QJEEM20Maaa93: JEE Main 2020 Mathematics - Class 11 JEEM20Maaa93 Solution: Let x i (1 i 10) be ten observations of a random variable X. If …

Question

Verified Solution • 2025–26 Session moderate

Let x_i (1

\le

i

\le

10) be ten observations of a random variable X. If

\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3

and

\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - p} \right)}^2}} = 9

where 0

\ne

p

\in

R, then the standard deviation of these observations is :

Accepted Answer

Standard deviation =

\sqrt {Variance}

= \sqrt {{{\sum {x_1^2} } \over n} - {{(\overline x )}^2}}

= \sqrt {{{\sum\limits_{i = 1}^{10} {{{({x_i} - p)}^2}} } \over {10}} - {{\left( {{{\sum\limits_{i = 1}^{10} {({x_i} - p)} } \over {10}}} \right)}^2}}

[ Standard deviation is free from shifting of origin.]

= \sqrt {{9 \over {10}} - {{\left( {{3 \over {10}}} \right)}^2}}

= \sqrt {{9 \over {10}} - {9 \over {100}}}

= \sqrt {{{90 - 9} \over {100}}}

= \sqrt {{{81} \over {100}}}

= {9 \over {10}}

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