Given that  \displaystyle \bar{X} is the mean and  \displaystyle | Filo
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Class 11

Math

Algebra

Statistics

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Given that  is the mean and  is the variance of  observations . Prove that the mean and variance of the observations  are  and  respectively .

Solution: The given   observation are 
 Mean =  
variance =
                   ....(i)
If each observation is multiplied by a and the new observation are  then 


Therefore mean of the observation,  is  
Substituting the values of  and  in (1) we obtain 


Thus the variance of the observation  is 
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