Question

The average of $11,12,13,14$ and $x$ is $13$. The value of $x$ is
A. $17$
B. $21$
C. $15$
D. $20$

Answer 1

Hint: According to the question given in the question we have to determine the value of $x$ when the average of $11,12,13,14$ and $x$ is $13$. So, first of all we have to understand about the average which is as explained below:
Average: Average is the result that we get when we add two or more than two numbers together and then divide the total by the number of that numbers we added together basically to determine the average we just have to find the sum of all the given numbers and then we have to count the numbers that we have already added so that we can divided the added number with the total numbers we counted.
Now, we have to add all the given numbers which are $11,12,13,14$ and $x$ to obtain the sum of all those given numbers.
Now, we count the numbers $11,12,13,14$ and $x$.
So, now we can obtain the average by dividing the sum of given numbers to the total numbers for which we found the sum.

Complete step-by-step solution:
Step 1: First of all we have to determine the sum of all the given numbers to determine the average for them which are $11,12,13,14$ and $x$. Hence,
\[
   = 11 + 12 + 13 + 14 + x \\
   = 50 + x
 \]
Step 2: Now, we have to determine the total numbers which we have added to obtain the average of the given numbers as mentioned in the solution hint. Hence,
$ \Rightarrow $$11,12,13,14$ and $x$.
So, there are a total of 5 numbers.
Step 3: Now, as we have already obtained the sum of all the given numbers and the total number so we have to determine the average we have to divide the sum of given numbers to the total numbers for which we found the sum. Hence,
$ \Rightarrow $Average$ = \dfrac{{11 + 12 + 13 + 14 + x}}{5}$……………..(1)
Step 4: Now, as mentioned in the question that the average of all the given numbers is 13. So, to determine the value of x we have to use the expression (1) and place the average in the expression. Hence,
$
   \Rightarrow \dfrac{{50 + x}}{5} = 13 \\
   \Rightarrow 50 + x = 65 \\
   \Rightarrow x = 65 - 50 \\
   \Rightarrow x = 15
 $
Hence, we have obtained the value of $x = 15$ with the help of the average of the given numbers.
Therefore option (C) is correct.

Note: It is not possible to determine the average of a single number and to determine the average we need a minimum two numbers.
To determine the average we just have to find the sum of all the given numbers and then we have to count the numbers that we have already added so that we can divide the added number with the total numbers we counted.