Question:
In an examination, 20% of the students scored 70 marks, 40% scored 80 marks, 30% scored 90 marks and the rest scored 100 marks. Then the mean score of the students is
In an examination, 20% of the students scored 70 marks, 40% scored 80 marks, 30% scored 90 marks and the rest scored 100 marks. Then the mean score of the students is
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Statistics Tip: Since the sum of weights is 100%, you can just multiply the score by the percentage in decimal form to find the mean directly: $0.2(70) + 0.4(80) + 0.3(90) + 0.1(100) = 14 + 32 + 27 + 10 = 83$.
Updated On: Apr 30, 2026
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The Correct Option is C
Solution and Explanation
Concept:
The mean (or expected value) of a grouped set of data is the weighted average of the scores. It is calculated by multiplying each score by its corresponding frequency (or percentage), summing these products, and then dividing by the total frequency.
Step 1: Determine the percentage for the final group.
The total percentage of all students must be 100%. We are given 20%, 40%, and 30%. The rest scored 100 marks: $$\text{Remaining Percentage} = 100\% - (20\% + 40\% + 30\%)$$ $$\text{Remaining Percentage} = 100\% - 90\% = 10\%$$
Step 2: Assume a total population for simplicity.
Assume there are exactly 100 students in the class. The percentages directly translate to the number of students: 20 students scored 70 marks. 40 students scored 80 marks. 30 students scored 90 marks. 10 students scored 100 marks.
Step 3: Calculate the total marks for each group.
Multiply the number of students by their respective scores: $$20 \times 70 = 1400$$ $$40 \times 80 = 3200$$ $$30 \times 90 = 2700$$ $$10 \times 100 = 1000$$
Step 4: Calculate the overall total marks.
Sum the marks from all groups: $$\text{Total Marks} = 1400 + 3200 + 2700 + 1000$$ $$\text{Total Marks} = 8300$$
Step 5: Calculate the final mean score.
Divide the total marks by the total number of students (100): $$\text{Mean} = \frac{8300}{100}$$ $$\text{Mean} = 83$$ Hence the correct answer is (C) 83.
The mean (or expected value) of a grouped set of data is the weighted average of the scores. It is calculated by multiplying each score by its corresponding frequency (or percentage), summing these products, and then dividing by the total frequency.
Step 1: Determine the percentage for the final group.
The total percentage of all students must be 100%. We are given 20%, 40%, and 30%. The rest scored 100 marks: $$\text{Remaining Percentage} = 100\% - (20\% + 40\% + 30\%)$$ $$\text{Remaining Percentage} = 100\% - 90\% = 10\%$$
Step 2: Assume a total population for simplicity.
Assume there are exactly 100 students in the class. The percentages directly translate to the number of students: 20 students scored 70 marks. 40 students scored 80 marks. 30 students scored 90 marks. 10 students scored 100 marks.
Step 3: Calculate the total marks for each group.
Multiply the number of students by their respective scores: $$20 \times 70 = 1400$$ $$40 \times 80 = 3200$$ $$30 \times 90 = 2700$$ $$10 \times 100 = 1000$$
Step 4: Calculate the overall total marks.
Sum the marks from all groups: $$\text{Total Marks} = 1400 + 3200 + 2700 + 1000$$ $$\text{Total Marks} = 8300$$
Step 5: Calculate the final mean score.
Divide the total marks by the total number of students (100): $$\text{Mean} = \frac{8300}{100}$$ $$\text{Mean} = 83$$ Hence the correct answer is (C) 83.
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