In a series of 2n observations half of them equals a and remaining half equals -a . If standard devi

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13.Statistics

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In a series of $2n$ observations half of them equals $a$ and remaining half equals $-a$. If the standard deviation of observations is $2$ then $\left| a \right|$ equals

A

$2$

B

$\sqrt 2$

C

$\frac{1}{n}$

D

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

Solution

mean $\bar{x}=0$

$\mathrm{x}_{1}=\mathrm{x}_{2}=\ldots=\mathrm{x}_{\mathrm{n}}=\mathrm{a}$

$x_{\mathrm{n}+1}=\mathrm{x}_{\mathrm{n}+2}=\ldots=\mathrm{x}_{2 \mathrm{n}}=-\mathrm{a}$

$2=\mathrm{S.D}=\sqrt{\frac{2 \mathrm{x}^{2}}{2 \mathrm{n}}-\overline{\mathrm{x}}^{2}}=\sqrt{\frac{2 \mathrm{na}^{2}}{2 \mathrm{n}}}=|\mathrm{a}|$

Standard 11

Mathematics

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