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Q.

Let X1,X2,......,X18  be eighteen observations such that ∑i=118Xi−α=36 and ∑i=118Xi−β2=90 , where α andβ  are distinct real numbers. If the standard deviation .of these observations is 1, then the value of α−β  is ________

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answer is 4.

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Detailed Solution

Given ∑i=118Xi−α=36 , ∑i=118Xi−β2=90 and the standard deviation is 1Varxi−β=∑i=118Xi−β218−∑i=118Xi−β1821=9018−2+α−β22+α−β=±2α−β=4
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