In a set of 2 n observations, half of them are equal to ' a ' and the remaining hall are equal to ' -a^ '. If the standard deviation of all the observations is 2 ; then the value of |a| is :

Correct answer: A. 2 Clearly mean A=0 Now, standard deviation σ= (x-A)^2 2 n aligned 2=& ((a-0)^2+(a-0)^2+ +(0-a)^2+ . .)/(2 n) &= (a^2 · 2 n)/(2 n) =|a| aligned Hence, |a|=2

JEE Main 201325 AprilOnline

Exam: JEE Main
Year: 2013
Date: 25 April
Mode: Online
Subject: Mathematics
Chapter: Statistics

JEE Main 2013 · 25 April · Online · Mathematics · Statistics

In a set of 2 n observations, half of them are equal to ' a ' and...

In a set of

2 n

observations, half of them are equal to '

\mathrm{a}

' and the remaining hall are equal to '

-\mathrm{a}^{\prime}

'. If the standard deviation of all the observations is 2 ; then the value of

|a|

is :

Options

A2
B $\sqrt{2}$
C4
D $2 \sqrt{2}$

Correct answer

A. 2

Step-by-step solution

Clearly mean

\mathrm{A}=0

Now, standard deviation

\sigma=\sqrt{\frac{\Sigma(x-\mathrm{A})^2}{2 n}}

\begin{aligned}2=& \sqrt{\frac{(a-0)^2+(a-0)^2+\ldots \ldots+(0-a)^2+\ldots . .}{2 n}}\\ &=\sqrt{\frac{a^2 \cdot 2 n}{2 n}}=|a| \end{aligned}

Hence,

|a|=2

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