JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Statistics

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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

Answer: 0

Solution

Variance is

\frac{\sum _{i = 1}^{7} ( x _{i} - 62 ) ^{2}}{7} = 20

, so

\sum_{i = 1}^{7} (x_{i} - 62)^{2} = 140

. If one student scores 49 (just failing), then

(49 - 62)^{2} = 169 > 140

, which exceeds the total sum of squared deviations. This is impossible. Therefore, no student can score below 50, and in the worst case, 0 students fail.

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Integer answer

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