The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q No. Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination?
3.02
Understanding Average Marks Calculation
The problem requires us to calculate the average marks obtained by the class in an examination. We are provided with data on student performance for three different questions, including the marks for each question and the number of students who answered correctly, wrongly, or not at all.
Data Analysis from Examination Performance
The table below summarizes the performance data:
| Q No. | Marks | Answered Correctly | Answered Wrongly | Not Attempted |
|---|---|---|---|---|
| 1 | 2 | 21 | 17 | 6 |
| 2 | 3 | 15 | 27 | 2 |
| 3 | 2 | 22 | 3 | 18 |
To find the average marks, we need two main pieces of information: the total marks scored by all students and the total number of students in the class.
Calculating Total Marks Scored by the Class
The total marks obtained are the sum of marks secured from each question. Marks for each question are calculated as the product of the number of students who answered it correctly and the marks awarded for that question.
- Marks from Q1: Number of students who answered Q1 correctly = 21. Marks for Q1 = 2. Total marks for Q1 = $21 \times 2 = 42$.
- Marks from Q2: Number of students who answered Q2 correctly = 15. Marks for Q2 = 3. Total marks for Q2 = $15 \times 3 = 45$.
- Marks from Q3: Number of students who answered Q3 correctly = 22. Marks for Q3 = 2. Total marks for Q3 = $22 \times 2 = 44$.
The total marks obtained by the class is the sum of marks from all questions:
Total Marks Obtained = $42 + 45 + 44 = 131$.
Determining the Total Number of Students
We determine the total number of students by summing the counts in each category (Correct, Wrong, Not Attempted) for each question. Ideally, this total should be consistent across all questions.
- For Q1: Total Students = 21 + 17 + 6 = 44.
- For Q2: Total Students = 15 + 27 + 2 = 44.
- For Q3: Total Students = 22 + 3 + 18 = 43.
There is a slight variation in the total number of students (44 vs 43). Based on the consistency in the first two questions, we will use 44 as the total number of students in the class for our calculation.
Calculating the Average Marks
The average marks are calculated using the formula:
$$ \text{Average Marks} = \frac{\text{Total Marks Obtained}}{\text{Total Number of Students}} $$
Plugging in the values we calculated:
$$ \text{Average Marks} = \frac{131}{44} $$
$$ \text{Average Marks} \approx 2.977 $$
The calculated average marks are approximately 2.977. Comparing this value to the given options, 3.02 is the closest value.
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