Analyzing Student Examination Marks Data

This question requires us to use the data provided in the table to calculate the total percentage marks obtained by two students, D and E, and then find the difference between these percentages.

Understanding the Examination Data Table

The table presents the marks secured by 6 students (A to F) across 6 different subjects. The maximum marks for each subject are indicated in brackets next to the subject name.

Calculating Total Maximum Marks

To find the overall percentage, we first need to determine the total maximum marks possible across all subjects. We sum the maximum marks for each subject:

Maximum Marks for Physics: 100

Maximum Marks for Chemistry: 100

Maximum Marks for Math: 100

Maximum Marks for History: 50

Maximum Marks for Computer Science: 50

Maximum Marks for Hindi: 50

Total Maximum Marks \( = 100 + 100 + 100 + 50 + 50 + 50 = 450 \)

Calculating Total Marks for Student D

Next, we sum the marks obtained by student D in all subjects:

• Physics: 75
• Chemistry: 79
• Math: 58
• History: 28
• Computer Science: 28
• Hindi: 34

Total Marks for Student D \( = 75 + 79 + 58 + 28 + 28 + 34 = 302 \)

Calculating Total Marks for Student E

Similarly, we sum the marks obtained by student E in all subjects:

• Physics: 45
• Chemistry: 65
• Math: 62
• History: 31
• Computer Science: 29
• Hindi: 28

Total Marks for Student E \( = 45 + 65 + 62 + 31 + 29 + 28 = 260 \)

Calculating Percentage Marks for Students D and E

The percentage marks are calculated using the formula:

\[ \text{Percentage} = \frac{\text{Total Marks Obtained}}{\text{Total Maximum Marks}} \times 100 \]

Percentage for Student D:

\[ \text{Percentage D} = \frac{302}{450} \times 100 \]

\[ \text{Percentage D} = \frac{30200}{450} = \frac{3020}{45} = \frac{604}{9} \]

Percentage for Student E:

\[ \text{Percentage E} = \frac{260}{450} \times 100 \]

\[ \text{Percentage E} = \frac{26000}{450} = \frac{2600}{45} = \frac{520}{9} \]

Calculating the Difference in Percentage Marks

We need to find the difference between the percentage marks of Student D and Student E.

Difference \( = \text{Percentage D} - \text{Percentage E} \)

\[ \text{Difference} = \frac{604}{9} - \frac{520}{9} = \frac{604 - 520}{9} = \frac{84}{9} = \frac{28}{3} \]

Now, we convert the fraction to a decimal:

\[ \frac{28}{3} \approx 9.3333... \]

Rounding this value to two decimal places, or comparing with the given options, the difference is approximately 9.34.

Revision Table: Key Calculations Summary

Additional Information on Percentage Differences

Calculating the difference in percentages is a common task in data analysis. It helps in comparing the performance or value between two entities relative to a whole.

In this case, the percentage difference shows how much higher Student D's overall performance percentage is compared to Student E's overall performance percentage in the examination. It is calculated by subtracting the lower percentage from the higher percentage.

It's important to calculate the individual percentages first and then find the difference, rather than finding the difference in raw scores and then calculating the percentage of that difference relative to the total maximum marks (unless specified otherwise, as "difference of percentage" implies subtraction of percentages).