Detailed Analysis of Student Performance Data

The question asks us to compare two average marks: the average of Math and Hindi marks for all four students, and the average of English and Science marks for all four students. We need to find the percentage difference between these two averages and determine if the first is more or less than the second, rounded to one decimal place.

Understanding the Student Marks Table

Let's first look at the marks obtained by the four students A, B, C, and D in the four subjects: English, Hindi, Math, and Science. The maximum marks for each subject are 100.

Calculating Average Marks for Math and Hindi

To find the average marks of Math and Hindi taken together for the four students, we first need to sum the marks for each subject across all students and then find the total sum for both subjects. Finally, we divide this total sum by the total number of marks added (4 students * 2 subjects = 8 marks).

• Sum of Math marks for all students: \(100 + 88 + 96 + 97 = 381\)
• Sum of Hindi marks for all students: \(89 + 86 + 92 + 90 = 357\)
• Total sum of Math and Hindi marks: \(381 + 357 = 738\)
• Average marks of Math and Hindi taken together: \(\frac{738}{8} = 92.25\)

Calculating Average Marks for English and Science

Similarly, we calculate the average marks for English and Science taken together for the four students.

• Sum of English marks for all students: \(90 + 85 + 94 + 87 = 356\)
• Sum of Science marks for all students: \(93 + 95 + 89 + 82 = 359\)
• Total sum of English and Science marks: \(356 + 359 = 715\)
• Average marks of English and Science taken together: \(\frac{715}{8} = 89.375\)

Comparing the Averages and Calculating Percentage Difference

Now we compare the two calculated averages:

• Average (Math + Hindi): \(92.25\)
• Average (English + Science): \(89.375\)

The average marks of Math and Hindi (\(92.25\)) are greater than the average marks of English and Science (\(89.375\)). So, the first average is more than the second.

To find out by what percentage the first average is more than the second, we use the formula:

Percentage difference \( = \frac{|\text{Average}_1 - \text{Average}_2|}{\text{Average}_2} \times 100 \)

In this case, Average\(_1\) is the average of Math and Hindi, and Average\(_2\) is the average of English and Science.

Difference \( = 92.25 - 89.375 = 2.875 \)

Percentage more \( = \frac{2.875}{89.375} \times 100 \)

Percentage more \( \approx 0.032165 \times 100 \)

Percentage more \( \approx 3.2165 \% \)

Rounding off to 1 decimal place, we get \(3.2 \%\).

Therefore, the average marks of Math and Hindi taken together of the four students is 3.2% more than the average marks of English and Science taken together.

Revision Table: Key Calculations

Additional Information: Understanding Averages and Percentages

The average (or mean) is a central value of a set of numbers, calculated by dividing the sum of the numbers by the count of the numbers. It gives a single value that represents the typical value in the set.

The percentage difference tells us the relative difference between two numbers. When we say 'what percentage more/less than Y', Y is the base for calculation. The formula is \(\frac{\text{Difference}}{\text{Base Value}} \times 100\). In this problem, we are comparing the Math+Hindi average to the English+Science average, so the English+Science average is the base value.

Data interpretation questions often require calculating sums, averages, ratios, and percentages from given data tables or charts. Carefully reading the question to understand which values to compare and which is the base for percentage calculation is crucial.