The average age of 30 students of a class is 14
years 4 months. After admission of 5 new students
in the class the average becomes 13 years 9
months. The youngest one of the five students is 9
years 11 months old. The average of the remain-
ing 4 new students is
Answers
Total number of students in the class = 30
Given that the mean of the ages of these 30 students is 14 years 4 months
Convert the age from years/months to months only.
So,
Mean becomes ( 14×12 + 4 )
{ Since, 1 year = 12 months }
==> 168 + 4
==> 172
But we know that,
Mean = Sum of all observations / Number of observations
☛ putting the values in the formula
☛ 172 = sum of ages of the students / 30
∴ sum of ages of the students = 5160
Also,
5 new students are added to the class, Now
Given,
Total number of students = 30 + 5 ==> 35
Mean = ( 13×12 + 9 ) ==> 165
Again,
Mean = Sum of the ages of all students / total number of students
☛ 165 = sum of the ages of all students / 35
∴ sum of the ages of all students = 5775
Now,
Sum of the ages of the five new students = ( sum of the ages after adding the five new students ) - ( sum of the ages before adding the five students )
☛ sum of the ages of five new students = 5775 - 5160
∴ sum of the ages of five new students = 615 ...(1)
Also,
The youngest of the five students is 9 years 11 months old or ( 9 × 12 + 11) ==> 119 months old
In eq.(1) ,
☛ sum of the ages of the five new students = 615
By subtracting the age of the youngest student from the five new students, we will get the sum of the ages of the remaining four students:
☛ sum of the ages of 4 students = 615 - 119
∴ sum of the ages of 4 students = 496
We now have,
Sum of the ages of the four students = 496
Number of students = ofcourse , 4 students
So,
Mean = Sum of the ages of the four students / Number of students
☛ Mean = 496 / 4
☛ Mean = 124
We got , Mean = 124 months , ( Convert it into years/months )
==> 12 × 10 = 120
==> 124 months = 10 years 4 months
Hence, Mean of the remaining four students is 10 years 4 months