Sung taee L. answered • 12/02/12

Teach Concepts, Thinking methods, Step by Step (Physics & Math)

Dear Shaik

Let Mr is the real mean, then Mr = ( ∑(i = 1 to n) xi ) / n ----------(1)

and then n(Mr) = ∑(i = 1 to n) xi ------------(1)'

Let Ma is the assumed mean, then (x1 - Ma) + (x2-Ma) + (x3-Ma) + ... + (xn -Ma) = R ----------(2)

If the assumed mean is the same as real mean then R should be zero.

If R is not zero, then assumed mean is not the same as real mean.

The equation (2) can be modified as below.

(x1 + x2 + x3+ .... + xn) - n(Ma) = R ---------------(2)'

From equation (1)' (x1+x2+...+xn) = ∑(i = 1 to n) xi =n(Mr) plug this to equation (2)'

Then n(Mr) - n(Ma) = R -----------------(3)

Divide the equation by n gives Mr = Ma + R/n -------------(4)

This is the relation between the real mean and the assumed mean.

The standard deviation is σ = √( ∑(i = 1 to n) ( xi - Mr)^{2} / n )-------------(5)

If you want to use assumed mean for standard deviation, you can use equation (4) to equation (5)

then σ = √( ∑(i = 1 to n)( xi - Ma - R/n )^{2} / n )

I hope you understand this and this will help you.