Question

The mean weight of 8 students is 45.5 kg. Two more students having weights 41.7 kg and 53.3 kg join the group. What is the new mean weight?

Answer 1

Hint: To find the new mean weight of the new group in this problem can be found by firstly finding the weight of old 8 students then finding the weight of two included student groups then use the formula of mean and finding the mean weight of the new group.

Complete step-by-step answer:
Given the mean weight of 8 students is 45.5 kg.
The weight of two more students having weight 41.7 kg and 53.3 kg
We have to find the new mean weight
Just apply the formula of mean for 8 students
We know the mean is defined as the ratio of total sum of observation and the total number of observations.
On putting the given values
We get,
 \[45.5 = \dfrac{{Total{\text{ }}weight{\text{ }}of{\text{ }}8{\text{ }}students}}{8}\]
Multiplying 8 to LHS we will get the total weight of 8 students
So the total weight of 8 students \[ = 45.5 \times 8\] kg
 $ = 364$ kg
Now two more students joined the group
Therefore the total weight of all 10 students \[ = 364 + 41.7 + 53.3\] kg
 \[ = 459\] kg
So the new mean
 \[ = \dfrac{{459}}{{10}} \\
   = 45.9 \] kg
 \[ = 45.9\] kg
New mean= \[ = 45.9\] kg
So, the correct answer is “ 45.9 kg”.

Note: In this question it is asked that the new mean when two more students joined the group. So what will be the solving method if two students are removed from the group. We will use the same method instead of adding the weight of two students. We will subtract the weight of two left students of this group.