Question

The mean monthly salary of $10$ members of a group is$Rs.1445$, one more member whose monthly salary is $Rs.1500$ has joined the group. Find the monthly salary of $11$ members of the group.

Answer 1

Hint:Try to write down the formula of mean and figure out the knowns and unknowns in the equation. Make two equations, one with $10$ members and another one with $11$ members with the formula of average.Then finally find the mean of $11$ members of the group.

Complete step-by-step answer:
Before moving forward, let us try to understand the question properly first. The mean or average salary of $10$ members is given to be $Rs.1445$. Then another member is added with a monthly salary of $Rs.1500$. Now we have to find the new mean monthly salary of $11$ members of the group.
Firstly, we should understand the concept of average or mean. Mean is the average taken from some observations by dividing the sum of all the observations with the total number of observations.
$ \Rightarrow Mean = \dfrac{{Sum}}{{Number}}\dfrac{{of}}{{of}}\dfrac{{Observations}}{{Observations}}$
So, given information is that mean monthly salary of $10$ members of a group is $Rs.1445$, let’s try to put these values in the above equation
$ \Rightarrow 1445 = \dfrac{{Sum}}{{10}}$ $ \Rightarrow $ The total salary of $10$ members $ = 1445 \times 10 = Rs.14450$
So now we got the total monthly salary of $10$ members and we already have a monthly salary of ${11^{th}}$ the member.
Therefore, the total salary of $11$ members of the group $ = 14450 + 1500 = Rs.15950$
Now, we got both the sum of observations and the number of observation for calculation our mean
$ \Rightarrow Mean = \dfrac{{15950}}{{11}} = Rs.1450$
Hence, the monthly salary for $11$ members of the group is $Rs.1450$

Note:Try to write down the formula for mean to figure out the unknown and known values in the equation.An alternative approach can be to use the definition of the mean itself, without working with the formula. But the process will still be the same.