Question

The mean of first ten natural numbers is:

• A. \(4\)
• B. \(4.5\)
• C. \(5\)
• D. \(5.5\)

Hint:

For first \(n\) natural numbers, mean is always: \[ \frac{n+1}{2} \] So for \(n=10\), mean \(= \frac{11}{2} = 5.5\).

Answer 1

The Correct Option is C

Concept: The mean (arithmetic average) of a set of numbers is defined as: \[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \] For natural numbers, we can either add them directly or use the formula for the sum of first \(n\) natural numbers: \[ S_n = \frac{n(n+1)}{2} \]

Step 1: Identify the first ten natural numbers.
The first ten natural numbers are: \[ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10 \] Total number of observations: \[ n = 10 \]

Step 2: Find the sum of the first 10 natural numbers.
Using the formula: \[ S_n = \frac{n(n+1)}{2} \] Substitute \(n=10\): \[ S_{10} = \frac{10(10+1)}{2} \] \[ = \frac{10 \times 11}{2} \] \[ = \frac{110}{2} \] \[ = 55 \]

Step 3: Compute the mean.
\[ \text{Mean} = \frac{55}{10} \] \[ = 5.5 \]

Step 4: Check the options carefully.
Option (1): \[ 4 \] Incorrect. Option (2): \[ 4.5 \] Incorrect. Option (3): \[ 5 \] Incorrect. Option (4): \[ 5.5 \] Correct. Final Conclusion: The mean of the first ten natural numbers is: \[ \boxed{5.5} \] Hence, the correct answer is option (4).