Q. 25.0( 1 Vote )

# What is the algeb

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.

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