Calculating the Average Weight of Students

The question asks us to find the average weight of a combined group of students when we know the average weight of two separate groups.

To find the average weight of the total group, we need two things:

1. The total weight of all the students.
2. The total number of students.

The formula for average is:

$$\text{Average} = \frac{\text{Total Sum}}{\text{Total Count}}$$

Step-by-Step Solution to Find the Combined Average Weight

Step 1: Calculate the total weight of the first group of students.

We are given:

• Number of students in the first group = 10
• Average weight of the first group = 25 kg

Using the average formula, we can find the total weight:

$$\text{Total Weight} = \text{Average Weight} \times \text{Number of Students}$$

Total weight of the first group = $$25 \text{ kg/student} \times 10 \text{ students} = 250 \text{ kg}$$

Step 2: Calculate the total weight of the second group of students.

We are given:

• Number of students in the second group = 10
• Average weight of the second group = 35 kg

Total weight of the second group = $$35 \text{ kg/student} \times 10 \text{ students} = 350 \text{ kg}$$

Step 3: Calculate the total number of students in both groups combined.

Total number of students = Number of students in group 1 + Number of students in group 2

Total number of students = $$10 + 10 = 20 \text{ students}$$

Step 4: Calculate the combined total weight of all 20 students.

Combined total weight = Total weight of group 1 + Total weight of group 2

Combined total weight = $$250 \text{ kg} + 350 \text{ kg} = 600 \text{ kg}$$

Step 5: Calculate the average weight of all 20 students.

Now we have the combined total weight and the total number of students. We can use the average formula again:

$$\text{Average Weight of 20 Students} = \frac{\text{Combined Total Weight}}{\text{Total Number of Students}}$$

Average weight = $$\frac{600 \text{ kg}}{20 \text{ students}}$$

Average weight = $$30 \text{ kg}$$

So, the average weight of these 20 students is 30 kg.

Summary of Average Weight Calculation

Here is a summary of the key values used in the calculation:

Average weight of combined group = $$\frac{600}{20} = 30 \text{ kg}$$

Revision Table: Average Weight Calculations

Additional Information: Understanding Averages

An average, also known as the mean, is a single value that represents the center of a set of numbers. It is calculated by adding up all the values in the set and dividing by the number of values.

When combining groups with different averages, you cannot simply average the averages (e.g., (25+35)/2 = 30 works in this specific case only because the number of students in both groups is the same). You must always calculate the total sum for each group first, combine the total sums, and then divide by the total number of items (students in this case).

This problem demonstrates how to correctly calculate a weighted average when the number of items in each group is equal. If the number of students in the groups were different (e.g., 10 students at 25 kg and 15 students at 35 kg), simply averaging the averages would give an incorrect result. The method used here (calculating total weight for each group first) is the correct approach for any number of students in the groups.