The average weight of 20 students of a class was 30.5 kg. After 6 new students joined the class, its average weight increased by 2 kg. Find the average weight of the 6 new students who joined the class (rounded off to one decimal place).
39.2 kg
Calculating Average Weight of New Students
The question asks us to find the average weight of 6 new students who joined a class, given the initial average weight of the class and how the average weight changed after the new students joined.
Step 1: Calculate the Initial Total Weight
We know the initial number of students and their average weight. The total weight is the number of students multiplied by their average weight.
- Initial number of students = 20
- Initial average weight = 30.5 kg
Initial Total Weight = Initial number of students $\times$ Initial average weight
Initial Total Weight $= 20 \times 30.5$ kg
Initial Total Weight $= 610$ kg
Step 2: Determine the New Number of Students and New Average Weight
6 new students joined the class. The average weight increased by 2 kg.
- Number of new students = 6
- New total number of students = Initial number of students + Number of new students
- New total number of students = $20 + 6 = 26$
- Increase in average weight = 2 kg
- New average weight = Initial average weight + Increase in average weight
- New average weight = $30.5$ kg + $2$ kg = $32.5$ kg
Step 3: Calculate the New Total Weight
Now that we know the new total number of students and the new average weight, we can find the new total weight of the class.
New Total Weight = New total number of students $\times$ New average weight
New Total Weight $= 26 \times 32.5$ kg
New Total Weight $= 845$ kg
Step 4: Calculate the Total Weight of the New Students
The difference between the new total weight and the initial total weight is the total weight of the 6 new students who joined.
Total weight of 6 new students = New Total Weight - Initial Total Weight
Total weight of 6 new students $= 845$ kg - $610$ kg
Total weight of 6 new students $= 235$ kg
Step 5: Calculate the Average Weight of the New Students
To find the average weight of the 6 new students, divide their total weight by the number of new students.
Average weight of 6 new students = Total weight of 6 new students / Number of new students
Average weight of 6 new students $= \frac{235}{6}$ kg
Calculating the value:
$\frac{235}{6} \approx 39.1666...$ kg
Step 6: Round the Average Weight to One Decimal Place
The question asks for the answer rounded off to one decimal place.
$39.1666...$ kg rounded to one decimal place is $39.2$ kg.
Therefore, the average weight of the 6 new students who joined the class is approximately 39.2 kg.
Revision Table: Key Data Points
| Description | Value | Unit |
|---|---|---|
| Initial Students | 20 | - |
| Initial Avg Weight | 30.5 | kg |
| Initial Total Weight | 610 | kg |
| New Students | 6 | - |
| New Total Students | 26 | - |
| Increase in Avg Weight | 2 | kg |
| New Avg Weight | 32.5 | kg |
| New Total Weight | 845 | kg |
| Total Weight of New Students | 235 | kg |
| Avg Weight of New Students | 39.2 (rounded) | kg |
Additional Information: Understanding Average
The average (or mean) of a set of numbers is calculated by summing all the numbers in the set and then dividing by the count of numbers in the set. In this problem, the average weight is the total weight of all students divided by the number of students.
Formula for Average = $\frac{\text{Sum of all values}}{\text{Number of values}}$
When new items (in this case, students with their weights) are added to a group, the total sum changes, and the number of items changes. The new average reflects these changes.
If the new average is higher than the old average, it means the new items added (the new students) must have had a total value (total weight) greater than the old average weight, and specifically, great enough to pull the overall average up.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
