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13.Statistics
hard
In a series of $2n$ observation, half of them are equal to $'a'$ and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals
A
$2$
B
$\sqrt 2 $
C
$4$
D
$2\sqrt 2 $
(JEE MAIN-2013)
Solution
Clerly mean $A=0$
Now, standard deviation $\sigma = \sqrt {\frac{{\sum {{{\left( {x – A} \right)}^2}} }}{{2n}}} $
$2 = \sqrt {\frac{{{{\left( {a – 0} \right)}^2} + {{\left( {a – 0} \right)}^2} + … + {{\left( {0 – a} \right)}^2} + …}}{{2n}}} $
$ = \sqrt {\frac{{{a^2}.2n}}{{2n}}} = \left| a \right|$
Hence, $\left| a \right| = 2$
Standard 11
Mathematics
