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JEE Main20236 Apr 2023Morning ShiftMathematicsStatisticsActual

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and σ 2 respectively. If the variance of all the 30 numbers in the two sets is 13 , then σ 2 is equal to

Options

  1. A10
  2. B11
  3. C9
  4. D12

Correct answer

A. 10

Step-by-step solution

Given that, For set 1 : Mean = 12 and Variance = 14 For set 2 : Mean = 14 and Variance = σ 2 Now, For set 1 we have, ⇒ ∑ i = 1 i = 15 x i 15 = 12 ⇒ ∑ i = 1 i = 15 x i = 15 × 12 Also, ∑ i = 1 i = 15 x i 2 15 - ∑ i = 1 i = 15 x i 15 2 = 14 ⇒ ∑ i = 1 i = 15 x i 2 15 - 12 2 = 14 ⇒ ∑ i = 1 i = 15 x i 2 = 14 + 144 × 15 Now for set 2 : ⇒ ∑ i = 1 i = 15 y i 15 = 14 and ⇒ ∑ i = 1 i = 15 y i = 15 × 14 Also, ∑ i = 1 i

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