The following table shows the marks scored by six students (A–F) in six different subjects S1 to S6 having maximum marks of 160, 160, 120, 120, 200, and 240 respectively. Based on the data in the table, answer the question that follows: Student-wise details of Marks ScoredStudents Marks Scored in Subject S1 (Out of 160) S2 (Out of 160) S3 (Out of 120) S4 (Out of 120) S5 (Out of 200) S6 (Out of 240) A 76 84 66 56 154 144 B 120 100 84 76 136 132 C 128 72 64 70 144 160 D 84 130 96 84 104 168 E 64 128 90 92 174 70 F 70 96 60 56 164 96
Finding Average Marks in Subject S5
This solution explains how to calculate the average marks scored by all six students (A to F) in subject S5, based on the provided table of marks.
Student Marks in Subject S5
First, let's identify the marks scored by each student in Subject S5 from the table:
| Student | S5 (Out of 200) |
| A | 154 |
| B | 136 |
| C | 144 |
| D | 104 |
| E | 174 |
| F | 164 |
Calculating the Average Marks
To find the average marks scored in subject S5, we need to sum up the marks of all students in S5 and then divide by the total number of students.
The formula for the average is:
$ \text{Average Marks} = \frac{\text{Sum of Marks in S5}}{\text{Total Number of Students}} $
Step 1: Sum the Marks in S5
Add the marks obtained by each student in subject S5:
Sum = 154 + 136 + 144 + 104 + 174 + 164
Let's calculate the sum:
- 154 + 136 = 290
- 290 + 144 = 434
- 434 + 104 = 538
- 538 + 174 = 712
- 712 + 164 = 876
So, the total sum of marks scored in S5 by all students is 876.
Step 2: Count the Total Number of Students
There are six students in total: A, B, C, D, E, and F.
Total Number of Students = 6
Step 3: Calculate the Average
Now, divide the sum of marks by the total number of students:
$ \text{Average Marks in S5} = \frac{876}{6} $
Performing the division:
$ \frac{876}{6} = 146 $
Conclusion
The average marks scored in subject S5 by all the students together is 146.
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?
