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## any rules applied to find assumed mean

how to find assumed mean while solving problems like standard deviation or finding mean by direct method?

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 )

Ok, I'm a little fuzzy about what exactly you're looking for, so I'll give an example that Wikipedia did on their site (I'm good at math, not creative math- I can't just whip up numbers). But I understand assumed mean to be just like this. If this isn't what you're needing, we'll talk it though a little more, and I'll try to find a better way to explain it than wikipedia.

The mean of the following numbers is sought:
219, 223, 226, 228, 231, 234, 235, 236, 240, 241, 244, 247, 249, 255, 262
Suppose we start with a plausible initial guess that the mean is about 240. Then the deviations from this "assumed" mean are the following:
−21, −17, −14, −12, −9, −6, −5, −4, 0, 1, 4, 7, 9, 15, 22
In adding these up, one finds that:
22 and −21 almost cancel, leaving +1,
15 and −17 almost cancel, levaing −2,
9 and −9 cancel,
7 + 4 cancels −6 − 5,
and so on. We are left with a sum of −30. The average of these 15 deviations from the assumed mean is therefore −30/15 = −2. Therefore that is what we need to add to the assumed mean to get the correct mean:
correct mean = 240 − 2 = 238.