Question

The annual rainfall in Vidarbha in five years is given below. What is the average rainfall for those $5$ years?
$900$ mm, $650$ mm, $450$ mm, $733$ mm, $400$ mm.

Answer 1

Hint: We will use the formula of average. First, we will take the total number of rainfalls in those five years by adding all the five-given data. Then, we will find the average based on the total rainfall and dividing it with $5$. We can also place the given data in the formula to get the answer directly.

Complete step-by-step answer:
We know that if n number of observations or points are given and we need to determine the average of them then the formula will be.
Let’s assume ${{x}_{1}},{{x}_{2}},{{x}_{3}},....,{{x}_{n}}$ are the n given observations or points and \[{{x}_{avg}}\] be the average value of those points then ${{x}_{avg}}=\dfrac{1}{n}\left[ {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+....+{{x}_{n}} \right]$.
For our given problem $5$ such points have been given in form rainfall in five years.
They are $900$ mm, $650$ mm, $450$ mm, $733$ mm, $400$ mm.
Now, we name those points for the formula.
So, ${{x}_{1}}=900,{{x}_{2}}=650,{{x}_{3}}=450,{{x}_{4}}=733,{{x}_{5}}=400$.
In this problem $n=5$.
We need to find average value = \[{{x}_{avg}}\].
Putting in the formula we get
${{x}_{avg}}=\dfrac{1}{n}\left[ {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+....+{{x}_{n}} \right]=\dfrac{1}{5}\left[ 900+650+450+733+400 \right]$
Solving the problem, we get
${{x}_{avg}}=\dfrac{1}{5}\left[ 900+650+450+733+400 \right]=\dfrac{3133}{5}=626.6$ mm.
So, the average rainfall in Vidarbha in those five years is $626.6$ mm.

Note: We have used the formula of average to find out the solution of the problem. We can also use the normal method of addition and division to get the solution. Although the calculation and method are similar to the process we already used, the only difference is that we don’t have to use the formula.
So, we will first find the total rainfall of those five years which is $\left[ 900+650+450+733+400 \right]$ mm, equal to $3133$ mm.
Then we will find average rainfall by dividing the total rainfall with $5$.
So, average rainfall will be $\dfrac{3133}{5}=626.6$ mm.