Suppose a class has 7 students. The average mark 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 wort case, the number of student can fail is _______.

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Detailed Solution

$\begin{array}{l} V a r i a n c e = \frac{\sum_{i = 1}^{7} {|x_{i} - 62|}^{2}}{7} = 20 \\ \Rightarrow {|x_{1} - 62|}^{2} + {|x_{2} - 62|}^{2} + \dots . + {|x_{7} - 62|}^{2} = 140 \end{array}$

If $x_{1} = 49$

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

then,

${|x_{2} - 62|}^{2} + \dots . + {|x_{7} - 62|}^{2} =$ Negative Number which is not possible, therefore, no student can fail.

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