Statistics And Probability Question 223
Question: In a series of 2n observation half of them equal a and remaining half equal $ -,a $ if the standard deviation of the observations is 2, then $ | a | $ equals
Options:
A) $ \frac{1}{n} $
B) $ \sqrt{2} $
C) 2
D) $ \frac{\sqrt{2}}{n} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] In the 2n observations, half of them equal to a and the remaining half equal to ? a. then the mean of total 2n observations is equal to zero. Therefore, $ S.D.=\sqrt{\frac{\Sigma ,{{(x-x)}^{2}}}{N}} $ $ 2=\sqrt{\frac{\Sigma x^{2}}{2n}} $
$ \Rightarrow 4=\frac{\Sigma x^{2}}{2n} $
$ \Rightarrow 4=\frac{2a^{2}}{2n} $
$ \Rightarrow a^{2}=4 $
$ \Rightarrow | a |=2 $
BETA
