Final answer:
To calculate the mean exam score, multiply each score by the corresponding number of students, sum the results, and divide by the total number of students. The mean score for the data provided is 79.8 when rounded to the nearest tenth.
Step-by-step explanation:
To find the mean of the exam scores, we need to multiply each score by the number of students who received that score, sum these products, and then divide by the total number of students. Using the provided scores and frequencies:
- 65 x 4 = 260
- 70 x 2 = 140
- 75 x 2 = 150
- 80 x 1 = 80
- 85 x 7 = 595
- 90 x 5 = 450
Now, add up all the products: 260 + 140 + 150 + 80 + 595 + 450 = 1675. Next, we find the total number of students, which is the sum of the frequencies: 4 + 2 + 2 + 1 + 7 + 5 = 21 students. To find the mean:
Mean = Total of products / Number of students = 1675 / 21 = 79.8 (to the nearest tenth)
The calculated mean should be reported with one more decimal place than the original data, but since we round to the nearest tenth, the mean score of the exam to the nearest 10th is 79.8.