Question

The mean of the first $$8$$ natural numbers is
A.$$4.5$$
B.$$5$$
C.$$4$$
D.$$5.5$$

Answer 1

Hint: To find the mean of the first $$8$$ natural number, we will first note down the first $$8$$ natural numbers, then we will add all these numbers and get a sum. And then finally to get their mean will divide their summation by the total numbers added, which in this case will be $$8$$ numbers.

Complete step-by-step answer:
The first 8 natural numbers are 1, 2, 3, 4, 5, 6, 7 and 8.
Now, their summation will be given as $$1+2+3+4+5+6+7+8=36$$.
As we want to find the mean of the first 8 natural numbers, we will divide their summation value by the total number of values, which is 8.
Thus, on dividing the summation value by 8 we get, $${\displaystyle \frac{36}{8}}=4.5$$.
Thus, the mean of the first 8 natural numbers will be 4.5.
Hence, option (A) is the correct option.

Note: In the above solution, there is one more way to find the summation rather than adding the values. We can use the formula for the sum of first $$n$$ natural numbers, which is given by $${\displaystyle \frac{n(n+1)}{2}}$$.
For the given question the value of $$n$$ will be equal to 8. So, after substituting the value of $$n$$ in the formula we get,
$$\begin{gathered} {\displaystyle \frac{n(n+1)}{2}} \\ ={\displaystyle \frac{8(8+1)}{2}} \\ ={\displaystyle \frac{8(9)}{2}} \\ =4(9) \\ =36 \end{gathered}$$.
This may take almost the same time as adding individual numbers, however this method of finding the summation can be useful when dealing with larger numbers, where adding each number will be futile.
And then to find the mean we can again divide the summation of numbers that is 36 by 8 and we will get 4.5.