Mean of 5 observations is 4.4 and their variance is 8.24 . If three observations are 1, 2 and 6 , ot

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13.Statistics

medium

The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1, 2$ and $6$, the other two observations are

$4$ and $8$

$4$ and $9$

$5$ and $7$

$5$ and $9$

(b) Let the two unknown items be $x$ and $y$.

Then, mean $ = 4.4 \Rightarrow \frac{{1 + 2 + 6 + x + y}}{5} = 4.4$

==> $x + y = 13$…..$(i)$

and variance $= 8.24$

==> $\frac{{{1^2} + {2^2} + {6^2} + {x^2} + {y^2}}}{5}$ -${({\rm{mean}})^2} = 8.24$

==> $41 + {x^2} + {y^2} = 5\,\{ {(4.4)^2} + 8.24\} $

==> ${x^2} + {y^2} = 97$…..$(ii)$

Solving $(i)$ and $(ii)$ for $x$ and $y$, we get

$x = 9,\,\,y = 4$ or $x = 4,y = 9$.

Standard 11

Mathematics

hard

medium

hard

medium

(JEE MAIN-2021)

medium

${x_i}$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
${f_i}$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$