randRange(8, 15) randRange( 5, 10 ) randRange( 2, 20 ) $.map( _.range(COUNT), function() { return round( randGaussian() * sqrt( TGT_VARIANCE ) + TGT_MEAN ); }) sortNumbers(DATA) SORTED_DATA[0] SORTED_DATA[COUNT - 1] COUNT % 2 === 0 ? 0.5 * (SORTED_DATA[COUNT / 2 - 1] + SORTED_DATA[COUNT / 2]) : SORTED_DATA[(COUNT - 1) / 2] COUNT % 4 === 0 ? 0.5 * (SORTED_DATA[COUNT / 4 - 1] + SORTED_DATA[COUNT / 4]) : COUNT % 4 === 1 ? 0.5 * (SORTED_DATA[(COUNT - 1) / 4 - 1] + SORTED_DATA[(COUNT - 1) / 4]) : COUNT % 4 === 2 ? SORTED_DATA[(COUNT - 2) / 4] : SORTED_DATA[(COUNT - 3) / 4] COUNT % 4 === 0 ? 0.5 * (SORTED_DATA[COUNT - COUNT / 4 - 1] + SORTED_DATA[COUNT - COUNT / 4]) : COUNT % 4 === 1 ? 0.5 * (SORTED_DATA[COUNT - (COUNT - 1) / 4 - 1] + SORTED_DATA[COUNT - (COUNT - 1) / 4]) : COUNT % 4 === 2 ? SORTED_DATA[COUNT - 1 - (COUNT - 2) / 4] : SORTED_DATA[COUNT - 1 - (COUNT - 3) / 4] createSorter()

Represent the following data using a box-and-whiskers plot. Exclude the median when computing the quartiles:

- `NUM`

If it helps, you may drag the numbers to put them in a different order. The order isn't checked with your answer. SORTER.init( "sortable" )

init({ range: [[ -0.5, 15.5 ], [ -6, 1.5 ]], scale: [ 30, 30 ] }); addMouseLayer(); line( [ 0, -2 ], [ 15, -2 ] ); for ( tick = 0; tick <= 15; tick += 1 ) { line( [ tick, -1.75 ], [ tick, -2.25 ] ); label( [ tick, -2.25 ], tick, "below" ); } graph.q0 = addMovablePoint({ coord: [ 3.5, 0 ], snapX: 0.5, constraints: { constrainY: true }, normalStyle: { fill: KhanUtil.BLUE, stroke: KhanUtil.BLUE } }); graph.moveQ0 = function(x) { graph.q0.setCoord([x, graph.q0.coord[1]]); graph.q0.updateLineEnds(); if (x >= graph.q1Line.coordA[0]) { graph.moveQ1(x + 0.5); } }; graph.q1top = addMovablePoint({ coord: [ 5.5, 1 ], visible: false }); graph.q1mid = addMovablePoint({ coord: [ 5.5, 0 ], visible: false }); graph.q1bot = addMovablePoint({ coord: [ 5.5, -1 ], visible: false }); graph.moveQ1 = function(x) { graph.q1top.setCoord([x, graph.q1top.coord[1]]); graph.q1mid.setCoord([x, graph.q1mid.coord[1]]); graph.q1bot.setCoord([x, graph.q1bot.coord[1]]); graph.q1top.updateLineEnds(); graph.q1mid.updateLineEnds(); graph.q1bot.updateLineEnds(); if (x <= graph.q0.coord[0]) { graph.moveQ0(x - 0.5); } else if (x >= graph.medianLine.coordA[0]) { graph.moveM(x + 0.5); } }; graph.mtop = addMovablePoint({ coord: [ 7.5, 1 ], visible: false }); graph.mbot = addMovablePoint({ coord: [ 7.5, -1 ], visible: false }); graph.moveM = function(x) { graph.mtop.setCoord([x, graph.mtop.coord[1]]); graph.mbot.setCoord([x, graph.mbot.coord[1]]); graph.mtop.updateLineEnds(); graph.mbot.updateLineEnds(); if (x <= graph.q1Line.coordA[0]) { graph.moveQ1(x - 0.5); } else if (x >= graph.q3Line.coordA[0]) { graph.moveQ3(x + 0.5); } }; graph.q3top = addMovablePoint({ coord: [ 9.5, 1 ], visible: false }); graph.q3mid = addMovablePoint({ coord: [ 9.5, 0 ], visible: false }); graph.q3bot = addMovablePoint({ coord: [ 9.5, -1 ], visible: false }); graph.moveQ3 = function(x) { graph.q3top.setCoord([x, graph.q3top.coord[1]]); graph.q3mid.setCoord([x, graph.q3mid.coord[1]]); graph.q3bot.setCoord([x, graph.q3bot.coord[1]]); graph.q3top.updateLineEnds(); graph.q3mid.updateLineEnds(); graph.q3bot.updateLineEnds(); if (x <= graph.medianLine.coordA[0]) { graph.moveM(x - 0.5); } else if (x >= graph.q4.coord[0]) { graph.moveQ4(x + 0.5); } }; graph.q4 = addMovablePoint({ coord: [ 11.5, 0 ], snapX: 0.5, constraints: { constrainY: true }, normalStyle: { fill: KhanUtil.BLUE, stroke: KhanUtil.BLUE } }); graph.moveQ4 = function(x) { graph.q4.setCoord([x, graph.q4.coord[1]]); graph.q4.updateLineEnds(); if (x <= graph.q3Line.coordA[0]) { graph.moveQ3(x - 0.5); } }; graph.leftLine = addMovableLineSegment({ pointA: graph.q0, pointZ: graph.q1mid, fixed: true }); graph.topLine = addMovableLineSegment({ pointA: graph.q1top, pointZ: graph.q3top, fixed: true }); graph.botLine = addMovableLineSegment({ pointA: graph.q1bot, pointZ: graph.q3bot, fixed: true }); graph.rightLine = addMovableLineSegment({ pointA: graph.q3mid, pointZ: graph.q4, fixed: true }); graph.q1Line = addMovableLineSegment({ pointA: graph.q1bot, pointZ: graph.q1top, snapX: 0.5, constraints: { constrainY: true }, }); graph.medianLine = addMovableLineSegment({ pointA: graph.mbot, pointZ: graph.mtop, snapX: 0.5, constraints: { constrainY: true }, }); graph.q3Line = addMovableLineSegment({ pointA: graph.q3bot, pointZ: graph.q3top, snapX: 0.5, constraints: { constrainY: true }, }); graph.q0.onMove = function(x, y) { if (x < 0 || x > 13) { return false; } graph.moveQ0(x); }; graph.q4.onMove = function(x, y) { if (x < 2 || x > 15) { return false; } graph.moveQ4(x); }; graph.q1Line.onMove = function( dX, dY ) { var newX = this.coordA[0]; var oldX = newX - dX; if (newX < 0.5 || newX > 13.5) { graph.moveQ1(oldX); return; } graph.moveQ1(newX); }; graph.medianLine.onMove = function( dX, dY ) { var newX = this.coordA[0]; var oldX = newX - dX; if (newX < 1 || newX > 14) { graph.moveM(oldX); return; } graph.moveM(newX); }; graph.q3Line.onMove = function( dX, dY ) { var newX = this.coordA[0]; var oldX = newX - dX; if (newX < 1.5 || newX > 14.5) { graph.moveQ3(oldX); return; } graph.moveQ3(newX); };
[ graph.q0.coord[0], graph.q1Line.coordA[0], graph.medianLine.coordA[0], graph.q3Line.coordA[0], graph.q4.coord[0] ]
if ( _.isEqual( guess, [ 3.5, 5.5, 7.5, 9.5, 11.5 ] ) ) { return ""; } return _.isEqual( guess, [abs(MIN), Q1, MEDIAN, Q3, MAX] );
graph.moveQ0(guess[0]); graph.moveQ1(guess[1]); graph.moveM(guess[2]); graph.moveQ3(guess[3]); graph.moveQ4(guess[4]);

Begin by putting the data in order:

`\qquad \large{SORTED_DATA.join( ", " )}`

Plot the sample minimum (smallest number):

`\qquad \large{\color{PINK}{MIN}, SORTED_DATA.slice( 1 ).join( ", " )}`

style({ stroke: PINK, fill: PINK }, function() { circle( [ MIN, -4.5 ], 0.13 ); });

Plot the sample maximum (largest number):

`\qquad \large{SORTED_DATA.slice( 0, -1 ).join( ", " ), \color{PINK}{MAX}}`

style({ stroke: PINK, fill: PINK }, function() { circle( [ MAX, -4.5 ], 0.13 ); });

Plot the median (middle number):

`\qquad \large{SORTED_DATA.slice( 0, (COUNT - 1) / 2 ).join( ", " ), \color{PINK}{MEDIAN}, SORTED_DATA.slice( (COUNT + 1) / 2 ).join( ", " )}`

Since the data has an odd number of elements, we exclude the median from the list when calculating the quartiles.

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ MEDIAN, -5.5 ], [ MEDIAN, -3.5 ] ); });

Plot the median (middle number):

`\qquad \large{SORTED_DATA.slice( 0, COUNT / 2 - 1 ).join( ", " ), \color{PINK}{SORTED_DATA[COUNT / 2 - 1]}, \color{PINK}{SORTED_DATA[COUNT / 2]}, SORTED_DATA.slice( COUNT / 2 + 1 ).join( ", " )}`

The median is the average of the middle numbers, so it's equal to `\dfrac{SORTED_DATA[COUNT / 2 - 1] + SORTED_DATA[COUNT / 2]}{2} = MEDIAN`.

Since the data has an even number of elements, we include the middle elements in the list when calculating the quartiles.

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ MEDIAN, -5.5 ], [ MEDIAN, -3.5 ] ); });

Plot the first quartile (halfway between the smallest number and the middle number):

`\qquad \large{SORTED_DATA.slice( 0, floor(COUNT / 4) ).join( ", " ), \color{PINK}{Q1}, SORTED_DATA.slice( floor(COUNT / 4) + 1 ).join( ", " )}`

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ Q1, -5.5 ], [ Q1, -3.5 ] ); });

Plot the first quartile (halfway between the smallest number and the middle number):

`\qquad \large{SORTED_DATA.slice( 0, floor(COUNT / 4) - 1 ).join( ", " ), \color{PINK}{SORTED_DATA[floor(COUNT / 4) - 1]}, \color{PINK}{SORTED_DATA[floor(COUNT / 4)]}, SORTED_DATA.slice( floor(COUNT / 4) + 1 ).join( ", " )}`

The first quartile is `\dfrac{SORTED_DATA[floor(COUNT / 4) - 1] + SORTED_DATA[floor(COUNT / 4)]}{2} = Q1`.

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ Q1, -5.5 ], [ Q1, -3.5 ] ); });

Plot the third quartile (halfway between the middle number and the largest number):

`\qquad \large{SORTED_DATA.slice( 0, COUNT - 1 - floor(COUNT / 4)).join( ", " ), \color{PINK}{SORTED_DATA[COUNT - 1 - floor(COUNT / 4)]}, SORTED_DATA.slice( COUNT - floor(COUNT / 4) ).join( ", " )}`

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ Q3, -5.5 ], [ Q3, -3.5 ] ); });

Plot the third quartile (halfway between the middle number and the largest number):

`\qquad \large{SORTED_DATA.slice( 0, COUNT - floor(COUNT / 4) - 1).join( ", " ), \color{PINK}{SORTED_DATA[COUNT - floor(COUNT / 4) - 1]}, \color{PINK}{SORTED_DATA[COUNT - floor(COUNT / 4)]}, SORTED_DATA.slice( COUNT - floor(COUNT / 4) + 1 ).join( ", " )}`

The third quartile is `\dfrac{SORTED_DATA[COUNT - floor(COUNT / 4) - 1] + SORTED_DATA[COUNT - floor(COUNT / 4)]}{2} = Q3`.

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ Q3, -5.5 ], [ Q3, -3.5 ] ); });

Your box-and-whisker plot should look like the example below the number line.

style({ stroke: PINK, strokeWidth: 2 }, function() { line( [ MIN, -4.5 ], [ Q1, -4.5 ] ); line( [ Q1, -5.5 ], [ Q3, -5.5 ] ); line( [ Q1, -3.5 ], [ Q3, -3.5 ] ); line( [ Q3, -4.5 ], [ MAX, -4.5 ] ); });