Statistics And Probability Question 448
Question: In a series of 2n observations, half of them equal to a and remaining half equal to ?a. If the standard deviation of the observations is 2, then |a| equals
[AIEEE 2004]
Options:
A) $ \frac{\sqrt{2}}{n} $
B) $ \sqrt{2} $
C) 2
D) $ \frac{1}{n} $
Show Answer
Answer:
Correct Answer: C
Solution:
Let a, a, ……..n times and ? a, ? a, ? a, ? a, ……..n times i.e., mean = 0 and S.D. $ =\sqrt{\frac{n{{(a-0)}^{2}}+n{{(-a-0)}^{2}}}{2n}} $ $ 2=\sqrt{\frac{na^{2}+na^{2}}{2n}}=\sqrt{a^{2}}=\pm a $ . Hence $ |a|\ =2 $ .
BETA
