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 mar

Question

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

TestHub · Accepted Answer

Applying the formula of variance we get,

$20 = \frac{\sum_{i = 1}^{7} {|x_{i} - 62|}^{2}}{7}$

$\Rightarrow {|x_{1} - 62|}^{2} + {|x_{2} - 62|}^{2} + \dots . + {|x_{7} - 62|}^{2} = 140$

If $x_{1} = 49$ (taking the least possibility)

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

then,

${|x_{2} - 62|}^{2} + \dots . + {|x_{7} - 62|}^{2} = 140 - 169 = - 29$ Negative Number which is not possible, therefore, no student can fail.

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