What is the arithmetic mean of 16 natural numbers ?

Options

A. A) 17/2
B. B) 33/2
C. C) 11
D. D) 187/2

Answer

To find the arithmetic mean of 16 natural numbers, we can follow these steps:

### Step 1: Understand the Definition of Natural Numbers
Natural numbers are the set of positive integers starting from 1. The first 16 natural numbers are: 1, 2, 3, ..., 16.

### Step 2: Calculate the Sum of the First 16 Natural Numbers
The formula for the sum of the first n natural numbers is given by:
\[ S = \frac{n(n + 1)}{2} \]
For our case, \( n = 16 \):
\[ S = \frac{16(16 + 1)}{2} = \frac{16 \times 17}{2} \]

### Step 3: Simplify the Sum
Now, we can simplify the expression:
\[ S = \frac{16 \times 17}{2} = \frac{272}{2} = 136 \]

### Step 4: Calculate the Arithmetic Mean
The arithmetic mean (AM) is calculated using the formula:
\[ AM = \frac{\text{Sum of the numbers}}{\text{Total number of observations}} \]
In this case, the total number of observations is 16:
\[ AM = \frac{136}{16} \]

### Step 5: Simplify the Arithmetic Mean
Now, we simplify \( \frac{136}{16} \):
\[ AM = \frac{136 \div 8}{16 \div 8} = \frac{17}{2} \]

### Final Answer
Thus, the arithmetic mean of the first 16 natural numbers is:
\[ \frac{17}{2} \]