This animation demonstrates the central limit theorem for a uniform sampling distribution.
Created
January 23, 2019 22:56
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The Central Limit Theorem
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| <!DOCTYPE html> | |
| <head> | |
| <meta charset="utf-8"> | |
| <script src="https://d3js.org/d3.v4.min.js"></script> | |
| <style> | |
| .ball { fill: #d62728; stroke: #000; stroke-width: 1px; } | |
| .bar rect { fill: #1f77b4; fill-opacity: 0.8; } | |
| .bar text { fill: white; } | |
| .line { fill: #636363; fill-opacity: 0.2; } | |
| .axis path { stroke: #636363; stroke-width: 2px; } | |
| .axis text { fill: #636363; } | |
| </style> | |
| </head> | |
| <body> | |
| <script> | |
| var margin = {top: 20, right: 10, bottom: 20, left: 10}; | |
| var width = 960 - margin.left - margin.right, | |
| height = 500 - margin.top - margin.bottom; | |
| var svg = d3.select("body") | |
| .append("svg") | |
| .attr("width", width + margin.left + margin.right) | |
| .attr("height", height + margin.top + margin.bottom) | |
| .append("g") | |
| .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); | |
| var dt = 1000, // time step | |
| n = 4; // sample size | |
| var f = { | |
| sample: Math.random, | |
| mu: 1/2, | |
| sigma: 1/(2*Math.sqrt(3)) | |
| }; | |
| var pdf = function(x) { return Math.sqrt(n)*Math.exp(-n*(x-f.mu)*(x-f.mu)/(2*f.sigma*f.sigma))/Math.sqrt(2*Math.PI)/f.sigma; }; | |
| var x = d3.scaleLinear() | |
| .domain([0, 1]) | |
| .rangeRound([0, width]); | |
| var y1 = height/3, | |
| y2 = height/2; | |
| var y = d3.scaleLinear() | |
| .domain([0, pdf(f.mu)]) | |
| .range([0, height - y2]); | |
| var histogram = d3.histogram() | |
| .domain(x.domain()) | |
| .thresholds(x.ticks(20)); | |
| var area = d3.area() | |
| .x(function(d) { return x(d[0])}) | |
| .y0(y2) | |
| .y1(function(d) { return y2 + y(d[1])}) | |
| .curve(d3.curveBasis); | |
| svg.append("path").attr("class", "line"); | |
| svg.append("g").attr("class", "bars"); | |
| var counts = []; | |
| var axis = svg.selectAll(".axis") | |
| .data([{y: 0, label: "draw"}, {y: y1, label: "average"}, {y: y2, label: "count"}]) | |
| .enter().append("g") | |
| .attr("class", "axis") | |
| .attr("transform", function(d) { return "translate(0," + d.y + ")"; }); | |
| axis.append("path") | |
| .attr("d", function(d) { return "M0,0H" + width; }) | |
| axis.append("text") | |
| .attr("dominant-baseline", "hanging") | |
| .attr("dy", 5) | |
| .text(function(d) { return d.label; }); | |
| function renderBars() { | |
| var data = histogram(counts) | |
| .map(d => { d.y = counts.length > 0 ? d.length/counts.length : 0; return d; }) | |
| .filter(d => d.x1 > d.x0); | |
| var ymax = d3.max(data, function(d) { return d.y; }); | |
| y.domain([0, ymax / (1/20)]); | |
| var bar = svg.select(".bars").selectAll(".bar").data(data); | |
| var g = bar.enter().append("g") | |
| .attr("class", "bar") | |
| .attr("transform", function(d) { return "translate(" + x(d.x0) + "," + y2 + ")"; }); | |
| g.append("rect") | |
| .attr("width", function(d) { return (x(d.x1) - x(d.x0)) - 2; }); | |
| g.append("text") | |
| .attr("x", x(1/40)) | |
| .attr("dy", 10) | |
| .attr("dominant-baseline", "hanging") | |
| .attr("text-anchor", "middle"); | |
| bar.select("rect").transition().duration(dt/4) | |
| .attr("height", function(d) { return y(d.y / (1/20)); }); | |
| bar.select("text") | |
| .text(function(d) { return d.y > 0 ? d3.format(".0%")(d.y) : ""; }); | |
| svg.select(".line").datum(d3.range(0, 1.05, 0.05).map(function(x) { return [x, pdf(x)]; })) | |
| .transition().duration(dt/4) | |
| .attr("d", area); | |
| } | |
| function renderBalls() { | |
| var data = d3.range(n).map(f.sample); | |
| var mean = d3.mean(data); | |
| var ball = svg.append("g").selectAll(".ball").data(data); | |
| var i = 0; | |
| ball.enter().append("circle") | |
| .attr("class", "ball") | |
| .attr("cx", function(d) { return x(d); }) | |
| .attr("cy", 0) | |
| .attr("r", 5) | |
| .transition().duration(dt).ease(d3.easeBounce) | |
| .attr("cy", y1 - 5) | |
| .on("end", function() { | |
| d3.select(this) | |
| .transition().duration(dt/4) | |
| .attr("cy", (y2 + y1) / 2) | |
| .transition().duration(dt/4) | |
| .attr("cx", x(mean)) | |
| .transition().duration(dt/4).ease(d3.easeBounce) | |
| .attr("cy", y2 - 3) | |
| .attr("r", 3) | |
| .each(function() { ++i; }) | |
| .on("end", function() { | |
| if (!--i) { | |
| counts.push(mean); | |
| } else { | |
| d3.select(this).remove(); | |
| }; | |
| }); | |
| }); | |
| } | |
| function renderAll() { | |
| renderBars(); | |
| renderBalls(); | |
| } | |
| d3.interval(renderAll, dt); | |
| </script> | |
| </body> |
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