QJEEM18Ma2db5: JEE Main 2018 Mathematics - Class 11 JEEM18Ma2db5 Solution: If and , then the standard deviation of the 9 items is

Question

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If

\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9

and

\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45

, then the standard deviation of the 9 items

{x_1},{x_2},.......,{x_9}

is

Accepted Answer

IMPORTANT POINT :-

When every number is added or subtracted by a fixed number then the standard Deviation remain unchanged.

so let

{x_i} - 5 = {y_i}

So, new equation is

\sum\limits_{i = 1}^9 {{y_i}} = 9

and

\sum\limits_{i = 1}^9 {y_i^2} = 45

As, we know. Standard Deviation (S.D)

= \sqrt {{{\sum\limits_{i = 1}^9 {y_i^2} } \over 9} - {{\left( {{{\sum\limits_{i = 1}^9 {yi} } \over 9}} \right)}^2}}

= \sqrt {{{45} \over 9} - {{\left( {{9 \over 9}} \right)}^2}}

= \sqrt {5 - 1}

=

\sqrt 4

=2

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