Normal Distributions Explained – With Real-World Examples

⏭️ 𝘾𝙤𝙣𝙣𝙚𝙘𝙩 𝙬𝙞𝙩𝙝 𝙪𝙨 𝙤𝙣 𝙋𝘼𝙏𝙍𝙀𝙊𝙉 https://www.patreon.com/socratica Why do so many things in the world follow the same smooth, bell-shaped curve? Heights, weights, test scores, daily revenues—they all tend to cluster around a central value and taper off symmetrically. This pattern is so common, it has a name: the Normal Distribution. Normal distributions are one of the most important ideas in statistics. Also called the bell curve, this recognizable shape appears again and again—in nature, in human behavior, in finance, and in science. In this video, we explore what a normal distribution is, why it’s so common, and how to describe it using just two numbers: the mean (μ) and standard deviation (σ). We also explore the Empirical Rule (68-95-99.7 Rule), the PDF, Z-scores, and calculating probabilities from real data including human head sizes and footballer heights. ⏭️ 𝙔𝙤𝙪 𝙘𝙖𝙣 𝙟𝙪𝙢𝙥 𝙩𝙤 𝙨𝙚𝙘𝙩𝙞𝙤𝙣𝙨 𝙤𝙛 𝙩𝙝𝙚 𝙫𝙞𝙙𝙚𝙤 𝙝𝙚𝙧𝙚: 0:00 A thousand people walk into a bar... 1:15 What is a distribution? 2:40 Mean & standard deviation 5:05 The Empirical Rule (68–95–99.7) 5:21 Measuring head sizes 7:38 Calculating the mean μ 7:50 Calculating standard deviation σ 9:09 Example 1: 1966 England World Cup team 10:11 Summary Stats 10:36 The Probability Density Function PDF 12:30 Example 2: Tall women in US (using PDF) 13:45 Z-scores and rare events ▶️ 𝙒𝘼𝙏𝘾𝙃 𝙉𝙀𝙓𝙏: Accuracy vs Precision https://youtu.be/_DMkcNomXpU Special thanks to our wonderful Patreon supporters: Umar Khan Tracy Karin Prell Thomas Myers NSS North Houston Space Society Michael Shebanow Marcos Silveira M Andrews KW Kevin B John Krawiec Jim Woodworth Jeremy Shimanek Eric Eccleston Christopher Kemsley Thank you, kind friends! 💜🦉 𝘽𝙚𝙘𝙤𝙢𝙚 𝙤𝙪𝙧 𝙋𝙖𝙩𝙧𝙤𝙣 𝙤𝙣 𝙋𝙖𝙩𝙧𝙚𝙤𝙣: https://www.patreon.com/socratica 📚 𝙒𝙚 𝙧𝙚𝙘𝙤𝙢𝙢𝙚𝙣𝙙 (affiliate links): The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow https://amzn.to/4j9n0YP The Art of Statistics: How to Learn from Data by David Spiegelhalter https://amzn.to/3S9E46a How to Be a Great Student (by Socratica!) ebook: https://amzn.to/2Lh3XSP paperback: https://amzn.to/3t5jeH3 🎬 𝘾𝙍𝙀𝘿𝙄𝙏𝙎: Written & Produced by: Michael Harrison & Kimberly Hatch Harrison Edited by: Alivia Brown 🎓 𝘼𝘽𝙊𝙐𝙏 𝙊𝙐𝙍 𝙄𝙉𝙎𝙏𝙍𝙐𝘾𝙏𝙊𝙍𝙎: Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google. Kimberly earned her BS in Biology and another BS in English at Caltech. She did her graduate work in Molecular Biology at Princeton, specializing in Immunology and Neurobiology. Kimberly spent 16+ years as a research scientist and a dozen years as a biology and chemistry instructor. Michael and Kimberly Harrison co-founded Socratica. Their mission? To create the education of the future. Ready to 🧠 𝙇𝙀𝘼𝙍𝙉 𝙈𝙊𝙍𝙀 with Socratica? 📺 𝙎𝙪𝙗𝙨𝙘𝙧𝙞𝙗𝙚 for SMART videos in Math, Science & Programming: http://bit.ly/SocraticaSubscribe ▶️ 𝙋𝙇𝘼𝙔𝙇𝙄𝙎𝙏𝙎: Study Tips http://bit.ly/StudyTipsPlaylist Python http://bit.ly/PythonSocratica Chemistry http://bit.ly/Chemistry_Playlist Calculus http://bit.ly/CalculusSocratica Geometry http://bit.ly/GeometrySocratica #normaldistribution #statistics #bellcurve