25:["$","title",null,{"children":"STAT311 | cse412 | Observable"}] 49:T4da,## Overview of the notebook: - [Welcome to the world of normal distribution!](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1801) - [Interactive Dice Visualization](https://observablehq.com/d/d8132e4f55bc1fcc#cell-608) - [Learning Goal](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1785) - [How to Use](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1789) - [Questions](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1791) - [Mean & Standard Deviation Visualization](https://observablehq.com/d/d8132e4f55bc1fcc#cell-495) - [The Impact of Sample Size Visualization](https://observablehq.com/d/d8132e4f55bc1fcc#cell-711) - [Average Heights Across Countries Visualization](https://observablehq.com/d/d8132e4f55bc1fcc#cell-995) - [Conclusion](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1895) - [Reflection](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1900) - [DATASET Description](https://observablehq.com/d/d8132e4f55bc1fcc#cell-817) - [Additional Code](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1112) - [Other Resources](https://observablehq.com/d/d8132e4f55bc1fcc#cell-974) - [Imports](https://observablehq.com/d/d8132e4f55bc1fcc#cell-465) - [Reference](https://observablehq.com/d/d8132e4f55bc1fcc#cell-1067)4a:T1760,p5(p => { let result = new Array(61).fill(0); let dice = []; let probabilities = []; let numDice; let rounds; let lastRolls = []; let sliders = []; let numDiceSlider; let roundsSlider; let autoTossing = false; let autoTossesLeft = 0; let roundSums = []; let tutorial; let playing; let playButton; p.preload = function() { dice[0] = p.loadImage(imageURL1); dice[1] = p.loadImage(imageURL2); dice[2] = p.loadImage(imageURL3); dice[3] = p.loadImage(imageURL4); dice[4] = p.loadImage(imageURL5); dice[5] = p.loadImage(imageURL6); }; p.setup = function() { p.createCanvas(900, 600); let tossButton = p.createButton('Toss'); tossButton.position(700, 500); tossButton.mousePressed(p.toss); tossButton.style('border', 'solid 1.5px rgb(100, 100, 200)'); let resetButton = p.createButton('Clear'); resetButton.position(700, 560); resetButton.mousePressed(p.reset); resetButton.style('border', 'solid 1.5px rgb(100, 100, 200)'); tutorial = p.createVideo(videoURL1); tutorial.position(400, 0); tutorial.size(500, 281); tutorial.style('border', 'solid 2px rgb(100, 100, 200)'); playButton = p.createButton('Tutorial'); playButton.position(700, 300); playButton.mousePressed(p.playVideo); playButton.style('border', 'solid 1.5px rgb(100, 100, 200)'); for(let i = 0; i < 5; i++){ sliders[i] = p.createSlider(0, 1, 0.166, 0.001); sliders[i].position(360+ i * 31, 380); sliders[i].style('width', '100px'); sliders[i].style('transform: scale(' + (1.2) + ') rotate(' + (270) + 'deg);'); } numDiceSlider = p.createSlider(1, 10, 10); numDiceSlider.position(720, 350); numDiceSlider.style('width', '100px'); let numDiceLabel = p.createP('Dices/Round'); numDiceLabel.position(590, 332); roundsSlider = p.createSlider(1, 10, 10); roundsSlider.position(720, 450); roundsSlider.style('width', '100px'); let roundsLabel = p.createP('Num of rounds'); roundsLabel.position(590, 432); let autoButton = p.createButton('Auto'); autoButton.position(700, 530); autoButton.mousePressed(() => { autoTossing = true; autoTossesLeft = 50; }); autoButton.style('border', 'solid 1.5px rgb(100, 100, 200)'); let textBox = p.createInput('Dice Probability'); textBox.position(400, 300); textBox.attribute('readonly', ''); textBox.style('font-size', '12px'); textBox.style('width', '150px'); textBox.style('text-align', 'center'); textBox.style('border', 'solid 1.5px rgb(100, 100, 200)'); }; p.draw = function() { p.background(255); p.image(tutorial, p.width - 200, 0, 200, 150, 0, 0, 200, 150); probabilities = sliders.map(slider => slider.value()); let totalProb = probabilities.reduce((a, b) => a + b, 0); if(totalProb > 1){ probabilities = probabilities.map(prob => prob/totalProb); } probabilities.push(1 - probabilities.reduce((a, b) => a + b, 0)); numDice = numDiceSlider.value(); rounds = roundsSlider.value(); p.displayInfo(); p.displayDiceImages(); p.drawHistogram(); p.drawInitialProbabilities(); if (autoTossing && autoTossesLeft > 0) { p.toss(); autoTossesLeft--; if (autoTossesLeft === 0) { autoTossing = false; } } }; p.playVideo = function() { if (playing) { tutorial.pause(); playButton.html('play'); } else { tutorial.loop(); playButton.html('pause'); } playing = !playing; } p.reset = function() { result.fill(0); lastRolls = []; roundSums = []; }; p.displayInfo = function(){ p.textSize(16); p.fill(0); p.text(numDice, 760, 342); p.text(rounds, 760, 442); } p.drawInitialProbabilities = function() { let binWidth = 31; let binHeight = 100; p.push(); for(let i = 0; i < probabilities.length; i++) { p.fill(100, 100, 200); p.rect(400 + binWidth * i , p.height - 30, binWidth-10, -(binHeight*probabilities[i])); p.image(dice[i],400 + binWidth * i, p.height - 22, 20,20); let prob = Math.round(probabilities[i]*100); p.textSize(12); p.text(prob + '%', 400 + binWidth * i, 470); } p.pop(); }; p.toss = function() { lastRolls = []; roundSums = []; for(let round = 0; round < rounds; round++) { let sum = 0; for(let i = 0; i < numDice; i++) { let roll = p.getRandomFace(probabilities); lastRolls.push(roll); sum += roll; } roundSums.push(sum); result[sum]++; } }; p.getRandomFace = function(probabilities) { let sum = probabilities.reduce((a, b) => a + b, 0); let r = p.random(sum); let total = 0; for(let i = 0; i < probabilities.length; i++) { total += probabilities[i]; if(r < total) return i + 1; } return 6; }; p.drawHistogram = function() { let binWidth = (p.width/2 - 100) / result.length; let minSum = numDice; let maxSum = 6 * numDice; p.push(); p.fill(0); p.line(10,p.height - 20,10,320); p.line(7,327,10,320); p.line(13,327,10,320); p.textSize(8); p.text('Count',13,325); p.pop(); p.push(); for(let i = numDice; i < result.length; i++) { let binColor = p.map(i, minSum, maxSum, 0, 255); p.fill(binColor, 100, 200); p.rect(binWidth * (i-numDice) + 10, p.height - 20, binWidth, -result[i]); } p.pop(); }; p.displayDiceImages = function() { let size = 30; let perRow = numDice; for(let i = 0; i < lastRolls.length; i++) { let x = (i % perRow) * size + 15; let y = Math.floor(i / perRow) * size + 20; p.image(dice[lastRolls[i]-1], x, y, size, size); } for(let i = 0; i < roundSums.length; i++) { let x = perRow * size + 20; let y = i * size + 30; p.fill(0); p.textSize(16); p.text("= " + roundSums[i], x, y+10); } }; }); 4b:T5e7,worlmap = { const svg = d3.create("svg") .style("display", "block") .attr("viewBox", [0, 0, 975, 475]) .attr("transform", "translate(0, 20) scale(1.15)"); // move down, make bigger const defs = svg.append("defs"); defs.append("path") .attr("id", "outline") .attr("d", path(outline)); defs.append("clipPath") .attr("id", "clip") .append("use") .attr("xlink:href", new URL("#outline", location)); const g = svg.append("g") .attr("clip-path", `url(${new URL("#clip", location)})`); g.append("use") .attr("xlink:href", new URL("#outline", location)) .attr("fill", "white"); const countryPaths = g.append("g") .selectAll("path") .data(countries.features.filter(d => d.properties.name !== "Antarctica")) .join("path") .attr("fill", d => color(yearData.get(d.properties.name))) .attr("d", path); countryPaths.append("title") .text(d => `${d.properties.name}\n${yearData.has(d.properties.name) ? yearData.get(d.properties.name) : "N/A"}`); g.append("path") .datum(topojson.mesh(world, world.objects.countries, (a, b) => a !== b)) .attr("fill", "none") .attr("stroke", "black") // Set the border stroke color to black .attr("stroke-linejoin", "round") .attr("stroke-width", 0.5) // Set the border stroke width to a wider value, e.g., 1.5 .attr("d", path); countryPaths.attr("stroke", "black") // Set the country outline stroke color to black .attr("stroke-width", 0.5); return svg.node(); };4c:T1241,# DATASET Description **Dataset Description** **NCD-RisC:** The dataset used in this study contains data on height and body mass index (BMI) of children and adolescents aged 5-19 years, collected from 2181 population-based studies, spanning 1985 to 2019. These studies include measurements of height and weight for about 65 million participants across 200 countries and territories. The data provides insights into the nutritional status and lifelong health advantages or risks for children and adolescents worldwide. For more information about the source and usage of the data, please visit the [NCD-RisC website](https://ncdrisc.org/data-downloads-height.html). **NHANES:** The National Health and Nutrition Examination Survey (NHANES) Body Measures (P_BMX) dataset is a compilation of health and nutrition data collected from 2017 through March 2020. The dataset primarily focuses on monitoring trends in infant and child growth, the prevalence of overweight and obesity in various age groups in the U.S., and the relationships between body weight and health and nutritional status. The dataset includes body measurements such as weight, head circumference, standing height, upper leg length, upper arm length, mid-upper arm circumference, waist circumference, and hip circumference for varying age groups. The NHANES program suspended field operations in March 2020 due to the COVID-19 pandemic, and therefore the 2019–2020 cycle data were combined with the 2017–2018 data to create a nationally representative sample referred to as the NHANES 2017-March 2020 pre-pandemic data. For more information about the source and usage of the data, please visit the [NHANES website](https://www.cdc.gov/nchs/nhanes/index.htm). **Data Transformation and Cleaning** **NCD-RisC:** The data has been organized by grouping the variables of 'year' and 'country' to create a structure that allows easy analysis of trends over time for different regions. The 'year' variable likely represents the year in which the height and BMI data were collected, while 'country' represents the country from which the data originated. In terms of cleaning, we remove all the “NA” value in the dataset to ensures that there are no gaps in the data that might negatively influence the visualization and subsequent analysis of the dataset. **NHANES:**For the purpose of this study, we filtered out all data for individuals below 12 years old, as their heights and weights are not generalizable across all age groups. Furthermore, we dropped all missing values to ensure the integrity and validity of our analysis. The transformation process is critical for us in the scope of this assignment as we are trying to explain the real life application of Central Limit Theorem and Normal distribution. **Dataset Integrity and Limitations** **NCD-RisC:** The dataset is drawn from a diverse range of 2181 population-based studies and includes 65 million participants from 200 countries and territories. This gives the dataset high statistical power and excellent representation of global patterns. The study uses a robust statistical methodology, a Bayesian hierarchical model, to estimate trends in mean height and mean BMI, accounting for non-linear changes over time. However, there is one limitation to the dataset. As the sample group is aged between 5-19 years, these samples may not be representative enough. Their heights could still change over time. **NHANES:**This dataset was collected by trained health technicians following strict protocols and procedures. The data collection was subjected to thorough quality assurance and quality control measures, making it a reliable source for conducting health and nutrition studies. However, there are a few limitations to consider. First, the dataset does not contain information about participants who had limb amputations, as this information could pose a disclosure concern. Second, the data file includes body measures for women who were pregnant at the time of their health examination, which could affect certain measurements like weight and waist circumference. Moreover, due to the COVID-19 pandemic, the 2019-2020 cycle data were not completed and thus not nationally representative on their own. To address this, these data were combined with the 2017-2018 cycle data to form the NHANES 2017-March 2020 pre-pandemic data. Lastly, the body measures examination protocol was determined by the participant’s age at the time of the screening interview, which is differed from the age at the time of the health examination by several weeks. Hence, data on age at examination may vary slightly from the age at screening.4d:T51e,rename = new Map([ ["Antigua and Barbuda", "Antigua and Barb."], ["Bolivia (Plurinational State of)", "Bolivia"], ["Bosnia and Herzegovina", "Bosnia and Herz."], ["Brunei Darussalam", "Brunei"], ["Czech Republic", "Czechia"], ["Cote d'Ivoire", "Côte d'Ivoire"], ["Central African Republic", "Central African Rep."], ["Cook Islands", "Cook Is."], ["Democratic People's Republic of Korea", "North Korea"], ["DR Congo", "Dem. Rep. Congo"], ["Dominican Republic", "Dominican Rep."], ["Equatorial Guinea", "Eq. Guinea"], ["Guinea Bissau", "Guinea-Bissau"], ["Iran (Islamic Republic of)", "Iran"], ["Lao PDR", "Laos"], ["Marshall Islands", "Marshall Is."], ["Micronesia (Federated States of)", "Micronesia"], ["Republic of Korea", "South Korea"], ["Republic of Moldova", "Moldova"], ["Russian Federation", "Russia"], ["Saint Kitts and Nevis", "St. Kitts and Nevis"], ["Saint Vincent and the Grenadines", "St. Vin. and Gren."], ["Sao Tome and Principe", "São Tomé and Principe"], ["Solomon Islands", "Somaliland"], ["", "eSwatini"], ["Syrian Arab Republic", "Syria"], ["The former Yugoslav Republic of Macedonia", "Macedonia"], ["United Republic of Tanzania", "Tanzania"], ["Venezuela (Bolivarian Republic of)", "Venezuela"], ["Viet Nam", "Vietnam"] 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","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1801,"value":"# Welcome to the world of normal distribution!","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1792,"value":"It's a fundamental concept in statistics that applies to various aspects of our lives. Variables like height, SAT scores, IQ scores, shoe sizes, and job satisfaction often follow a normal distribution. This distribution is defined by two parameters: the mean (µ) and the standard deviation (σ). The mean represents the average value, while the standard deviation indicates the spread of the data. Together, they shape the normal distribution and its variability. Get ready to explore interactive visualizations that will enhance your understanding of this concept and its relevance in daily life.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":96,"value":"**Formula:**\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":289,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"**μ** = mean of x (sample)\n\n**σ** = Standard Deviation of x (sample)\n\n**π** = 3.1415926...\n\n**e** = the base of the natural logarithm, approximately equal to 2.71828","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":608,"value":"# Interactive Dice Visualization\n\nOur first interactive visualization is designed to take you through an exploration of how a normal distribution is formed. You can simulate a roll of the dice and view the resulting distribution. With each roll of the dice, patterns of observation begin to emerge and your understanding of key statistical concepts is solidified before your eyes.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1785,"value":"## Learning Goals\n\nThrough interacting with this visualization, you can gain a deeper understanding of several concepts in statistics and probability:\n\n1. **Uncertainty and Probability**: Adjust the dice face probabilities and observe how this impacts outcome uncertainty.\n\n2. **The Central Limit Theorem**: Rolling multiple dice reveals that outcome distributions approximate a normal distribution.\n\n4. **The Law of Large Numbers**: Increasing the rounds stabilizes and makes outcome distributions more predictable, demonstrating how more data brings us closer to the real probabilities.\n \nWhile each roll's outcome is random, overall patterns are governed by probability laws！","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1789,"value":"\n## How to Use\n\nClick the Tutorial button to see a video demonstration of how to interact with this visualization.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1791,"value":"## Questions:\n\n1. Will the probability of the dice affect the resulting distribution?\n\n2. Will the resulting distribution still be normal if we use a unfair dice?\n\n3. Under what circumstances will we get a distribution that does not look like a bell shape curve?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":879,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":495,"value":"# How will the Distribution change by Mean & Standard Deviation？\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":906,"value":"\nIn our second visualization, you can observe how changes in the mean (µ) and standard deviation (σ) impact the shape and position of the distribution curve. By manipulating these parameters, you'll witness how the curve shifts and its spread changes. ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":484,"value":"{\nconst mean = avgg;\nconst stdDev = stdv;\nconst scalingFactor = 4;\nconst xValues = d3.range(mean - scalingFactor * stdDev, mean + scalingFactor * stdDev, 0.1);\nconst yValues = xValues.map((x) => {\n const exponent = -((x - mean) ** 2) / (2 * stdDev ** 2);\n return Math.exp(exponent) / (stdDev * Math.sqrt(2 * Math.PI));\n});\nconst data = xValues.map((x, i) => ({ x, y: yValues[i] }));\nreturn vl.markLine()\n .data(data)\n .encode(\n vl.x().fieldQ('x').title('Number of Rolling').scale({domain: [-400, 400]}),\n vl.y().fieldQ('y').title('Probabilities').scale({domain: [-0.0000001, 0.02]}),\n vl.color().value('green')\n )\n .width(400)\n .height(400)\n .render();\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":736,"value":"viewof stdv = Inputs.range([20, 90], {step: 2, label: \"Standard Deviation\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":491,"value":"viewof avgg = Inputs.range([-35, 35], {step: 1, label: \"Mean\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":650,"value":"The **\"Standard Deviation\"** slider allows you to control the spread or dispersion of the distribution:\n* Increasing the value makes the curve **wider and more dispersed**.\n* Decreasing the value makes it more **narrower and more concentrated**.\n\nThe **\"Mean\"** slider enables you to shift the entire distribution to the left or right along the x-axis:\n* Increasing the value moves the curve to the right - **Left Skewed**.\n* Decreasing the value moves it to the left - **Right Skewed**.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":711,"value":"# Unveiling the Bell Curve Phenomenon: Exploring the Impact of Sample Size on Distribution","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1157,"value":"Next, we will explore real-life dataset called [**NHANES** (National Health and Nutrition Examination Survey)](https://www.cdc.gov/nchs/nhanes/index.htm), specifically focusing on the **height variable**. This dataset consist of body measures of individuals collected by NHANES. We' ll visualize the height data to gain insights and understand how it align with the concept of the normal distribution. For more info about the dataset, please refer to the [**dataset description**](https://observablehq.com/d/d8132e4f55bc1fcc#cell-817).\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":703,"value":"printTable(dataset.slice(0, 10), null, null)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":456,"value":"As we increase the sample size, the histogram gradually transforms into a **bell curve shape**. With a larger sample size, the curve becomes more normalized. The tallest bar represents the _average height_, with more samples concentrated around this average and fewer towards the extremes.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":284,"value":"vl.markBar()\n .data(sampledData)\n .encode(\n vl.x().fieldQ('height').title('Height (cm)').bin({ maxbins: 30 }),\n vl.y().count().title('Count of Records'),\n vl.color().fieldQ('height').title('Height (cm)')\n\n )\n .title(`Distribution of Heights with Sample Size: ${sampleSize}`)\n .width(500)\n .height(300)\n .render();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1493,"value":"{\n function calculateMeanAndStdDev(dataset) {\n const validData = dataset.filter(value => !isNaN(value));\n\n const sum = validData.reduce((accumulator, value) => accumulator + value, 0);\n const mean = sum / validData.length;\n\n const squaredDifferences = validData.map((value) => (value - mean) ** 2);\n const sumOfSquaredDifferences = squaredDifferences.reduce((accumulator, value) => accumulator + value, 0);\n const variance = sumOfSquaredDifferences / validData.length;\n const stdDev = Math.sqrt(variance);\n\n return { mean, stdDev };\n }\n\n const heights = sampledData.map(data => data['height']);\n const { mean, stdDev } = calculateMeanAndStdDev(heights);\n\n const formattedMean = mean.toFixed(2);\n const formattedStdDev = stdDev.toFixed(2);\n\n const outputText = ` Mean: ${formattedMean} cm | Standard Deviation: ${formattedStdDev} cm`;\n\n return outputText;\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1890,"value":"Sample Size in hundreds:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":782,"value":"// viewof sampleSize = Inputs.range([10, 9862], {step: 1, label: \"Sample size\"});\n\nviewof sampleSizeRaw = Scrubber(Array.from({length: 98}, (_, i) => i+1), {\n delay: 10,\n autoplay: false,\n step: 100,\n loop: false\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":995,"value":"# Exploring Average Boy Heights Across Countries and Their Distribution","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1104,"value":"For our next visualization, we will continue using another real-world dataset from the [**NCD Risk Factor Collaboration (NCD-RisC)**](https://ncdrisc.org/data-downloads-height.html) to demonstrate how the normal distribution manifests in our daily lives. The dataset comprises the average heights of boys and girls, derived from 2181 population-based studies involving 65 million participants spanning from 1985 to 2019.\n\nBy interacting with the map, you'll be able to explore the global distribution of boys' and girls' heights and observe significant changes in height trends across countries. For more detailed information about the dataset, please refer to the [**dataset description**](https://observablehq.com/d/d8132e4f55bc1fcc#cell-817).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1245,"value":"printTable(data_map.slice(0, 10), null, null)\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1107,"value":"The slider below can be dragged, or you can click Play to let it loop through years, allowing you to see the changes in average heights over the years. We use color gradients to denote different height ranges, with blue indicating shorter heights and Red indicating taller ones. The Grey areas represent countries for which we lack sufficient data.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":998,"value":"viewof date = Scrubber(years, {\n delay: 100,\n loopDelay: 300,\n autoplay: false\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1000,"value":"legend({color, title: \"Average Height(cm)\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1003,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1146,"value":"The histogram below is another representation of the dataset. This visualization is built on the previous map visualization. Changes in the map visualization will correspondingly affect the histogram.\n\nAs you can observe, in some years, the graph may not resemble a bell curve due to variations in sample sizes across different countries. Larger countries tend to have larger samples, while smaller countries may have smaller samples, leading to inaccuracies and a deviation from the expected bell curve shape.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1009,"value":"vl.markBar()\n .data(Array.from(yearData, ([country, height]) => ({ country, height })))\n .encode(\n vl.x().fieldQ('height').bin({ maxbins: 20 }).axis({ title: 'Average Height' }),\n vl.y().count().axis({ title: 'Count' }),\n vl.color().fieldQ('height').scale({ scheme: [\"#74ADD1\", \"#ABD9E9\", \"#E0F3F8\", \"#FFFFBF\", \"#FEE090\", \"#FDAE61\", \"#F46D43\", \"#D73027\", \"#A50026\"] })\n )\n .width(400)\n .height(300)\n .title('Average Heights Distribution')\n .render();\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1895,"value":"# Conclusion\n\nWe have made great progress in comprehending this statistical concept, while also identifying areas where we may improve. Our work will continue as we attempt to understand more complicated applications and discover the full potential of normal distributions in evaluating and explaining the world around us.\n\nIn the future, we can improve our work by including statistical concepts like hypothesis testing and confidence intervals. These ideas will allow us to generate more precise predictions, estimate unknown parameters, and provide a comprehensive view of the data. By doing so, we can improve our understanding of the power of normal distributions in data analysis.\n\nFinally, we acknowledge that, while this notebook is comprehensive, it only covers a small portion of the normal distribution's potential applications. There are plenty of other fields and areas where this concept could be applied, as well as other datasets waiting to be explored.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1900,"value":"# Reflection\n\n- **Simplified Assumptions:** Our analysis simplifies certain aspects to facilitate understanding, which may not capture the complexity of real-world scenarios.\n\n- **Explore More Data:** Further exploration of diverse datasets can provide a broader understanding of the normal distribution in different fields and uncover new insights.\n\n- **Advanced Concepts:** Incorporating advanced statistical concepts, such as hypothesis testing or confidence intervals, can deepen the exploration of the normal distribution and its applications.\n\n- **Limited Scope:** The notebook focuses on specific examples and datasets related to the normal distribution, and does not cover all possible variations and applications. \n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":817,"value":"$4c","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1112,"value":"## Additional Code","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1090,"value":"#### The data processing and map processing code for the Choropleth Map","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1092,"value":"Since the code part for the Choropleth map is very long. We decide to put the data processing and map processing part at the end of the notebook so that it won't interrupt the reading experience for readers.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":938,"value":"##### Data processing for Choropleth Map","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":944,"value":"$4d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":940,"value":"entries = d3.csvParse(await FileAttachment(\"average_height _map.csv\").text(), function(d) {\n return {\n year: +d.Year,\n country: rename.get(d.Country) || d.Country,\n meanHeight: +d['Mean height'],\n };\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":949,"value":"data = new Map(\n [...d3.rollup(entries, v => d3.mean(v, d => d.meanHeight), d => d.year, d => d.country,)]\n);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1240,"value":"data_map =await FileAttachment(\"average_height _map.csv\").csv({ typed: true });","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":951,"value":"dataDomain = d3.extent(entries, d => d.meanHeight);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":955,"value":"years = Array.from(data.keys()).filter(year => !isNaN(year));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1862,"value":"sampleSize = 100 * sampleSizeRaw","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":957,"value":"yearData = data.get(date)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1778,"value":"dataset = await FileAttachment(\"heights_weights@1.csv\").csv({typed: true});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1781,"value":"sampledData = dataset.slice().sort(() => 0.5 - Math.random()).slice(0, sampleSize);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":961,"value":"##### Map Processing for Choropleth Map","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":963,"value":"color = d3.scaleSequential()\n .domain(dataDomain)\n .interpolator(d3.interpolateRgbBasis([\"#74ADD1\", \"#ABD9E9\", \"#E0F3F8\", \"#FFFFBF\", \"#FEE090\", \"#FDAE61\", \"#F46D43\", \"#D73027\", \"#A50026\"]))\n .unknown(\"#ccc\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":965,"value":"projection = d3.geoEqualEarth()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":967,"value":"path = d3.geoPath(projection)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":972,"value":"outline = ({type: \"Sphere\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":974,"value":"## Other Resources","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":147,"value":"imageURL1 = await FileAttachment(\"dice1.jpg\").url();","pinned":false,"hidden":true,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"imageURL2 = await FileAttachment(\"dice2.jpg\").url();","pinned":false,"hidden":true,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"imageURL3 = await FileAttachment(\"dice3.jpg\").url();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"imageURL4 = await FileAttachment(\"dice4.jpg\").url();","pinned":false,"hidden":true,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"imageURL5 = await FileAttachment(\"dice5.jpg\").url();","pinned":false,"hidden":true,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"imageURL6 = await FileAttachment(\"dice6.jpg\").url();","pinned":false,"hidden":true,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1420,"value":"videoURL1 = await FileAttachment(\"Dice_tutorial@3.mp4\").url();","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":313,"value":"size = 10","pinned":false,"hidden":true,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":310,"value":"face1 = (x, y) => htl.svg.fragment`\n \n`;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"face2 = (x, y) => htl.svg.fragment`\n \n \n`;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":329,"value":"face3 = (x, y) => htl.svg.fragment`\n \n ${face1(x, y)}\n \n`;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"face4 = (x, y) => htl.svg.fragment`\n \n \n \n \n`;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":335,"value":"face5 = (x, y) => htl.svg.fragment`\n ${face1(x, y)}\n ${face4(x, y)}\n`;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":338,"value":"face6 = (x, y) => htl.svg.fragment`\n \n \n \n \n \n \n`;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":465,"value":"## Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":121,"value":"import {p5} from \"@tmcw/p5\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":461,"value":"import {vl} from \"@vega/vega-lite-api-v5\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":471,"value":"import {printTable} from \"@jonfroehlich/data-utilities\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":479,"value":"import {printTableTypes} from 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require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":979,"value":"d3 = require(\"d3@6\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":981,"value":"import {Scrubber} from \"@mbostock/scrubber\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":984,"value":"import {countries, world} from 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Reference","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":1072,"value":"Based on: \n- @d3/color-schemes (inpiration for colors)\n- @d3/world-choropleth (inpiration for map building)\n- @gcmleon/choropleth-map-animation#rename (for major inspiration)\n- @gcmleon/designing-world-maps-part-1 (for inspiration on buttons and scales)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"}],"files":"$W4e","stdlib":"1"}} 24:null