To solve the problem, we need to calculate the average (mean) of the given scores and determine how many students scored above this average.

Step 1: Calculate the Total Number of Students

The total number of students is the sum of the frequencies:

$\text{Total students} = 15 + 22 + 41 + 30 + 12 = 120$

Step 2: Calculate the Sum of All Scores

The sum of all scores is the weighted sum of the scores, which is each score multiplied by its frequency:

$\text{Sum of scores} = (5 \times 15) + (6 \times 22) + (7 \times 41) + (8 \times 30) + (9 \times 12)$

Calculating each term:

$5 \times 15 = 75$ $6 \times 22 = 132$ $7 \times 41 = 287$ $8 \times 30 = 240$ $9 \times 12 = 108$

Adding these together gives:

$\text{Sum of scores} = 75 + 132 + 287 + 240 + 108 = 842$

Step 3: Calculate the Average Score

The average score is the sum of all scores divided by the total number of students:

$\text{Average} = \frac{842}{120} \approx 7.0167$

Step 4: Determine the Number of Students Scoring Above the Average

We need to count the students with scores above 7.0167, which means considering scores of 8 and 9:

• Frequency of score 8: 30
• Frequency of score 9: 12

Adding these together:

$\text{Number of students scoring above the average} = 30 + 12 = 42$

So, the number of students who passed (scored above the average) is:

(D) 42

Summary

The answer is 42 students who scored above the average.

Would you like details or have any questions? Here are 5 related questions for further exploration:

1. How would the median score be calculated from the given data?
2. What is the mode of the scores in the provided table?
3. How would the variance and standard deviation of the scores be calculated?
4. How many students scored below the average?
5. How would the average change if one more student scored 9?

Tip: When calculating the average of a dataset, ensure to account for all occurrences of each value correctly by using their frequencies.