Question

Find the mean of the first seven natural numbers.

Answer 1

Hint: Here we need to calculate the mean of the first seven natural numbers. So, we will write down the first seven natural numbers at a place. For calculating the mean we need to calculate the sum of the numbers, so we will sum all the numbers which we have written. For mean we also need the number of variables that are participated in the summations. In the problem they have mentioned to take the first seven numbers, so the number of variables is taken as seven. Now we have the number of variables and the sum of the variables. By dividing the sum of the variables with the number of variables, we will get the mean of the given variables.

Formula Used: If ${{a}_{1}},{{a}_{2}},{{a}_{3}},....,{{a}_{n}}$ are the $n$ variables, then the mean of the $n$ variables is given by
$M=\dfrac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+.....+{{a}_{n}}}{n}$.

Complete step by step solution:
Considering the first seven natural numbers. They are $1$, $2$, $3$, $4$, $5$, $6$, $7$. Now the sum of the all the above natural numbers is given by
$1+2+3+4+5+6+7=28$
So, the mean of the first seven natural numbers is given by
$M=\dfrac{1+2+3+4+5+6+7}{7}$
Substituting the value of $1+2+3+4+5+6+7$ as $28$ in the above equation, then we will get
$\Rightarrow M=\dfrac{28}{7}$
Dividing the value $28$ with $7$ we will get $4$, then
$M=4$
Hence the mean of the first seven natural numbers is $4$.

Note: We can also solve the problem without writing the first seven natural numbers. We know that the sum of the $n$ natural numbers is $\dfrac{n\left( n+1 \right)}{2}$. From this the sum of first seven natural numbers are
$\begin{align}
  & S=\dfrac{7\left( 7+1 \right)}{2} \\
 & \Rightarrow S=\dfrac{7\times 8}{2} \\
 & \Rightarrow S=7\times 4 \\
 & \Rightarrow S=28 \\
\end{align}$
We have seven natural numbers, so the mean is
$\begin{align}
  & M=\dfrac{S}{7} \\
 & \Rightarrow M=\dfrac{28}{7} \\
 & \Rightarrow M=4 \\
\end{align}$
From both the methods we got the same answer.