Question
Download Solution PDFIf the mean and the standard deviation of n observations x1, x2, _ _ _ _ _, xn be x̅ and σ respectively, then the mean and standard deviation of -x1, -x2, -x3, _ _ _ _ _, -xn are, respectively,:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation
Mean of x1, x2, ---------,xn = x̅
⇒ Mean of -x1, -x2 -------- -xn
⇒ Mean of -(x1 + x2 --------xn)/n
⇒ Mean of new observation = - x̅
Standard deviation = √[(∑(xi - x̅)2/N]
(xi - x̅)2 is always positive
∴ Mean and standard deviation is - x̅ and σ
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