Statistics And Probability Question 219
Question: The variance of the first n natural numbers is
[AMU 1994; SCRA 2001]
Options:
A) $ \frac{n^{2}-1}{12} $
B) $ \frac{n^{2}-1}{6} $
C) $ \frac{n^{2}+1}{6} $
D) $ \frac{n^{2}+1}{12} $
Show Answer
Answer:
Correct Answer: A
Solution:
Variance $ ={{(S\text{.D}\text{.})}^{2}} $ $ =\frac{1}{n}\Sigma x^{2}-{{( \frac{\Sigma x}{n} )}^{2}} $ , $ ( \because \ \ \bar{x}=\frac{\Sigma x}{n} ) $ $ =\frac{n(n+1)\ (2n+1)}{6n}-{{( \frac{n(n+1)}{2n} )}^{2}}=\frac{n^{2}-1}{12} $ .
BETA
