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 On his way to fitness (Posted on 2015-06-15)
Johny, trying to reduce, followed a certain diet
during the month of April.
He recorded his weight daily at 8:00, naked, using the same balance.
Some of his entries are given below:

Apr 3...........102.6 kg
Apr 8...........101.1 kg
Apr 14.........99.4 kg
Apr 18.........98.7 kg
Apr 22.........98.0 kg
Apr 28..........97.6 kg

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Using calculator app and Excel | Comment 9 of 10 |
Using linear interpolation (similar to using trapezoidal rule):

` 1   103.2 2   102.9 3   102.6 4   102.3 5   102.0 6   101.7 7   101.4 8   101.1 9   100.816666666666710   100.533333333333311   100.2512    99.9666666666666713    99.68333333333334 14    99.4 15    99.22516    99.0517    98.87518    98.7 19    98.525           20    98.3521    98.17522    98.0 23    97.9333333333333424    97.8666666666666725    97.826    97.7333333333333527    97.666666666666728    97.6 29    97.5333333333333330    97.46666666666667`

Excel gives 99.61166667 as the average of the numbers.

Perhaps we should give less weight to day 1's figure (pun accidental) as the 24 hours centered on that extrapolated "reading" include 4 hours in March, and more weight to day 30's reading. But at that point, we're in a quandary as to merely give extra weight to the 97.46666... figure, or give a 4/24 weighting to the next extrapolated figure:  97.4.

I think I'll subtract 1/6 of 103.2 and add 1/6 of 97.4, but adjusted by a factor of 1/30:

(97.4 - 103.2) / 6 / 30 ~= -.032222....

The resulting average is 99.57944444....

 Posted by Charlie on 2015-06-16 08:59:42

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