Data Interpretation: Student Marks Percentage Analysis

The question asks us to analyze the provided table showing the percentage of marks obtained by six students in five different subjects. We need to calculate two totals: the total marks of Amit, Abhi, and Anuj in Subject E, and the total marks of all six students in Subject B. Finally, we need to find out what percentage the first total is more than the second total, rounded to one decimal place.

First, let's understand how to convert the percentage of marks into actual marks obtained. For each subject, the maximum marks are given. The marks obtained by a student in a subject can be calculated using the formula:

\(\text{Marks Obtained} = \left( \frac{\text{Percentage Obtained}}{100} \right) \times \text{Maximum Marks}\)

Here is the data presented in the table:

Calculating Total Marks in Subject E for Amit, Abhi, and Anuj

Subject E has a maximum mark of 150. We will calculate the marks obtained by Amit, Abhi, and Anuj in Subject E using their respective percentages:

• Amit: 80% of 150
• \(\text{Marks by Amit in E} = \left( \frac{80}{100} \right) \times 150 = 0.80 \times 150 = 120\)
• Abhi: 74% of 150
• \(\text{Marks by Abhi in E} = \left( \frac{74}{100} \right) \times 150 = 0.74 \times 150 = 111\)
• Anuj: 84% of 150
• \(\text{Marks by Anuj in E} = \left( \frac{84}{100} \right) \times 150 = 0.84 \times 150 = 126\)

Total marks obtained by Amit, Abhi, and Anuj in Subject E:

\(\text{Total E (Amit, Abhi, Anuj)} = 120 + 111 + 126 = 357\)

Calculating Total Marks in Subject B for All Six Students

Subject B has a maximum mark of 80. We will calculate the marks obtained by all six students in Subject B:

• Manju: 85% of 80
• \(\text{Marks by Manju in B} = \left( \frac{85}{100} \right) \times 80 = 0.85 \times 80 = 68\)
• Amit: 65% of 80
• \(\text{Marks by Amit in B} = \left( \frac{65}{100} \right) \times 80 = 0.65 \times 80 = 52\)
• Rekha: 75% of 80
• \(\text{Marks by Rekha in B} = \left( \frac{75}{100} \right) \times 80 = 0.75 \times 80 = 60\)
• Anuj: 55% of 80
• \(\text{Marks by Anuj in B} = \left( \frac{55}{100} \right) \times 80 = 0.55 \times 80 = 44\)
• Abhi: 65% of 80
• \(\text{Marks by Abhi in B} = \left( \frac{65}{100} \right) \times 80 = 0.65 \times 80 = 52\)
• Vikram: 70% of 80
• \(\text{Marks by Vikram in B} = \left( \frac{70}{100} \right) \times 80 = 0.70 \times 80 = 56\)

Total marks obtained by all six students in Subject B:

\(\text{Total B (All students)} = 68 + 52 + 60 + 44 + 52 + 56 = 332\)

Calculating the Percentage 'More Than'

We need to find out what percent the total marks obtained by Amit, Abhi, and Anuj in Subject E (357) is more than the total marks obtained by all six students in Subject B (332).

The difference between the two totals is:

\(\text{Difference} = 357 - 332 = 25\)

The percentage 'more than' the total in Subject B is calculated using the formula:

\(\text{Percentage More} = \left( \frac{\text{Difference}}{\text{Total B (All students)}} \right) \times 100\)

Substituting the values:

\(\text{Percentage More} = \left( \frac{25}{332} \right) \times 100\)

Let's calculate the value:

\(\text{Percentage More} \approx 0.075301... \times 100 \approx 7.5301...\)

Rounding the result to one decimal place, we get 7.5%.

Revision Table: Key Data Points

Additional Information: Understanding Percentage Calculations

A percentage is a way of expressing a number as a fraction of 100. To find a percentage of a quantity, you can convert the percentage to a decimal by dividing by 100 and then multiply by the quantity.

The formula for finding what percentage 'X' is more than 'Y' is: \( \left( \frac{X - Y}{Y} \right) \times 100 \). In this problem, X is the total marks in Subject E for the three students, and Y is the total marks in Subject B for all six students. The result tells us how much larger X is compared to Y, expressed as a percentage of Y.