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 = $\frac{5 + 13}{2} = \frac{18}{2} = 9$
Similar Questions
- Find the mean marks of the following distribution.
Marks obtained No. of students 25 5 30 6 35 3 40 1 - The Table given below represents the ages of students in a private music school. What is the average age of the students?
Age Band Students 0 - 10 4 10 - 20 5 20 - 30 15 30 - 40 4 - Find the mean of the following numbers:
20, 18, 16, 25, 19, 22, 18, 16, 23, 14 - The average age of a family of 5 members is 20 years, with the youngest member being 5 years old. What was the average age (in years) of the family just before the birth of the youngest member?
The median of the observations 4, 14, 11, 8, 7, 8, 9, 12, 4, and 6 is:
The weights (in kg) of 9 members of a school cricket team are 50, 63, x, 62, 64, 48, 51, 55, 48. If the mean weight is 56 kg, then the value of x is:
A group of people consists of men, women, and children. 40% of them are men, 35% are women, and the rest are children, and their average weights are 70 kg, 60 kg, and 30 kg, respectively. The average weight of the group is:
If the mean of 22, 25, 27, 24, and x is 26, then the value of x is:
The average of 70 values is 40. If each value is multiplied by 20, what will be the changed average?
- A class of 30 students appeared in a test. The average score of 12 students is 68, and that of the rest is 70. What is the average score of the class?
Important Questions from Average
- Find the mean marks of the following distribution.
Marks obtained No. of students 25 5 30 6 35 3 40 1 - The average of first 169 even numbers is
- The average weight (in kg) of a family of five members whose weights are 40 kg, 49 kg, 56 kg, 74 kg and 35 kg is:
- The average of first 152 odd natural numbers, is:
The average runs scored by a batsman in 23 matches is 40. In the next 10 matches, the batsman scored an average of 16 runs. Find his average runs scored (rounded off to two decimals) in all the 33 matches.
