Sum of 100 observations and sum of their squares are 400 and 2475 , respectively. Later on, three ob

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Gujarati

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13.Statistics

hard

The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3, 4$ and $5$, were found to be incorrect . If the incorrect observations are omitted, then the variance of the remaining observations is

A

$8.25$

B

$8.50$

C

$8$

D

$9$

(JEE MAIN-2017)

Solution

$\sum\limits_{i = 1}^{100} {{x_i}} = 400$ $\sum\limits_{i = 1}^{100} {x_i^2} = 2475$

Variance

${\sigma ^2} = \frac{{\sum {x_i^2} }}{N} – {\left( {\frac{{\sum {{x_i}} }}{N}} \right)^2}$

$ = \frac{{2475}}{{97}} – {\left( {\frac{{388}}{{97}}} \right)^2}$

$ = \frac{{2425 – 1552}}{{97}} = \frac{{873}}{{97}} = 9$

Standard 11

Mathematics

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