To calculate the mean number of questions students got correct on a quiz, we need to follow these steps methodically. Here is a detailed, step-by-step solution:
1. Identify the Data:
- Questions Correct: [tex]\(3, 4, 5, 6, 7, 8\)[/tex]
- Frequency: [tex]\(13, 20, 15, 12, 8, 4\)[/tex]
2. Calculate the Total Number of Students:
To find the total number of students, we add up all the frequencies:
[tex]\[
\text{Total Students} = 13 + 20 + 15 + 12 + 8 + 4 = 72
\][/tex]
3. Calculate the Weighted Sum of Correct Questions:
To determine the total number of correct responses, we multiply each question category by its respective frequency and then sum those products:
[tex]\[
\text{Weighted Sum} = (3 \times 13) + (4 \times 20) + (5 \times 15) + (6 \times 12) + (7 \times 8) + (8 \times 4)
\][/tex]
[tex]\[
= 39 + 80 + 75 + 72 + 56 + 32 = 354
\][/tex]
4. Calculate the Mean:
The mean number of questions correct is the weighted sum divided by the total number of students:
[tex]\[
\text{Mean} = \frac{\text{Weighted Sum}}{\text{Total Students}} = \frac{354}{72} \approx 4.916666666666667
\][/tex]
5. Round the Mean to the Nearest Whole Number:
We should round 4.916666666666667 to the nearest whole number, which gives us:
[tex]\[
5
\][/tex]
Therefore, the mean number of questions correct, rounded to the nearest whole number, is 5.
The correct answer is:
C. 5.0
