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The common solution for these 3 examples is the Harmonic average.
I. 2/(1/100+1/200)=133.33 mph
II. 5*4/(1/4+1/3+1/6+1/4)=20 km
III. 70/(1/188+1/189+1/194+...+1/204+1/205)
We may have an elegant AFL definition
function HarmonicMean(array,n)
{
return n/Sum(1/array,n);
}
or the equivalent
function HarmonicMean(array,n)
{
return 1/MA(1/array,n);
}
The 3 averages are at
http://finance.groups.yahoo.com/group/amibroker-ts/files/3%20means/
where the T/A analysis applications will be added.
Dimitris Tsokakis
--- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS" <TSOKAKIS@xxxx>
wrote:
> Montoya example was rather simple.
> Common sense usually goes to arithmetic average, but it was not
the
> case.
> The average speed follows some different rules than the average
> length or the average weight.
> The solution was 133.33, which, BTW, is 2/(1/100+1/200)
> The next example is more complicated:
>
> Example II
> Johnnie, the well known walker, was walking last Sunday afternoon
for
> 5h.
> The 1st part AB was horizontal and he was moving with 4km/h.
> The 2nd part BC was ascending with 3km/h.
> He was tired and he decided to come back, following the same path.
> The 3rd part CB was, of course, descending with 6km/h.
> The last way to home BA was horizontal like before with 4km/h.
> What was the total lenght ABCBA of the walk ?
> [you dont need more info to find the unique solution]
> The next is closer to reality and we have to set aside any tricks.
>
> Example III
> Michael ran the 70 Bahrein laps with average speed per lap
> v1=188
> v2=189
> v3=194
> ...
> ...
> v69=204
> v70=205
> If all the speeds are well known, what was the average Ferrari
speed ?
> The speed V is an array now and the solution *IS NOT* MA(V,70) as
> the common sense may suppose. We need a different averaging method.
> Dimitris Tsokakis
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
<TSOKAKIS@xxxx>
> wrote:
> > Juan Pablo Montoya in the recent Bahrein trials ran the first lap
> at
> > 100mph and then the 2nd lap at 200mph.
> > What was the average speed ?
> > [the answer is not 150mph and it is not included at
> > http://www.jpmontoya.com/jpmontoya2002/En/index.asp]
> > Dimitris Tsokakis
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