JEE Main2016MathematicsStatisticsActual

If the standard deviation of the numbers 2 , 3 , a and 11 is 3 . 5 , then which of the following is true ?

Options

A3 a 2 - 34 a + 91 = 0.
B3 a 2 - 23 a + 44 = 0.
C3 a 2 - 26 a + 55 = 0.
D3 a 2 - 32 a + 84 = 0.

Correct answer

D. 3 a 2 - 32 a + 84 = 0.

Step-by-step solution

x x 2 2 4 3 9 a a 2 11 121 Sum → 16 + a Sum → 134 + a 2 σ = ∑ x 2 4 - ∑ x i 4 2 134 + a 2 4 - 16 + a 4 2 = 35 10 1 2 134 + a 2 - 16 + a 2 4 = 7 2 536 + 4 a 2 - 256 - a 2 - 32 a =14 ⇒ 280 + 3 a 2 - 32 a = 196 ⇒ 3 a 2 - 32 a + 84 = 0.

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