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On his way to fitness (Posted on 2015-06-15) Difficulty: 2 of 5
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

Please provide your estimate of his average April weight.

No Solution Yet Submitted by Ady TZIDON    
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Solution 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   100.8166666666667
10   100.5333333333333
11   100.25
12    99.96666666666667
13    99.68333333333334 
14    99.4 
15    99.225
16    99.05
17    98.875
18    98.7 
19    98.525           
20    98.35
21    98.175
22    98.0 
23    97.93333333333334
24    97.86666666666667
25    97.8
26    97.73333333333335
27    97.6666666666667
28    97.6 
29    97.53333333333333
30    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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