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JEE Main202331 Jan 2023Morning ShiftMathematicsStatisticsActual

If the variance of the frequency distribution x i 2 3 4 5 6 7 8 Frequency f i 3 6 16 α 9 5 6 is 3 , then α is equal to

Correct answer

0

Step-by-step solution

We have, x i f i d i = x i - 5 f i d i 2 f i d i 2 3 - 3 27 - 9 3 6 - 2 24 - 12 4 16 - 1 16 - 16 5 α 0 0 0 6 9 1 9 9 7 5 2 20 10 8 6 3 54 18 σ x 2 = σ d 2 = ∑ f i d i 2 ∑ f i - ∑ f i d i ∑ f i 2 ⇒ 3 = 150 45 + α - 0 ⇒ 150 = 135 + 3 α ⇒ 3 α = 15 ⇒ α = 5

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