What is the average percentage of marks obtained by students in the mathematics subject?
Show Hint
To find the average of numbers clustered around a value, choose a baseline like 80 and calculate the deviations:
- Dev: \(-2, 0, +1, -2, -6, -9, -4, +2 = -20\).
- Average Dev $= -20 / 8 = -2.5$.
- Actual Average $= 80 - 2.5 = 77.5%$.
Step 1: Understanding the Concept:
To find the average percentage of marks obtained by all students in Mathematics, we sum the Mathematics marks of all 8 students and divide the total by the number of students (8). Key Formula or Approach:
\[ \text{Average Marks in Math} = \frac{\sum (\text{Math Marks of all 8 students})}{8} \]
Step 2: Detailed Explanation:
Let us list the Mathematics marks for each student from the table:
- Sarika: 78
- Vedika: 80
- Purvansh: 81
- Bhavin: 78
- Parth: 74
- Rudra: 71
- Vaishali: 76
- Anjali: 82
Calculate the sum of these marks:
\[ \text{Sum} = 78 + 80 + 81 + 78 + 74 + 71 + 76 + 82 \]
Let us group and add the numbers:
- \( 78 + 80 = 158 \)
- \( 158 + 81 = 239 \)
- \( 239 + 78 = 317 \)
- \( 317 + 74 = 391 \)
- \( 391 + 71 = 462 \)
- \( 462 + 76 = 538 \)
- \( 538 + 82 = 620 \)
The sum of the Mathematics marks for all students is 620.
Now, divide this sum by the total number of students (8):
\[ \text{Average} = \frac{620}{8} \]
Perform the division:
- \( 620 \div 2 = 310 \)
- \( 310 \div 2 = 155 \)
- \( 155 \div 2 = 77.5 \)
The average percentage of marks obtained by the students in Mathematics is 77.5%. Step 3: Final Answer:
The correct option is (A).
