Calculating the Combined Weight of a Teacher and Principal Using Average Formula

In this article, we will explore how to calculate the combined weight of a teacher and a principal using the concept of average weight. This problem involves basic calculations and can be a helpful exercise for students and educators familiarizing themselves with averages and their applications.

Understanding the Problem

Suppose we have a class of 48 students with an average weight of 36 kg. When we include the teacher and the principal, the average weight of the entire group (now totaling 50 individuals) becomes 36.76 kg. The objective is to find the combined weight of the teacher and the principal.

Step-by-Step Solution

Let's break down the solution into manageable steps:

Step 1: Calculate the Total Weight of 48 Students

The average weight of the 48 students is given as 36 kg. To find the total weight of these students, we use the formula for average weight:

Total weight of students Average weight of students × Number of students

Substituting the values:

Total weight of students 36 kg × 48 1728 kg

Step 2: Calculate the Total Weight of 50 Individuals

Now, when we include the teacher and the principal, the total number of individuals becomes 50. The new average weight is given as 36.76 kg. Using the formula for average weight again:

Total weight of 50 individuals New average weight × Number of individuals

Substituting the values:

Total weight of 50 individuals 36.76 kg × 50 1838 kg

Step 3: Calculate the Combined Weight of the Teacher and Principal

The combined weight of the teacher and the principal is the difference between the total weight of the 50 individuals and the total weight of the 48 students:

Combined weight of teacher and principal Total weight of 50 individuals - Total weight of 48 students

Substituting the values:

Combined weight of teacher and principal 1838 kg - 1728 kg 110 kg

Conclusion

Thus, the combined weight of the teacher and the principal is 110 kg. This problem demonstrates the practical application of average weight calculations and reinforces the formula for calculating averages.

Related Concepts

Average Weight: In statistics, the average weight (also known as the arithmetic mean) is a measure of central tendency that is calculated by summing all values and dividing by the number of values.

Teacher Weight: The total weight of the principal and additional staff members.

Principal Weight: The total weight of the principal alone, which can be derived from the combined weight when the teacher's weight is known or can be calculated separately.