Deming's funnel: Difference between revisions
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=={{header|Mathematica}}==
<lang Mathematica>
dxs = {-0.533, 0.27, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275,
1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.15, 0.001, -0.382,
0.161, 0.915, 2.08, -2.337, 0.034, -0.126, 0.014, 0.709,
0.129, -1.093, -0.483, -1.193, 0.02, -0.051, 0.047, -0.095, 0.695,
0.34, -0.182, 0.287, 0.213, -0.423, -0.021, -0.134, 1.798,
0.021, -1.099, -0.361, 1.636, -1.134, 1.315, 0.201, 0.034,
0.097, -0.17, 0.054, -0.553, -0.024, -0.181, -0.7, -0.361, -0.789,
0.279, -0.174, -0.009, -0.323, -0.658, 0.348, -0.528, 0.881,
0.021, -0.853, 0.157, 0.648, 1.774, -1.043, 0.051, 0.021,
0.247, -0.31, 0.171, 0., 0.106, 0.024, -0.386, 0.962,
0.765, -0.125, -0.289, 0.521, 0.017,
0.281, -0.749, -0.149, -2.436, -0.909, 0.394, -0.113, -0.598,
0.443, -0.521, -0.799, 0.087};
dys = {0.136, 0.717, 0.459, -0.225, 1.392, 0.385, 0.121, -0.395,
0.49, -0.682, -0.065, 0.242, -0.288, 0.658, 0.459, 0., 0.426,
0.205, -0.765, -2.188, -0.742, -0.01, 0.089, 0.208, 0.585,
0.633, -0.444, -0.351, -1.087, 0.199, 0.701, 0.096, -0.025, -0.868,
1.051, 0.157, 0.216, 0.162, 0.249, -0.007, 0.009, 0.508, -0.79,
0.723, 0.881, -0.508, 0.393, -0.226, 0.71, 0.038, -0.217, 0.831,
0.48, 0.407, 0.447, -0.295, 1.126, 0.38, 0.549, -0.445, -0.046,
0.428, -0.074, 0.217, -0.822, 0.491, 1.347, -0.141, 1.23, -0.044,
0.079, 0.219, 0.698, 0.275, 0.056, 0.031, 0.421, 0.064, 0.721,
0.104, -0.729, 0.65, -1.103, 0.154, -1.72, 0.051, -0.385, 0.477,
1.537, -0.901, 0.939, -0.411, 0.341, -0.411, 0.106,
0.224, -0.947, -1.424, -0.542, -1.032};
(*Mathematica's StandardDeviation function computes the unbiased standard deviation. The solutions seem to be using the biased standard deviation, so I'll create a custom function for that.*)
BiasedStandardDeviation[data_] :=
With[
{mean = Mean@data},
Sqrt[Total[(# - mean)^2 & /@ data]/Length[data]]
]
(*Mathematica's FoldPair functionality will work well with this if we provide a properly defined function to fold with.*)
DemingRule[1][funnelPosition_, diff_] := {funnelPosition + diff, 0};
DemingRule[2][funnelPosition_, diff_] := {funnelPosition + diff, -diff};
DemingRule[3][funnelPosition_, diff_] := {funnelPosition + diff, -funnelPosition - diff};
DemingRule[4][funnelPosition_, diff_] := {funnelPosition + diff, funnelPosition + diff};
(*The core implementation.*)
MarblePositions[rule_][diffs_] := FoldPairList[DemingRule[rule], 0, diffs];
(*This is to help format the output.*)
Results[rule_, diffData_] :=
With[
{positions = MarblePositions[rule][diffData]},
StringForm["Rule `1`\nmean: `2`\nstd dev: `3`", rule,
Mean[positions], BiasedStandardDeviation[positions]]
];
TableForm[Results[#, Transpose[{dxs, dys}]] & /@ Range[4], TableSpacing -> 5]
</lang>
{{out}}
<pre>
Rule 1
mean: {0.0004,0.07023}
std dev: {0.715271,0.646206}
Rule 2
mean: {0.00087,-0.01032}
std dev: {1.03714,0.899948}
Rule 3
mean: {0.04386,-0.0063}
std dev: {7.98712,4.77842}
Rule 4
mean: {3.13412,5.42102}
std dev: {1.58739,3.93036}
</pre>
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