Solving for Number of Students with Average Decrease
The problem involves finding the number of students based on a change in the class average due to an incorrect marks entry.
Difference in Marks
The marks were entered as 35 instead of 99. The actual difference is:
Difference = Correct Marks - Incorrect Marks
Difference = \(99 - 35 = 64\)
Impact on Average
This total difference of 64 marks, when distributed among all students, caused the average marks to decrease by \(\frac{8}{3}\).
Calculating Number of Students
Let 'N' be the number of students in the class.
The decrease in average is calculated as:
Decrease in Average = Total Difference / Number of Students
We are given that the decrease in average is \(\frac{8}{3}\). So, the equation is:
\( \frac{64}{N} = \frac{8}{3} \)To find N, we rearrange the equation:
\( N = \frac{64}{\frac{8}{3}} \) \( N = 64 \times \frac{3}{8} \) \( N = \frac{64}{8} \times 3 \) \( N = 8 \times 3 \) \( N = 24 \)Therefore, the number of students in the class is 24.
Similar Questions
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?
- 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?
Important Questions from Average
Average of 40 numbers is 71, if the number 100 replaced by 140, then average is increased by
The captain of a football team of 11 members is 28 years old and the goalkeeper is 4 years older than him. If the ages of these two are removed, then the average age of the remaining players is two years less than the average age of the whole team. What is the average age of the team?
There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.
Consider the following statements:
1. The average score of Class-B will definitely decrease.
2. The average score of Class-A will definitely increase.
Which of the above statements is/are correct?
The average weight of A, B, Cis 40 kg, the average weight of B, D, Eis 42 kg and the weight of Fis equal to that of B. What is the average weight of A, B, C, D, Eand F?
A cow costs more than 4 goats but less than 5 goats. If a goat costs between Rs. 600 and Rs. 800, which of the following is a most valid conclusion?
