Calculate Teacher's Weight
We need to find the teacher's weight given the initial average weight of students and the new average weight after including the teacher.
Initial Calculation
The initial group consists of 10 students with an average weight of 50 kg.
- Number of students: $10$
- Average weight of students: $50 \text{ kg}$
- Total weight of students: $10 \times 50 \text{ kg} = 500 \text{ kg}$
Calculation with Teacher Included
When the teacher is included, the group size increases, and the average weight also increases.
- New number of people (students + teacher): $10 + 1 = 11$
- The average weight increases by 1 kg: New average weight = $50 \text{ kg} + 1 \text{ kg} = 51 \text{ kg}$
- New total weight of the group (students + teacher): $11 \times 51 \text{ kg} = 561 \text{ kg}$
Determine Teacher's Weight
The teacher's weight is the difference between the new total weight and the initial total weight of the students.
- Teacher's weight = New total weight - Total weight of students
- Teacher's weight = $561 \text{ kg} - 500 \text{ kg}$
- Teacher's weight = $61 \text{ kg}$
Therefore, the teacher's weight is 61 kg.
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?
