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Step Deviation Method to Calculate R

In a series o...

Question

In a series of $2 n$ observations, half of them equal $a$ and remaining half equation $- a$ . 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 $2$
Mean $= \frac{a + a + \dots . . + a + (a) + (- a) + \dots \dots + (- a)}{2 n}$

$¯ X =$ Mean $= 0$

Number of observations $= 2 n$
$σ =$ Standard Deviation $= \sqrt{\frac{\sum (x - ¯ x)^{2}}{2 n}}$
$2 = \sqrt{\frac{2 n a^{2}}{2 n}}$
$∴ | a | = 2$

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

The correct option is C 2Mean =a+a+…..+a+(a)+(−a)+……+(−a)2n ¯X=Mean =0 Number of observations =2nσ= Standard Deviation =√∑(x−¯x)22n2=√2na22n∴|a|=2

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

The correct option is C $2$
Mean $= \frac{a + a + \dots . . + a + (a) + (- a) + \dots \dots + (- a)}{2 n}$

$¯ X =$ Mean $= 0$

Number of observations $= 2 n$
$σ =$ Standard Deviation $= \sqrt{\frac{\sum (x - ¯ x)^{2}}{2 n}}$
$2 = \sqrt{\frac{2 n a^{2}}{2 n}}$
$∴ | a | = 2$