JEE MAIN - Mathematics (2022 - 28th June Evening Shift - No. 21)
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 _________.
Answer
0
Explanation
According to given data
$${{\sum\limits_{i = 1}^7 {{{({x_i} - 62)}^2}} } \over 7} = 20$$
$$ \Rightarrow \sum\limits_{i = 1}^7 {{{({x_i} - 62)}^2} = 140} $$
So for any xi, $${({x_i} - 62)^2} \le 140$$
$$ \Rightarrow {x_i} > 50\,\forall i = 1,2,3,\,\,.....\,\,7$$
So no student is going to score less than 50.
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