Identifying the Marks Difference
The problem states that a student's marks were recorded incorrectly. We need to find the actual difference between the correct marks and the incorrectly entered marks.
- Incorrect Marks Entered: 21
- Correct Marks: 69
The total difference in marks is calculated as:
Difference = Correct Marks - Incorrect Marks
Difference = \(69 - 21 = 48\)
Average Decrease Explained
This difference of 48 marks affected the class average. The problem states the average marks decreased by \(\frac{6}{5}\).
Let '\(N\)' be the total number of students in the class.
The decrease in the average is the total difference in marks divided by the number of students.
Decrease in Average = \(\frac{\text{Total Difference in Marks}}{N}\)
Calculating the Number of Students
We can now set up an equation using the information provided:
\(\frac{48}{N} = \frac{6}{5}\)
To solve for '\(N\)', we can cross-multiply:
\(48 \times 5 = 6 \times N\)
\(240 = 6N\)
Now, divide both sides by 6 to find the value of '\(N\)':
\(N = \frac{240}{6}\)
\(N = 40\)
Thus, there are 40 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.
