Question

The mean of first 5 odd natural numbers is
A. 5
B. 10
C. 7
D. $\dfrac{5}{2}$

Answer 1

First of all, we will write the first 5 natural numbers and then, we will find the sum of all the numbers and then dividing that sum by 5 will give us the required answer.

Complete step-by-step solution:
Let us first write the first five odd natural numbers.
The first one is definitely 1 because it is an odd and natural number as well.
Now, the next number will be 3 because 2 is even.
Similarly, the third number is 5 because 4 is even.
Then, the fourth number is 7 (because 6 is even) and the fifth number is 9 (because 8 is even).
Now, we have to sum up all these 5 numbers.
Sum of first 5 odd natural numbers = 1 + 3 + 5 + 7 + 9 = 25
Now, we will use the formula of mean which is given by the following expression:-
$\Rightarrow$ Mean is given by the division of sum of observations by the number of observations.
This can be written as the following expression:-
$\Rightarrow Mean = \dfrac{S}{n}$, where S represents the sum of the observations and n represents the number of observations.
$\Rightarrow Mean = \dfrac{{25}}{5}$
Now, we can write the numerator as following:-
$\Rightarrow Mean = \dfrac{{5 \times 5}}{5}$
Simplifying the calculations on the numerator of the right hand side to get:-
$\Rightarrow$ Mean = 5
$\therefore$ the mean of the first five odd natural numbers is 5.

Hence, the correct option is (A).

Note: The students must commit to the memory the following formula:-
$\Rightarrow$ Mean is given by the division of sum of observations by the number of observations.
$\Rightarrow Mean = \dfrac{S}{n}$, where S represents the sum of the observations and n represents the number of observations.
The students must also know the definitions of Natural Numbers and Odd numbers as well so as they can select the right numbers to evaluate the given.
Natural Numbers are the counting numbers. They start from 1 and keep on increasing with the interval of 1.
Odd numbers are those numbers which do not have 2 as their factor. Example:- 3, 5 and 15 are odd numbers.