Deming's funnel: Difference between revisions

[[wp:W. Edwards Deming|W Edwards Deming]] was an American statistician and management guru who used physical demonstrations to illuminate his teachings. In one demonstration Deming repeatedly dropped marbles through a funnel at a target, marking where they landed, and observing the resulting pattern. He applied a sequence of "rules" to try to improve performance. In each case the experiment begins with the funnel positioned directly over the target.

 

* [https://www.youtube.com/watch?v=2VogtYRc9dA Video demonstration] of the funnel experiment at the Mayo Clinic.

 

{{trans|Python}}

 

 

return xs.sum / xs.length;

}

 

immutable m = xs.mean;

return sqrt(xs.map!(x => (x - m) ^^ 2).sum / xs.length);

}

 

 

auto funnel(T)(in T[] dxs, in T[] dys, in TF rule) {

}

 

}

 

immutable rs = funnel(dxs, dys, rule);

label.writeln;

writeln;

}

experiment("Rule 3:", dxs, dys, (z, dz) => -(z + dz));

experiment("Rule 4:", dxs, dys, (z, dz) => z + dz);

{{out}}

<pre>Rule 1:

Mean x, y: 3.1341, 5.4210

Std dev x, y: 1.5874, 3.9304</pre>

 

=={{header|Python}}==

{{trans|Racket}}

 

dxs = [-0.533, 0.27, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275, 1.251,

experiment('Rule 2:', lambda z, dz: -dz)

experiment('Rule 3:', lambda z, dz: -(z+dz))

 

{{output}}

 

'''Alternative''': [Generates pseudo-random data and gives some interpretation.] The funnel experiment is performed in one dimension. The other dimension would act similarly.

from math import sqrt

from pprint import pprint as pp

for rule, comment in rcomments:

printit(rule)

 

{{out}}

=={{header|Racket}}==

The stretch solutions can be obtained by uncommenting radii etc. (delete the 4 semi-colons) to generate fresh data, and scatter-plots can be obtained by deleting the #; .

(require math/distributions math/statistics plot)

 

;(define dys (map (λ (r theta) (* r (sin theta))) radii angles))

 

(set! x (rule x dx))

 

(define (experiment label rule)

(define (p s) (real->decimal-string s 4))

(displayln label)

(printf "Mean x, y : ~a, ~a\n" (p (mean rxs)) (p (mean rys)))

(experiment "Rule 2:" (λ (z dz) (- dz)))

(experiment "Rule 3:" (λ (z dz) (- (+ z dz))))

 

{{output}}

Mean x, y : 3.1341, 5.4210

Std dev x, y: 1.5874, 3.9304

</pre>