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Übung: Standardabweichung erkunden

-7 -1 * LOWER_BOUND randRange( 10, 20 ) roundTo( 1, randRange( 7, 20 ) / 10 )

Ordne die POINTS orangefarbenen Punkte in dem Histogramm so an, dass die Standardabweichung ungefähr localeToFixed(STDDEV,1) entspricht.

graph.targetStddev = STDDEV; graph.numPoints = POINTS; init({ range: [ [LOWER_BOUND - 0.3, UPPER_BOUND + 0.3], [-2, 5] ], scale: 35 }); style({ stroke: "#bbb" }); line( [ LOWER_BOUND, -0.2 ], [ UPPER_BOUND, -0.2 ] ); for ( var x = LOWER_BOUND; x <= UPPER_BOUND; x++ ) { line( [ x, -0.4 ], [ x, -0.2 ] ); } style({ strokeWidth: 3.5 }); line( [ 0, -0.4 ], [ 0, -0.2 ] ); label( [ -6, -0.73 ], "\\llap{-}6", "center", {}); label( [ -4, -0.73 ], "\\llap{-}4", "center", {}); label( [ -2, -0.73 ], "\\llap{-}2", "center", {}); label( [ 0, -0.73 ], "0", "center", {}); label( [ 2, -0.73 ], "2", "center", {}); label( [ 4, -0.73 ], "4", "center", {}); label( [ 6, -0.73 ], "6", "center", {}); addMouseLayer(); graph.points = []; for ( var x = 0; x < POINTS; x++ ) { graph.points[x] = addMovablePoint({ coord: [ MatheguruHelper.roundToNearest( 0.5, x * ( 8 / POINTS ) - 4 ), 0 ], constraints: { constrainY: true }, snapX: 0.5 }); } var stddev = stdDev( $.map( graph.points, function( el ) { return el.coord[0]; } ) ); style({ strokeWidth: 2, stroke: GREEN, fill: GREEN }); graph.stddevLeft = path([ [ 0, -1.1 ], [ 0.05, -1.1 ], [ 0, -1 ], [ -0.05, -1.1 ], [ 0, -1.1 ], [ 0, -1.4 ] ]); graph.stddevRight = path([ [ 0, -1.1 ], [ 0.05, -1.1 ], [ 0, -1 ], [ -0.05, -1.1 ], [ 0, -1.1 ], [ 0, -1.4 ] ]); graph.stddevLine = path([ [ 0, -1.4 ], [ 1, -1.4 ] ]); graph.stddevValueLabel = label( [ stddev / 2, -1.3 ], "\\bar{x} \\approx " + roundTo( 1, stddev ), "below", { color: GREEN }); graph.pdf = bogusShape; graph.stddevArea = bogusShape; graph.meanLine = bogusShape; graph.meanValueLabel = bogusShape; updateMeanAndStddev(); graph.moved = false; $.each( graph.points, function( idx, point ) { this.onMove = function( x, y ) { graph.moved = true; return onMovePoint( point, x, y, updateMeanAndStddev ); }; }); onMovePoint( graph.points[0], graph.points[0].coord[0] + 1, graph.points[0].coord[1] );
Verschiebe die orangefarbenen Punkte um verschiedene Stichprobenverteilungen zu untersuchen.
$.map( graph.points, function( el ) { return el.coord[0]; } )
if ( roundTo( 1, stdDev( guess ) ) === STDDEV ) { return true; } else if ( graph.moved ) { return false; } else { return ""; }
$.each( guess, function( i, x ) { onMovePoint( graph.points[i], x, 0 ); }); updateMeanAndStddev();

Die Standardabweichung ist geringer, wenn die Punkte näher am Erwartungswert liegen. Die Standardabweichung ist größer, wenn die Punkte weiter ausgebreitet sind. Versuche einen Punkt näher oder weiter von dem Mittelwert der Stichprobe (\bar{x}) entfernen um zu sehen wie sich die Standardabweichung (\sigma) verhält.

Es gibt viele verschiedene Arten die Punkte so anzuordnen, dass eine Standardabweichung von localeToFixed(STDDEV,1) entsteht.