Question

The mean of first 15 positive whole numbers is
A. 150
B. 120
C. 7
D. 125

Answer 1

In this question, we have to find the mean of the first 15 whole numbers. Whole numbers are all non-negative integers which start from 0. Now, the mean of the first 15 numbers will be the mean of numbers from 0 to 14, as the count of numbers from 0 to 14 is 15. Here we get the value of n and by using formula for calculating Sum of first n positive whole numbers, we will calculate the mean of first 15 positive whole numbers as discussed below.

Formula used: ${\text{Mean = }}\dfrac{{{\text{Sum of numbers}}}}{{{\text{Count of numbers}}}}$

Complete step-by-step answer:
Sum of first n positive whole numbers = $\dfrac{{n\left( {n + 1} \right)}}{2}$
As we know mean of the number is equal to the sum of the numbers divided by the count of the number that is
${\text{Mean = }}\dfrac{{{\text{Sum of numbers}}}}{{{\text{Count of numbers}}}}$
To find the mean of the first 15 whole numbers. First, we need to calculate the sum of numbers from 0 to 14 as 0-14 are the first 15 whole numbers.
Here, the first number is 0, so we are left with 1 to 14 (positive whole numbers).
So, we conclude that n=14 for calculating Sum of first n positive whole numbers.
We use a formula for calculating Sum of first n positive whole numbers as shown below.
Sum of first n positive whole numbers = $\dfrac{{n\left( {n + 1} \right)}}{2}$
= $\dfrac{{14\left( {14 + 1} \right)}}{2}$
= $\dfrac{{14\left( {15} \right)}}{2}$
= 105
Now, as we know,
${\text{Mean = }}\dfrac{{{\text{Sum of numbers}}}}{{{\text{Count of numbers}}}}$
As we know for calculating mean we have to count all numbers. So, here we also include 0.
Thus, Count of numbers = 15
Put the value of Sum of first n positive whole numbers in above formula and we will get-
${\text{Mean = }}\dfrac{{105}}{{15}}$
Mean = $7$

Therefore, option (C) is the correct answer.

Note: Whenever we face such types of problems the key point that we need to recall is that Mean or Arithmetic mean is the average of given numbers. It is found by calculating the sum of the given numbers and dividing it by how many numbers there are. These types of questions are totally based only on this definition and can be easily solved using this.