Question

Find the arithmetic mean of the first ten odd natural numbers.

Answer 1

Hint: We will write the first ten odd natural numbers and then add them to find their sum. We will then substitute the values in the formula of arithmetic mean , $\dfrac{{{a_1} + {a_2}... + {a_n}}}{n}$, where $n$ is the number of terms and ${a_1},{a_2},..{a_n}$ are $n$ observations.

Complete step-by-step answer:
We have to find the arithmetic mean of first ten odd natural numbers .
Natural numbers are counting numbers and starts from 1.
Odd numbers are not multiples of 2.
The first ten odd natural numbers are 1,3,5,7,9,11,13,15,17,19.
Arithmetic mean is calculated by adding all the observations by the total number of observations.
Arithmetic mean is given by $\dfrac{{{a_1} + {a_2}... + {a_n}}}{n}$, where $n$ is the number of terms and ${a_1},{a_2},..{a_n}$ are $n$ observations.
Therefore, we will calculate the sum of the first ten odd natural numbers.
$
   \Rightarrow 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \\
   \Rightarrow 100 \\
$
Now, we will divide this by 10 as there are a total 10 numbers.
$\dfrac{{100}}{{10}} = 10$
Hence, the arithmetic mean of first ten odd natural numbers is 10.

Note: Arithmetic mean is also known as average or simply mean. Odd numbers are not divisible by 2. The sum of $n$ odd natural numbers is also given by ${n^2}$