Calculating the Average Weight of Students: Methods and Solutions

Understanding how to calculate the average weight of students in a class is a fundamental concept in statistics. This article discusses various methods to find the average weight, including direct summation and the use of the formula for the pooled mean. We'll walk through multiple solutions and methods to ensure a comprehensive understanding.

Introduction to Average Weight Concepts

The average weight is a statistical measure that represents the central tendency of a dataset. It is calculated by dividing the sum of all values by the number of values. In the context of a class, the average weight can be determined for different groups within the class, and then a combined average can be calculated.

Method 1: Direct Summation

The first method involves summing the weights of all individual students and then dividing by the total number of students. This is a straightforward approach, but it requires a clear breakdown of the weights and the number of students in each group.

Example: Let's consider a class with 24 boys. 16 boys have an average weight of 50.25 kg, and 8 boys have an average weight of 45.15 kg.

Step-by-Step Calculation:

16 boys * 50.25 kg 804 kg

8 boys * 45.15 kg 361.2 kg

Total weight 804 kg 361.2 kg 1165.2 kg

Average weight 1165.2 kg / 24 48.55 kg

Note that in the provided data, there was an error. The total weight for 16 boys should be 804 kg and for 8 boys, 361.2 kg, not 880 and 321.2 as mentioned earlier. Thus, the correct average weight is 48.55 kg, not 51.67 or 46.88.

Method 2: Pooling the Two Means

The second method involves using the formula for the pooled mean, which is a specialized formula to find the combined average when different groups have different sample sizes. This method is particularly useful when dealing with different sample sizes or different average values.

Formula:

M (n1*m1 n2*m2) / (n1 n2)

Step-by-Step Calculation:

n1 16, m1 50.25, n2 8, m2 45.15

M (16*50.25 8*45.15) / (16 8)

16*50.25 8*45.15 804 361.2 1165.2

16 8 24

M 1165.2 / 24 48.55 kg

Conclusion

Both methods yield the same result for the average weight of the boys in the class, 48.55 kg. This demonstrates the reliability of the pooled mean formula and the importance of accurate data processing in statistical analysis.

Understanding how to calculate the average weight using both direct summation and the pooled mean formula is crucial for various practical applications, from health sciences to educational research. Whether you're working with small or large group data, these methods provide a robust and accurate way to determine the central tendency of weights in a class.