Question

The mean of $x,x+3,x+6,x+9$ and $x+12$ is
A. $x+6$
B. $x+3$
C. $x+9$
D. $x+12$

Answer 1

Hint: We can define the Mean as the ratio of the total sum of the observations to the total number of observations. Here we will take the given values as the observations and calculate the sum of the observations by adding them. Now we will calculate the total number of given values. Then we will find the ratio between them and declare the result as the mean of the given values.

Complete step-by-step answer:
Given,
Numbers are $x$, $x+3$, $x+6$, $x+9$, $x+12$
The number of variables is $5$, hence $n=5$
The sum of the variables is given by
$s=x+\left( x+3 \right)+\left( x+6 \right)+\left( x+9 \right)+\left( x+12 \right)$
We know that when we multiply a positive sign/integer with a positive sign/integer then we will get the result as a positive integer/sign. Hence, we will get
$\Rightarrow s=x+x+3+x+6+x+9+x+12$
Rearranging the above equation by writing all the variables at one place and numbers at one place, then we have
$\begin{align}
  & s=x+x+x+x+x+3+6+9+12 \\
 &\Rightarrow s=5x+30 \\
\end{align}$
Taking $5$ common from the above equation, then we will get
$\begin{align}
  & s=5\left( \dfrac{5x}{5}+\dfrac{30}{5} \right) \\
 &\Rightarrow s=5\left( x+6 \right) \\
\end{align}$
For finding the value of mean we have to divide the total number of variables$\left( n \right)$ with the total sum of the variables$\left( s \right)$, Mathematically
$\text{Mean}=\dfrac{\text{Sum of variables}\left( s \right)}{\text{Number of variables}\left( n \right)}$
Substituting the values of $s=5\left( x+6 \right)$ and $n=5$ in the above equation to get the value of mean, hence
$\begin{align}
  &\Rightarrow \text{Mean}=\dfrac{s}{n} \\
 &\Rightarrow \text{Mean}=\dfrac{5\left( x+6 \right)}{5} \\
 &\Rightarrow \text{Mean}=x+6 \\
\end{align}$
Hence the value of the mean of the variables $x,x+3,x+6,x+9,x+12$ is $x+6$.

Note: Students sometimes forget the process of finding the Mean but they remember the answer as $x+6$. Then they will find the mid-term as $x+6$ and they conclude the answer as $x+6$ by saying it at the mid position. So, it is recommended that students understand the difference between Mean and Median. When you write the mid-term of the ascending or descending arrangement it is called Median not Mean.