The number of students in a class who have answered correctly, wrongly, or not…

2015

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

\(\begin{array}{|c|c|c|c|c|} \hline \textbf{Q No.} & \textbf{Marks} &\textbf{Answered}&\textbf{Answered}&\textbf{Not}\\&&\textbf{ Correctly} &\textbf{Wrongly} & \textbf{Attempted} \\\hline \text{1} & \text{2} &\text{21} &\text{17} &\text{6}\\ \text{2} & \text{3} &\text{15} & \text{27}& \text{2}\\\text{3} & \text{1} &\text{11} & \text{29} & \text{4}\\ \text{4} & \text{2} &\text{23} & \text{18} & \text{3}\\ \text{5} & \text{5} &\text{31} & \text{12} & \text{1} \\\hline \end{array}\)

What is the average of the marks obtained by the class in the examination?

  1. A.

    2.290

  2. B.

    2.970

  3. C.

    6.795

  4. D.

    8.795

Attempted by 16 students.

Show answer & explanation

Correct answer: C

Solution:

  1. Find the class size. Check any question: 21 (correct) + 17 (wrong) + 6 (not attempted) = 44 students.

  2. Compute marks obtained for each question (marks × number correct):

    • Question 1: 2 × 21 = 42

    • Question 2: 3 × 15 = 45

    • Question 3: 1 × 11 = 11

    • Question 4: 2 × 23 = 46

    • Question 5: 5 × 31 = 155

  3. Total marks obtained by the class = 42 + 45 + 11 + 46 + 155 = 299.

  4. Average marks per student = total marks ÷ class size = 299 ÷ 44 ≈ 6.795 (rounded to three decimal places).

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