Question

show that sum of deviation of the mean from the observations 25,27,19,23,25,31 is zero

Answer 1

The sum of deviations of all the observations from the mean is always zero.

   $E (x - \bar X )=0$

   Total of observations = 150      Mean =  150/6 = 25

   deviations from the mean of the observations are respectively :
          25 - 25, 25-27, 25 - 19, 25 - 23 ,  25 - 25 , 25 - 31
                 = 0, -2, 6, 2, 0, -6
     Sum of deviations = 0

Answer 2

The sum of deviations of all the observations from the mean is always zero.

  

   Total of observations = 150      Mean =  150/6 = 25

   deviations from the mean of the observations are respectively :

          25 - 25, 25-27, 25 - 19, 25 - 23 ,  25 - 25 , 25 - 31

                 = 0, -2, 6, 2, 0, -6

The sum of deviations is 0