Question

The mean weight of a class of 10 students is 60kg.
A student weighing 55kg leaves the class and two
new students are admitted who weigh 62kg and
42kg respectively. Find the mean weight of the
class.​

Answer 1

I am going to focus on the “or more” part of the question. Otherwise it is a rather simple calculation, as some others have pointed out.

Let x denote the number of 58kg student that join and y denote the number of 60kg students who join.

As correctly pointed out by another person, the initial total weight of the class, TW20=20⋅48kg=960kg.

Here I am just using the subscript TW20 to indicate the number of people in the class so we can differentiate between different total weights (initial vs after having added more students)

I think it’s worth pointing out the equation for the mean is

w^=1Ntot∑i=1Ntotwi

Where, for the first 20 people:

w^=1Ntot∑i=1Ntotwi=120∑i=120wi=960kg20=48kg

We also need to figure out how many people are in this new class. Since we started off with 20 people and added x of a certain weight and y of another weight, the total number of people becomes:

Ntot=20+x+y

We can also calculate the total weight of the class by adding the weight of the new people to the total class weight to obtain the new total weight:

TWNtot=∑i=1Ntotwi=∑i=1N20wi+∑i=21Ntotwi=960+58x+60y

The last step to solve the problem in generality is to divide the total weight of the new class, TWNtot , by the number of students in the new class, Ntot

So our new mean, w^ is:

w^