Q. 25.0( 4 Votes )

The algebraic sum

Answer :

Suppose x1, x2, … , xn are n observations with mean as x.


By definition of mean, [i.e. The mean or average of observations, is the sum of the values of all the observations divided by the total number of observations]


We have,


and


nx = x1 + x2 + … + xn …[1]


So, in this case we have assumed mean(a) is equal to mean of the observations(x)


And we know that


di = xi - a


where, di is deviation of a (i.e. assumed mean) from each of xi i.e. observations.


So, In the above case we have


d1 = x1 - x


d2 = x2 - x


.


.


.


dn = xn - x


and sum of deviations


d1 + d2 + … + dn = x1 - x + x2 - x + … + xn - x


= x1 + x2 + … + xn - (x + x + … {upto n times})


= nx - nx [Using 1]


= 0


Hence, sum of deviations is zero.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses