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Explain Assumed mean method with an example based question

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Answer 1

Hello !

Assumed mean is used to calculate the actual mean as well as the variance and standard deviation as we'll see..

In statistics the assumed mean is the method for calculating the arithmetic mean and standard deviation of a data set. It simplifies calculating accurate values by hand. Its interest today is chiefly historical but it can be used to quickly estimate these statistics.

[1] There are other rapid calculation methods which are more suited for computers which also ensure more accurate results than the obvious methods

Example

First: 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, leaving −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.

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