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Coefficient of Variation

In a series o...

Question

In a series of $2 n$ observations, half of them equal $a$ and remaining half equal $- a$ . If the standard deviation of the observations is $2$ , then $| a |$ equals:

\frac{1}{n}

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\sqrt{2}

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2

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\frac{\sqrt{2}}{n}

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Solution

The correct option is C $2$
In the 2n observation , half of them equal to $a$ and remaining half equal to $- a$ . Then the mean of total 2n observation is equal to zero.
$∴ S . D . = \sqrt{\frac{\sum {(x - ¯ x)}^{2}}{N}} \Rightarrow 2 = \sqrt{\frac{\sum x^{2}}{2 n}}$
$\Rightarrow 4 = \frac{\sum x^{2}}{2 n} = \frac{2 n a^{2}}{2 n} \Rightarrow a^{2} = 4 \Rightarrow | a | = 2$

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In a series of 2n observations, half of them equal a and remaining half equal −a. If the standard deviation of the observations is 2, then |a| equals:

The correct option is C 2In the 2n observation , half of them equal to a and remaining half equal to −a. Then the mean of total 2n observation is equal to zero.∴S.D.=√∑(x−¯x)2N⇒2=√∑x22n⇒4=∑x22n=2na22n⇒a2=4⇒|a|=2

In a series of $2 n$ observations, half of them equal $a$ and remaining half equal $- a$ . If the standard deviation of the observations is $2$ , then $| a |$ equals: