Question

how can we take assumed mean in statistics

Answer 1

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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