Understanding the Data and the Question

The question asks for the average of the *percentages* of female students across all the listed departments. It's important to note that this is different from finding the overall percentage of female students in the entire institute, which would require summing the actual number of female students from each department and dividing by the total number of students in the institute.

The table provides the following information for each department:

• Department Name
• Total Number of Students
• Percentage of Female Students
• Percentage of Male Students

We need to focus on the 'Percentage of Female Students' column to calculate the average percentage.

Identifying Female Percentages per Department

Let's list the percentage of female students for each department:

1. Computer: 45%
2. Civil: 35%
3. Mechanical: 23%
4. Electrical: 65%
5. Electronics: 44%
6. Mining: 40%

There are 6 departments listed in the table.

Calculating the Average Percentage of Female Students

To find the average percentage, we sum up the percentages for all departments and divide by the number of departments.

Sum of Female Percentages = 45% + 35% + 23% + 65% + 44% + 40%

Sum of Female Percentages = 252%

Number of Departments = 6

Average Percentage of Females = $\frac{\text{Sum of Female Percentages}}{\text{Number of Departments}}$

Average Percentage of Females = $\frac{252\%}{6}$

Average Percentage of Females = $42\%$

Conclusion

The average of the percentage of female students in the whole Institute, based on the given percentages for each department, is 42.0%.

Average calculation: $\frac{252}{6} = 42\%$

Revision Table: Key Concepts Revisited

Additional Information: Distinguishing Average Percentage from Overall Percentage

It is crucial to understand the difference between calculating the average of given percentages and calculating the overall percentage for a combined group. In this question, we were asked for the average of the *departmental percentages* of females.

If the question had asked for the *overall percentage* of females in the *entire institute*, the calculation would be different:

1. Calculate the actual number of female students in each department (Total Students * Percentage of Female / 100).
2. Sum the number of female students from all departments to get the total number of females in the institute.
3. Sum the total number of students from all departments to get the total number of students in the institute.
4. Divide the total number of females by the total number of students and multiply by 100%.

For example, in the Computer department, the number of female students is $840 \times \frac{45}{100} = 378$. This calculation would be repeated for all departments, and then the sums would be used to find the overall percentage. This is a common point of confusion in data interpretation problems.