Question

Mean of ages of 20students is 10years. 5students with mean age of 12 years leave the class. Mean of ages of remaining students will be-
• 4
• 5.66
• 6.25
• 9.33

Answer 1

Let x1,x2,x3,......,x20 be the 20 students.

Mean of 20 students is 10years. i.e.,
(x1+x2+......+x20) / 20 = 10
=>(x1+x2+......+x20)=200                   ----(equation1)

Mean of 5 students is 12 years. i.e.,
(x16+x17+x18+x19+x20)/5=12
=> (x16+x17+x18+x19+x20) =60.       ----(equation 2)

Lets suppose mean of the remaining 15 students is...

(x1+x2+.....+x15)/15= y
=>(x1+x2+....+x15)=15y                      -----(equation 3)

substitute equation 2 and equation 3 in equation 1,

=> (x1+x2+.....+x15)+(x16+......+x20)=200
=>15y+60=200
=>15y=140
=>y=140/15
=>y=9.33.

Therefore, the mean of remaining students is 9.33.

Answer 2

Mean age of remaining students is 9.33 years.

Step-by-step explanation:

We are given that Mean of ages of 20 students is 10 years.

Also, 5 students with mean age of 12 years leave the class and we have to find the Mean age of remaining students.

As we know that Mean formula,  

where, = Total Sum of n observation

                 n = Number of observation

So, Total Sum of n observation () =  

                           

So, Total sum of ages of 20 students =   = 200

Also, Total sum of ages of 5 students who leave the class =  = 60

Now, Mean age of remaining 15 students =

                               

Here, Total sum of ages of remaining 15 students = 200 - 60 = 140

         Number of remaining students = 15

Hence, Mean age of remaining students =  = 9.33 years.