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 __________.

Answer 1

The correct answer is 0
According to given data
$\frac{\sum_{i=1}^{7}(x_i - 62)^2}{7} = 20$
$\sum_{i=1}^{7} (x_i - 62)^2 = 140$
So for any xi , (xi – 62)2 ≤ 140
⇒ xi > 50 ∀ i = 1, 2, 3, …7
Therefore, no student is going to score less than 50.