3 times).

Section B:

Scores: 25, 24, 24, 20, 18, 18, 17, 10, 9, 7

• Mean:
  $\text{Mean} = \frac{25 + 24 + 24 + 20 + 18 + 18 + 17 + 10 + 9 + 7}{10} = \frac{172}{10} = 17.2$

• Median: Arrange scores in ascending order: 7, 9, 10, 17, 18, 18, 20, 24, 24, 25. The median is the average of the 5th and 6th terms (18 and 18), so: $\text{Median} = 18$

• Mode: The most frequent score is 18 (it appears 2 times).

Section C:

Scores: 25, 25, 25, 22, 21, 21, 21, 18, 18, 18

• Mean:
  $\text{Mean} = \frac{25 + 25 + 25 + 22 + 21 + 21 + 21 + 18 + 18 + 18}{10} = \frac{214}{10} = 21.4$

• Median: Arrange scores in ascending order: 18, 18, 18, 21, 21, 21, 22, 25, 25, 25. The median is the average of the 5th and 6th terms (21 and 21), so: $\text{Median} = 21$

• Mode: The most frequent score is 25 (it appears 3 times).

Problem 2: What is the class average if 20 students averaged 80% and 30 others averaged 90%?

We can calculate the overall class average by using a weighted average formula: $\text{Class Average} = \frac{(20 \times 80) + (30 \times 90)}{20 + 30}$ $= \frac{1600 + 2700}{50} = \frac{4300}{50} = 86\%$

Would you like further details on any step?

Here are 5 related questions to expand on the topic:

1. How do you calculate the range of scores for each section?
2. What is the variance and standard deviation for each section?
3. How would adding another student's score affect the mean and median?
4. Can you explain how outliers affect the mode of a data set?
5. How would the class average change if there were 25 students in each group instead?

Tip: When calculating the median, always ensure that the data is sorted in ascending order.