The average age of 40 students is 21 years. It was observed that while…
2024
The average age of 40 students is 21 years. It was observed that while calculating the average age, the age of a student was taken as 20 years instead of 30 years. What will be the correct average age?
- A.
21.25 years
- B.
21.22 years
- C.
12.12 years
- D.
23.84 years
Attempted by 22 students.
Show answer & explanation
Correct answer: A
To find the correct average age after correcting the error, follow these steps:
Step-by-Step Calculation
Identify the given data:
Number of students: 40
Incorrect average age: 21 years
Incorrect age used: 20 years
Correct age that should have been used: 30 years
Determine the difference in age:
Difference = Correct age - Incorrect age
Difference = 30 - 20 = 10 years
This means the total sum of the students' ages was underestimated by 10 years.
Calculate the effect on the average:
The average is the total sum divided by the number of students.
Average increase = Total difference / Number of students
Average increase = 10 / 40 = 0.25 years
Find the correct average:
Correct average = Incorrect average + Average increase
Correct average = 21 + 0.25 = 21.25 years