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.
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....
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Posted by Charlie
on 2015-06-16 08:59:42 |
Using calculator app and Excel
