What is the mean of n odd natural numbers.
(a)n
(b)`(n+1)/(2)`
(c)`(n(n+1))/(2)`
(d)n+1

Options

A. n
B. `(n+1)/(2)`
C. `(n(n+1))/(2)`
D. n+1

Answer

To find the mean of the first n odd natural numbers, we can follow these steps:

### Step 1: Identify the first n odd natural numbers
The first n odd natural numbers are:
1, 3, 5, 7, ..., (2n - 1)

### Step 2: Calculate the sum of the first n odd natural numbers
The sum of the first n odd natural numbers can be calculated using the formula:
\[ \text{Sum} = n^2 \]
This is a known result, where the sum of the first n odd numbers equals \( n^2 \).

### Step 3: Determine the number of observations
In this case, the number of observations (n) is simply the count of the odd numbers we are considering, which is n.

### Step 4: Calculate the mean
The mean (or average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Substituting the values we have:
\[ \text{Mean} = \frac{n^2}{n} \]

### Step 5: Simplify the expression
Now, simplify the expression:
\[ \text{Mean} = n \]

### Conclusion
Thus, the mean of the first n odd natural numbers is:
**n**

The correct option is (a) n.

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