Calculating Number of Students from Average Decrease
1. Identify the Mark Difference
The marks were incorrectly entered as 34 instead of the correct value of 70.
The total difference in marks is:
\( \text{Difference} = \text{Correct Marks} - \text{Incorrect Marks} \)
\( \text{Difference} = 70 - 34 = 36 \)
2. Relate Mark Difference to Average Decrease
Let \(N\) be the total number of students in the class.
The total difference in marks (36) is distributed across all \(N\) students, causing the average to decrease.
The decrease in the average marks is given as \(\frac{4}{3}\).
Therefore, the relationship is:
\( \frac{\text{Total Difference}}{\text{Number of Students}} = \text{Average Decrease} \)
\( \frac{36}{N} = \frac{4}{3} \)
3. Solve for the Number of Students (\(N\))
To find \(N\), we can rearrange the equation:
\( 4 \times N = 36 \times 3 \)
\( 4N = 108 \)
\( N = \frac{108}{4} \)
\( N = 27 \)
Thus, there are 27 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.
