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If standard deviation of 3xi – 2 is 8 then variance of (2/3)xi is ________ (a) (144/81)

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If standard deviation of 3xi – 2 is 8 then variance of (2/3)xi is  ________

(a) (144/81)

(b) (81/144)

(c) (16/9)

(d) (4/3)

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1 Answer

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Best answer

The correct option  (a) (144/81)   

Explanation:

Let yi = 3xi – 2

∴ (yi/3) + (2/3) = xi

∴ (2/3)xi = (2yi/9) + (4/9) ......(1)

also S.D. of yi = 6

i.e. Sy = 6 

∴ S.D. of (2/3)xi = 6 × (2/9) = (12/9)

∴ Variance = (SD)2 = (12/9)2 = (144/81). 

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