There are two sections A and B of a class, consisting of 38 and 42 students respectively. if the average weight of the students of section A is 55 Kg and that of section B is 32 Kg. find the average weight of all the students in the class.
42.925 Kg
Calculating the Average Weight of Students Across Two Sections
This problem asks us to find the average weight of all students in a class that is divided into two sections, A and B. We are given the number of students and the average weight for each section separately. To find the overall average weight of the class, we need to calculate the total weight of all students and divide it by the total number of students.
Understanding Average Weight
The average weight of a group is calculated by dividing the total weight of all individuals in the group by the number of individuals in the group.
Formula:
$\text{Average Weight} = \frac{\text{Total Weight}}{\text{Number of Students}}$
From this formula, we can also find the total weight if we know the average weight and the number of students:
$\text{Total Weight} = \text{Average Weight} \times \text{Number of Students}$
Step-by-Step Calculation
Step 1: Find the total weight of students in Section A
Section A has 38 students, and their average weight is 55 Kg.
Total weight of Section A students = Average weight of A $\times$ Number of students in A
Total weight of Section A = $55 \text{ Kg} \times 38$
Total weight of Section A = $2090 \text{ Kg}$
Step 2: Find the total weight of students in Section B
Section B has 42 students, and their average weight is 32 Kg.
Total weight of Section B students = Average weight of B $\times$ Number of students in B
Total weight of Section B = $32 \text{ Kg} \times 42$
Total weight of Section B = $1344 \text{ Kg}$
Step 3: Find the total number of students in the entire class
The total number of students is the sum of students in Section A and Section B.
Total number of students = Number of students in A + Number of students in B
Total number of students = $38 + 42$
Total number of students = $80$
Step 4: Find the total weight of all students in the class
The total weight of all students is the sum of the total weight of Section A and Section B.
Total weight of all students = Total weight of Section A + Total weight of Section B
Total weight of all students = $2090 \text{ Kg} + 1344 \text{ Kg}$
Total weight of all students = $3434 \text{ Kg}$
Step 5: Calculate the average weight of all students in the class
Now, we use the overall total weight and the overall total number of students to find the average weight of the entire class.
Overall Average Weight = $\frac{\text{Total weight of all students}}{\text{Total number of students}}$
Overall Average Weight = $\frac{3434 \text{ Kg}}{80}$
Let's perform the division:
$3434 \div 80 = 42.925$
So, the average weight of all the students in the class is 42.925 Kg.
Summary of Calculations
| Section | Number of Students | Average Weight (Kg) | Total Weight (Kg) |
|---|---|---|---|
| A | 38 | 55 | $38 \times 55 = 2090$ |
| B | 42 | 32 | $42 \times 32 = 1344$ |
| Total Class | Total Number of Students | Total Weight (Kg) | Overall Average Weight (Kg) |
|---|---|---|---|
| A + B | $38 + 42 = 80$ | $2090 + 1344 = 3434$ | $\frac{3434}{80} = 42.925$ |
Final Answer
The average weight of all the students in the class is 42.925 Kg.
Revision Table: Average Weight Calculation
Here is a quick table summarizing the key values used in the calculation:
| Quantity | Value |
|---|---|
| Students in Section A | 38 |
| Average Weight of Section A | 55 Kg |
| Total Weight of Section A | 2090 Kg |
| Students in Section B | 42 |
| Average Weight of Section B | 32 Kg |
| Total Weight of Section B | 1344 Kg |
| Total Students in Class | 80 |
| Total Weight of Class | 3434 Kg |
| Overall Average Weight | 42.925 Kg |
Additional Information: Weighted Average
This type of problem is an example of finding a weighted average. A weighted average is used when combining averages from different groups that have different sizes. The average of each group is 'weighted' by the number of items (students in this case) in that group.
The formula for a weighted average of two groups is:
$\text{Weighted Average} = \frac{(N_1 \times A_1) + (N_2 \times A_2)}{N_1 + N_2}$
Where:
- $N_1$ = Number of items in Group 1 (students in Section A)
- $A_1$ = Average of Group 1 (average weight of Section A)
- $N_2$ = Number of items in Group 2 (students in Section B)
- $A_2$ = Average of Group 2 (average weight of Section B)
In our problem:
- $N_1 = 38$
- $A_1 = 55 \text{ Kg}$
- $N_2 = 42$
- $A_2 = 32 \text{ Kg}$
Plugging these values into the formula:
Weighted Average = $\frac{(38 \times 55) + (42 \times 32)}{38 + 42}$
Weighted Average = $\frac{2090 + 1344}{80}$
Weighted Average = $\frac{3434}{80}$
Weighted Average = $42.925 \text{ Kg}$
This weighted average approach confirms the result obtained by calculating total weight and total students.
Important Questions from Average
The average height of 20 students of class 8 is 152 cm and the average height of 15 students of class 9 is 168 cm. What is the average height (to the nearest cm) of the students of both classes?
The average of 4, 6, 8, 12 and x is 7 and the average of x, 9, 13, 15 and y is 9. What is the value of 2x - 3y?
The average weight of 20 girls in a school was 52 kg. Two new students of weight 54 kg and 50 kg were admitted. The ratio of this new average to the old one is:
If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:
If the average of 5 consecutive odd integers in increasing order is 11 , then the average of the last 3 of them is:
