Question

Standard deviation of first \( n \) odd natural numbers is:

• A. \( \sqrt{n} \)
• B. \( \sqrt{\frac{(n+2)(n+1)}{3}} \)
• C. \( \sqrt{\frac{n^2 - 1}{3}} \)
• D. \( n \)
• E. \( 2n \)

Hint:

The variance of an Arithmetic Progression with common difference \( d \) is \( \sigma^2 = \frac{(n^2-1)d^2}{12} \). For odd numbers, \( d=2 \). Thus, \( \sigma^2 = \frac{(n^2-1)4}{12} = \frac{n^2-1}{3} \).

Answer 1

The Correct Option is C