Calculate Initial Total Marks
The initial group has 16 students with an average score of 20. The total marks for these 16 students can be calculated as:
Total Marks (Initial) = Number of students $\times$ Average marks
Total Marks (Initial) = $16 \times 20 = 320$
Calculate Marks of the Student Who Left
When one student left, the group size became 15, and the average marks increased to 21. The total marks for the remaining 15 students are:
Total Marks (15 students) = $15 \times 21 = 315$
The marks obtained by the student who left is the difference between the initial total marks and the total marks after they left:
Marks (Student Left) = Total Marks (Initial) - Total Marks (15 students)
Marks (Student Left) = $320 - 315 = 5$
Calculate Marks of the Student Who Joined
After the student left, another student joined the group, bringing the total number of students back to 16. The average marks of this group of 16 students became 20.5. The new total marks are:
Total Marks (New 16 students) = $16 \times 20.5 = 328$
The marks obtained by the student who joined is the difference between the new total marks (with 16 students) and the total marks of the 15 students (before the new one joined):
Marks (Student Joined) = Total Marks (New 16 students) - Total Marks (15 students)
Marks (Student Joined) = $328 - 315 = 13$
Calculate the Average Marks of Both Students
The question asks for the average marks obtained by the student who left and the one who joined. We have the marks for both:
- Marks of the student who left = 5
- Marks of the student who joined = 13
The average is calculated as:
Average Marks = $\frac{\text{Marks (Student Left)} + \text{Marks (Student Joined)}}{2}$
Average Marks = $\frac{5 + 13}{2} = \frac{18}{2} = 9$
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?
