Marks Correction and Average Impact
The problem states that a student's mark was recorded incorrectly. The correct mark was 91, but it was entered as 70. This error caused the class average to decrease by \(7/3\). We need to find the total number of students in the class.
Calculating Marks Difference
First, find the difference between the correct mark and the incorrectly entered mark:
Difference in marks = Correct Mark - Incorrect Mark
Difference in marks = \(91 - 70 = 21\)
Relating Marks Difference to Average Change
This total difference of 21 marks, when distributed among all students, resulted in a decrease in the average marks by \(7/3\). Let \(N\) be the number of students in the class.
The change in average is calculated as the total difference in marks divided by the number of students:
Change in Average = Total Difference in Marks / Number of Students
\( \frac{7}{3} = \frac{21}{N} \)
Solving for Number of Students
To find \(N\), we can rearrange the equation:
\( N = \frac{21}{\frac{7}{3}} \)
\( N = 21 \times \frac{3}{7} \)
\( N = \frac{21 \times 3}{7} \)
\( N = \frac{63}{7} \)
\( N = 9 \)
Therefore, there are 9 students in the class.
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 average marks obtained by a group of 16 students was 20. One student left the group as a result of which the average of the remaining students rose to 21. But another student joined, as a result of which the average marks of the group dropped a bit and became 20.5. What was the average marks obtained by the student who left and the one who joined?
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?
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.
