If mean and standard deviation of 5 observations x₁ ,x₂ ,x₃ ,x₄ ,x₅ are 10 and 3 , respect

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13.Statistics

hard

If mean and standard deviation of $5$ observations $x_1 ,x_2 ,x_3 ,x_4 ,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1 ,x_2 ,.....,x_3$ and $-50$ is equal to

$509.5$

$586.5$

$582.5$

$507.5$

(JEE MAIN-2019)

$\sum {x = 50} $

${\left( 3 \right)^2} = \frac{1}{5}\left( {e{x^2} – \frac{{{{\left( {ex} \right)}^2}}}{5}} \right)$

$9 = \frac{1}{5}\left( {\sum {{x^2} – \frac{{2500}}{5}} } \right)$

$\therefore \sum {{x^2} = 545} $

New variable $ = \frac{1}{6}\left( {3045 – \frac{0}{6}} \right) = 507.5$

Standard 11

Mathematics

hard

(JEE MAIN-2018)

hard

(JEE MAIN-2019)

easy

medium

medium

(JEE MAIN-2023)

$X_i$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_i$	$3$	$6$	$16$	$\alpha$	$9$	$5$	$6$