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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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statistical approach | Comment 1 of 10
I've taken a statistical approach to this problem that may be more sophisticated than was intended for a D2 problem.

First, plot the data points based on (day of month,weight)
Second, connect each point with a straight line.

Now we are missing data points for the first and last day of April (days 1 and 30).  To get this I take his average weight loss as
(97.6kg-102.6kg)/(28-3)=0.2 kg/day
I then use this to project back and forward in time respectively from the first and last measurements to get his projected weights on the first and last days
namely
day 1, 103kg
day 30, 97.2kg

Now that I have these points added.  I now use the calculus definition for average value of a function over an interval which is simply the area under the curve divided by the length of the interval.

So calculating the area under each line segment, adding them up, I get a total area of 2887.55
dividing this by 30 I get
96.3 kg

So I estimate his average weight during the month of April as being 96.3 kg.

I'm curious to see what other methods get for the average

  Posted by Daniel on 2015-06-15 12:51:38
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