Understanding the Student Distribution Data

The problem provides a table showing the percentage distribution of the total number of students and the total number of girls across six different colleges (A to F). We are given the total number of students across all colleges and the total number of girls across all colleges.

• Total Students (all colleges) = 60000
• Total Girls (all colleges) = 24000

The table shows the percentage of these totals that belong to each college.

The question asks for the average number of boys studying in Colleges A, B, and C. To find the number of boys in a college, we need to subtract the number of girls in that college from the total number of students in that college. The number of boys in any college is calculated as:

\(\text{Number of Boys} = \text{Number of Students} - \text{Number of Girls}\)

Calculating Students and Girls in Colleges A, B, and C

First, let's calculate the actual number of students and girls in each of the specified colleges (A, B, and C) based on the given percentages and total numbers.

College A

• Number of Students in A: \(10\%\) of \(60000 = \frac{10}{100} \times 60000 = 0.10 \times 60000 = 6000\)
• Number of Girls in A: \(15\%\) of \(24000 = \frac{15}{100} \times 24000 = 0.15 \times 24000 = 3600\)

Number of Boys in A = Number of Students in A - Number of Girls in A = \(6000 - 3600 = 2400\)

College B

• Number of Students in B: \(9\%\) of \(60000 = \frac{9}{100} \times 60000 = 0.09 \times 60000 = 5400\)
• Number of Girls in B: \(12\%\) of \(24000 = \frac{12}{100} \times 24000 = 0.12 \times 24000 = 2880\)

Number of Boys in B = Number of Students in B - Number of Girls in B = \(5400 - 2880 = 2520\)

College C

• Number of Students in C: \(23\%\) of \(60000 = \frac{23}{100} \times 60000 = 0.23 \times 60000 = 13800\)
• Number of Girls in C: \(18\%\) of \(24000 = \frac{18}{100} \times 24000 = 0.18 \times 24000 = 4320\)

Number of Boys in C = Number of Students in C - Number of Girls in C = \(13800 - 4320 = 9480\)

Calculating the Average Number of Boys

Now that we have the number of boys in Colleges A, B, and C, we can calculate their average. The average is the sum of the number of boys in these colleges divided by the number of colleges (which is 3).

• Total number of boys in A, B, and C = Boys in A + Boys in B + Boys in C
• Total number of boys in A, B, and C = \(2400 + 2520 + 9480 = 14400\)

Average number of boys in A, B, and C = \(\frac{\text{Total boys in A, B, C}}{3}\)

Average number of boys in A, B, and C = \(\frac{14400}{3} = 4800\)

Therefore, the average number of boys studying in Colleges A, B, and C is 4800.

Revision Table: Key Calculations

Additional Information: Data Interpretation Tips

Data interpretation questions often involve analyzing tables, charts, or graphs to extract relevant information and perform calculations. Here are some tips:

• Read the question carefully to understand exactly what is being asked.
• Identify the total values for the given distributions (e.g., total students, total girls).
• Understand what each column or section of the table/chart represents.
• Pay attention to percentages and base values. Remember that percentages are always calculated with respect to a base value. In this problem, the base for student percentage is 60000, and the base for girl percentage is 24000.
• Break down complex problems into smaller steps, like calculating individual values before finding sums or averages.
• Double-check your calculations, especially when dealing with multiple steps.
• Practice interpreting different types of data representations to improve your skills.