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

Arrange the POINTS orange sample points in this histogram so the sample standard deviation is approximately STDDEV.

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: [ KhanUtil.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(); // track whether any points have been moved to prevent answer being submitted too early 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] );
Move the orange dots to experiment with different sample distributions.
$.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();

The standard deviation is smaller if the points are closer to the mean. The standard deviation is larger if the points are more spread out. Try moving a point closer to and further away from the sample mean (\bar{x}) to see how the sample standard deviation (s) is affected.

There are many ways to arrange the points so the sample standard deviation is STDDEV.