Understanding the Student Distribution Data

The question provides data about the distribution of students and girls across six colleges (A to F). We are given the total number of students and the total number of girls across all colleges. We need to use this information to find the difference between the number of boys and girls in a specific college, College D.

The key information provided is:

• Total number of students in all colleges = 60000
• Total number of girls in all colleges = 24000
• A table showing the percentage distribution for each college for both total students and total girls.

Let's look at the distribution table again:

Calculating Students and Girls in College D

To find the difference between boys and girls in College D, we first need to determine the exact number of students and girls studying in College D. The table gives us the percentage for College D relative to the total numbers.

• Percentage of total students in College D = 18%
• Percentage of total girls in College D = 14%

Let's calculate the actual numbers:

Number of students in College D:

This is 18% of the total students (60000).

\(\text{Number of students in College D} = 18\% \text{ of } 60000\)

\(\text{Number of students in College D} = \frac{18}{100} \times 60000\)

\(\text{Number of students in College D} = 18 \times 600\)

\(\text{Number of students in College D} = 10800\)

Number of girls in College D:

This is 14% of the total girls (24000).

\(\text{Number of girls in College D} = 14\% \text{ of } 24000\)

\(\text{Number of girls in College D} = \frac{14}{100} \times 24000\)

\(\text{Number of girls in College D} = 14 \times 240\)

\(\text{Number of girls in College D} = 3360\)

Finding the Number of Boys in College D

The total number of students in any college is the sum of the number of boys and the number of girls in that college. Therefore, we can find the number of boys in College D by subtracting the number of girls from the total number of students in College D.

\(\text{Number of boys in College D} = \text{Number of students in College D} - \text{Number of girls in College D}\)

\(\text{Number of boys in College D} = 10800 - 3360\)

\(\text{Number of boys in College D} = 7440\)

Calculating the Difference between Boys and Girls in College D

Now that we have the number of boys and the number of girls in College D, we can find the difference between them.

• Number of boys in College D = 7440
• Number of girls in College D = 3360

\(\text{Difference} = |\text{Number of boys} - \text{Number of girls}|\)

\(\text{Difference} = |7440 - 3360|\)

\(\text{Difference} = |4080|\)

\(\text{Difference} = 4080\)

The difference between the number of boys and number of girls studying in College D is 4080.

Revision Table: Key Calculations for College D

Additional Information on Data Interpretation

Data interpretation questions often involve analyzing tables, charts, or graphs to extract specific information and perform calculations. Key skills required include:

• Reading Data Accurately: Carefully understanding what each part of the table or chart represents (e.g., percentages, absolute numbers, categories).
• Understanding Percentages: Knowing how to calculate a percentage of a given total number. The formula is \(\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\) or \(\text{Part} = \frac{\text{Percentage}}{100} \times \text{Whole}\).
• Calculating Ratios and Differences: Being able to compare different quantities by finding their ratio or the difference between them.
• Logical Reasoning: Using the given information to deduce unknown values, such as finding the number of boys when total students and girls are known.

Practice with different types of data representations like bar graphs, pie charts, line graphs, and tables is crucial for mastering data interpretation.