Suppose a class has 7 students. average marks of these students in mathematics examination is 62 , a

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Suppose a class has $7$ students. The average marks of these students in the mathematics examination is $62$, and their variance is $20$ . A student fails in the examination if $he/she$ gets less than $50$ marks, then in worst case, the number of students can fail is

A

$5$

B

$3$

C

$4$

D

$0$

(JEE MAIN-2022)

Solution

$20=\frac{\sum\limits_{ i =1}^{7}\left| x _{ i }-62\right|^{2}}{7}$

$\Rightarrow\left| x _{1}-62\right|^{2}+\left| x _{2}-62\right|^{2}+\ldots .+\left| x _{7}-62\right|^{2}=140$

$If$ $x _{1}=49$

$|49-62|^{2}=169$

then, $\left| x _{2}-62\right|^{2}+\ldots .+\left| x _{7}-62\right|^{2}=$ Negative Number which is not possible, therefore, no student can fail.

Standard 11

Mathematics

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