[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"sanity-S6m4fvgawDxTEcU0Fs3ma-bwHTbkbhkqOlJ_kmjwG04":3,"sanity-llVPmomZso3bC6bnstJ4XApNQ_gA7IMZM41AIrR0vKE":299},{"data":4,"sourceMap":-1},{"latestPodcast":5,"latestReleases":14,"post":39,"recent":274},[6],{"_id":7,"publishedAt":8,"slug":9,"sponsored":12,"title":13},"7ebd76d2-cebc-4b88-82f9-3dfb2c8bc5ca","2026-07-08T04:40:00.000Z",{"_type":10,"current":11},"slug","what-s-left-for-infrastructure-as-code-after-ai-moves-in",true,"What's left for infrastructure-as-code after AI moves in?",[15,21,27,33],{"_id":16,"publishedAt":17,"slug":18,"title":20},"eb5b66eb-9410-4329-83bb-22bbff39402a","2026-04-28T13:00:00.000Z",{"_type":10,"current":19},"turn-scattered-knowledge-into-trusted-intelligence","Turning scattered knowledge into trusted intelligence: Stack Internal 2026.3",{"_id":22,"publishedAt":23,"slug":24,"title":26},"369c2401-b62e-4a37-8ff8-bf603023ecad","2026-03-02T15:03:00.988Z",{"_type":10,"current":25},"what-s-new-at-stack-overflow-march-2026","What’s new at Stack Overflow: March 2026",{"_id":28,"publishedAt":29,"slug":30,"title":32},"5e9053a4-07ea-447c-91ea-29e0b6228537","2026-02-02T15:00:00.000Z",{"_type":10,"current":31},"what-s-new-at-stack-overflow-february-2026","What’s new at Stack Overflow: February 2026",{"_id":34,"publishedAt":35,"slug":36,"title":38},"a1b538eb-a8a6-46d0-80a1-ac70ec9bb935","2026-01-05T10:00:00.000-05:00",{"_type":10,"current":37},"what-s-new-at-stack-overflow-january-2026","What’s new at Stack Overflow: January 2026",{"_createdAt":40,"_id":41,"_rev":42,"_type":43,"_updatedAt":44,"author":45,"body":76,"comments":12,"dateUrl":236,"excerpt":237,"image":238,"legacyBody":241,"product":100,"publishedAt":244,"slug":245,"sponsored":100,"tags":247,"title":273,"visible":12},"2023-05-25T09:39:17Z","wp-post-17550","9HpbCsT2tq0xwozQfkgBTj","blogPost","2023-07-13T14:55:53Z",[46,64],{"_createdAt":47,"_id":48,"_rev":49,"_system":50,"_type":53,"_updatedAt":54,"avatar":55,"employee":60,"name":61,"slug":62},"2023-05-23T16:27:18Z","wp-author-213","nRfzWrvFg3DIXOd15U9uv8",{"base":51},{"id":48,"rev":52},"9xJoPFf2DISyAMMJXP7Ct6","blogAuthor","2025-07-29T19:37:47Z",{"_type":56,"asset":57},"image",{"_ref":58,"_type":59},"image-e81c84dcaeb58be1002795a6544b595bd6fc8071-1024x1024-jpg","reference","former","Ben Popper",{"current":63},"benpopper",{"_createdAt":47,"_id":65,"_rev":66,"_type":53,"_updatedAt":67,"avatar":68,"bio":71,"employee":72,"name":73,"slug":74},"wp-author-cap-17508","07ZbrKPSUrjrV4wQ6fDpaa","2023-06-20T15:05:10Z",{"_type":56,"asset":69},{"_ref":70,"_type":59},"image-8c28cb2ef9d5c7ef909c7685c3808e5c66f17aeb-400x400-jpg","Curriculum Developer, Codecademy","none","Sophie Sommer",{"current":75},"sophie-sommer",[77,102,110,118,126,130,138,149,160,171,200,217],{"_key":78,"_type":79,"children":80,"markDefs":96,"style":101},"29a037955d46","block",[81,87,92],{"_key":82,"_type":83,"marks":84,"text":86},"29a037955d460","span",[85],"em","Welcome back! This is the fourth class in our Level Up series on statistics with Python. If you’re just tuning in, you can catch up on what we’re doing and review the first lesson ",{"_key":88,"_type":83,"marks":89,"text":91},"29a037955d461",[85,90],"0423d5e5aaf9","here",{"_key":93,"_type":83,"marks":94,"text":95},"29a037955d462",[85],".",[97],{"_key":90,"_type":98,"href":99,"reference":100},"link","https:\u002F\u002Fstackoverflow.blog\u002F2021\u002F02\u002F16\u002Flevel-up-mastering-statistics-with-python\u002F",null,"normal",{"_key":103,"_type":79,"children":104,"markDefs":109,"style":101},"0b9b811d4d27",[105],{"_key":106,"_type":83,"marks":107,"text":108},"0b9b811d4d270",[],"In this lesson we'll learn about the Central Limit Theorem (CLT) by simulating it in Python.",[],{"_key":111,"_type":79,"children":112,"markDefs":117,"style":101},"8ca594a95fc6",[113],{"_key":114,"_type":83,"marks":115,"text":116},"8ca594a95fc60",[],"The CLT is the basis for a few common statistical hypothesis tests, like Z-tests and t-tests. While many introductory statistics classes teach the CLT, very few actually attempt to prove it because that requires some complex math. In this session, we'll bypass all that math by using Python loops to simulate the CLT. This helps build intuition for how hypothesis testing works, while also practicing our Python programming skills and avoiding math-y equations!",[],{"_key":119,"_type":79,"children":120,"markDefs":125,"style":101},"f2676137a668",[121],{"_key":122,"_type":83,"marks":123,"text":124},"f2676137a6680",[],"This is a fun stream because it is our first step into the world of inferential statistics. We're no longer interested in simply looking at a sample of data by itself -- we're now starting to think about how to use a sample to gain an understanding of a population we cannot observe.",[],{"_key":127,"_type":128,"markDefs":100,"url":129},"e2201b544082","embed","https:\u002F\u002Fwww.youtube.com\u002Fembed\u002FNsfrdRlV0mg?start=80",{"_key":131,"_type":79,"children":132,"markDefs":137,"style":101},"02a506769e32",[133],{"_key":134,"_type":83,"marks":135,"text":136},"02a506769e320",[],"Here are some StackOverflow questions related to the work we did in today's session:",[],{"_key":139,"_type":79,"children":140,"markDefs":146,"style":101},"70637be03bcc",[141],{"_key":142,"_type":83,"marks":143,"text":145},"70637be03bcc0",[144],"9d9a9891cb26","Finding distribution of sample mean by Central Limit Theorem",[147],{"_key":144,"_type":98,"href":148,"reference":100},"https:\u002F\u002Fstackoverflow.com\u002Fquestions\u002F20306262\u002Ffinding-distribution-of-sample-mean-by-central-limit-theorem",{"_key":150,"_type":79,"children":151,"markDefs":157,"style":101},"36c4823d2527",[152],{"_key":153,"_type":83,"marks":154,"text":156},"36c4823d25270",[155],"d3a1dd854440","Implementing the Central Limit Theorem - Which Random Number Generator?",[158],{"_key":155,"_type":98,"href":159,"reference":100},"https:\u002F\u002Fstackoverflow.com\u002Fquestions\u002F63229931\u002Fimplementing-the-central-limit-theorem-which-random-number-generator",{"_key":161,"_type":79,"children":162,"markDefs":168,"style":101},"96e6911be449",[163],{"_key":164,"_type":83,"marks":165,"text":167},"96e6911be4490",[166],"eb6a51c3fcd1","For loops in Python",[169],{"_key":166,"_type":98,"href":170,"reference":100},"https:\u002F\u002Fstackoverflow.com\u002Fquestions\u002F56040789\u002Fhow-to-make-a-for-loop-more-understandable-in-python",{"_key":172,"_type":79,"children":173,"markDefs":195,"style":101},"ab59488c6769",[174,178,183,187,192],{"_key":175,"_type":83,"marks":176,"text":177},"ab59488c67690",[],"If you enjoyed this lesson, you can catch up on the ",{"_key":179,"_type":83,"marks":180,"text":182},"ab59488c67691",[181],"16ae486b07f2","rest of the series",{"_key":184,"_type":83,"marks":185,"text":186},"ab59488c67692",[]," on YouTube. If you’d like to watch a session live, follow the ",{"_key":188,"_type":83,"marks":189,"text":191},"ab59488c67693",[190],"ea3b569bafb7","Codecademy YouTube channel",{"_key":193,"_type":83,"marks":194,"text":95},"ab59488c67694",[],[196,198],{"_key":181,"_type":98,"href":197,"reference":100},"https:\u002F\u002Fwww.youtube.com\u002Fplaylist?list=PLFzsFUO-y0HDWkdsBMtufEThI2I3c9WlZ",{"_key":190,"_type":98,"href":199,"reference":100},"https:\u002F\u002Fwww.youtube.com\u002Fc\u002Fcodecademy\u002Ffeatured",{"_key":201,"_type":79,"children":202,"markDefs":214,"style":101},"a5cadd3c908b",[203,207,211],{"_key":204,"_type":83,"marks":205,"text":206},"a5cadd3c908b0",[],"Every Tuesday from now until March 2nd, we’ll be streaming a new session at 4PM EST. You can set a reminder for the stream for March 2nd ",{"_key":208,"_type":83,"marks":209,"text":91},"a5cadd3c908b1",[210],"657a69592dfb",{"_key":212,"_type":83,"marks":213,"text":95},"a5cadd3c908b2",[],[215],{"_key":210,"_type":98,"href":216,"reference":100},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=gblWwOrRmAw",{"_key":218,"_type":79,"children":219,"markDefs":233,"style":101},"61ae9b57235f",[220,224,229],{"_key":221,"_type":83,"marks":222,"text":223},"61ae9b57235f0",[],"Finally, if you want even more stats content, you can sign up for the ",{"_key":225,"_type":83,"marks":226,"text":228},"61ae9b57235f1",[227],"4f8171bbe954","Master Statistics with Python",{"_key":230,"_type":83,"marks":231,"text":232},"61ae9b57235f2",[]," interactive course this series was based on. This course was developed by Sophie and has many more quizzes, projects, and helpful nuggets that we can’t fit into our streams!",[234],{"_key":227,"_type":98,"href":235,"reference":100},"https:\u002F\u002Fwww.codecademy.com\u002Flearn\u002Fpaths\u002Fmaster-statistics-with-python?utm_source=stack_overflow&utm_medium=partners&utm_content=cclive_stats_4","2021\u002F03\u002F02","While many introductory statistics classes teach the CLT, very few actually attempt to prove it because that requires some complex math. In this session, we'll bypass all that math by using Python loops to simulate the CLT. ",{"_type":56,"asset":239},{"_ref":240,"_type":59},"image-9ee6ed35aa69969e0279dc197092655a5e9dd7bd-2083x875-png",{"code":242,"language":243},"\u003C!-- wp:paragraph -->\n\u003Cp>\u003Cem>Welcome back! This is the fourth class in our Level Up series on statistics with Python. If you’re just tuning in, you can catch up on what we’re doing and review the first lesson \u003Ca href=\"https:\u002F\u002Fstackoverflow.blog\u002F2021\u002F02\u002F16\u002Flevel-up-mastering-statistics-with-python\u002F\">here\u003C\u002Fa>.\u003C\u002Fem>\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>In this lesson we'll learn about the Central Limit Theorem (CLT) by simulating it in Python. \u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>The CLT is the basis for a few common statistical hypothesis tests, like Z-tests and t-tests. While many introductory statistics classes teach the CLT, very few actually attempt to prove it because that requires some complex math. In this session, we'll bypass all that math by using Python loops to simulate the CLT. This helps build intuition for how hypothesis testing works, while also practicing our Python programming skills and avoiding math-y equations!\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>This is a fun stream because it is our first step into the world of inferential statistics. We're no longer interested in simply looking at a sample of data by itself -- we're now starting to think about how to use a sample to gain an understanding of a population we cannot observe.\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:html -->\n\u003Ciframe width=\"560\" height=\"315\" src=\"https:\u002F\u002Fwww.youtube.com\u002Fembed\u002FNsfrdRlV0mg?start=80\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen>\u003C\u002Fiframe>\n\u003C!-- \u002Fwp:html -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>Here are some StackOverflow questions related to the work we did in today's session:\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>\u003Ca href=\"https:\u002F\u002Fstackoverflow.com\u002Fquestions\u002F20306262\u002Ffinding-distribution-of-sample-mean-by-central-limit-theorem\">Finding distribution of sample mean by Central Limit Theorem\u003C\u002Fa>\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>\u003Ca href=\"https:\u002F\u002Fstackoverflow.com\u002Fquestions\u002F63229931\u002Fimplementing-the-central-limit-theorem-which-random-number-generator\">Implementing the Central Limit Theorem - Which Random Number Generator?\u003C\u002Fa>\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>\u003Ca href=\"https:\u002F\u002Fstackoverflow.com\u002Fquestions\u002F56040789\u002Fhow-to-make-a-for-loop-more-understandable-in-python\">For loops in Python\u003C\u002Fa>\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>If you enjoyed this lesson, you can catch up on the \u003Ca href=\"https:\u002F\u002Fwww.youtube.com\u002Fplaylist?list=PLFzsFUO-y0HDWkdsBMtufEThI2I3c9WlZ\">rest of the series\u003C\u002Fa> on YouTube. If you’d like to watch a session live, follow the \u003Ca href=\"https:\u002F\u002Fwww.youtube.com\u002Fc\u002Fcodecademy\u002Ffeatured\">Codecademy YouTube channel\u003C\u002Fa>.\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>Every Tuesday from now until March 2nd, we’ll be streaming a new session at 4PM EST. You can set a reminder for the stream for March 2nd \u003Ca href=\"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=gblWwOrRmAw\">here\u003C\u002Fa>.\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->\n\n\u003C!-- wp:paragraph -->\n\u003Cp>Finally, if you want even more stats content, you can sign up for the \u003Ca href=\"https:\u002F\u002Fwww.codecademy.com\u002Flearn\u002Fpaths\u002Fmaster-statistics-with-python?utm_source=stack_overflow&utm_medium=partners&utm_content=cclive_stats_4\">Master Statistics with Python\u003C\u002Fa> interactive course this series was based on. This course was developed by Sophie and has many more quizzes, projects, and helpful nuggets that we can’t fit into our streams!\u003C\u002Fp>\n\u003C!-- \u002Fwp:paragraph -->","html","2021-03-02T20:15:21.000Z",{"current":246},"level-up-mastering-statistics-with-python-part-4",[248,256,260,265,269],{"_createdAt":249,"_id":250,"_rev":251,"_type":252,"_updatedAt":249,"slug":253,"title":255},"2023-05-23T16:43:21Z","wp-tagcat-code-for-a-living","9HpbCsT2tq0xwozQfkc4ih","blogTag",{"current":254},"code-for-a-living","Code for a Living",{"_createdAt":249,"_id":257,"_rev":251,"_type":252,"_updatedAt":249,"slug":258,"title":259},"wp-tagcat-codecademy",{"current":259},"codecademy",{"_createdAt":249,"_id":261,"_rev":251,"_type":252,"_updatedAt":249,"slug":262,"title":264},"wp-tagcat-level-up",{"current":263},"level-up","level up",{"_createdAt":249,"_id":266,"_rev":251,"_type":252,"_updatedAt":249,"slug":267,"title":268},"wp-tagcat-python",{"current":268},"python",{"_createdAt":249,"_id":270,"_rev":251,"_type":252,"_updatedAt":249,"slug":271,"title":272},"wp-tagcat-statistics",{"current":272},"statistics","Level Up: Mastering statistics with Python - part 4",[275,281,287,293],{"_id":276,"publishedAt":277,"slug":278,"sponsored":100,"title":280},"76c9771b-34e6-4d98-8641-ecefc711f0ef","2026-07-06T15:23:34.559Z",{"_type":10,"current":279},"when-the-sensor-starts-thinking-snortml-agentic-ai-and-the-evolving-architecture-of-intrusion-detection","When the sensor starts thinking: SnortML, agentic AI, and the evolving architecture of intrusion detection",{"_id":282,"publishedAt":283,"slug":284,"sponsored":100,"title":286},"28e560af-f0aa-4d46-bd90-f435ad604aa7","2026-06-26T14:00:27.102Z",{"_type":10,"current":285},"paging-charity-how-can-engineering-leaders-avoid-becoming-bond-villains","Paging Charity! How can engineering leaders avoid becoming Bond villains?",{"_id":288,"publishedAt":289,"slug":290,"sponsored":100,"title":292},"4b22c2a3-3779-4966-93eb-5230391dbdce","2026-06-23T14:08:58.595Z",{"_type":10,"current":291},"your-ai-shipped-a-backend-that-boots-that-is-the-whole-problem","Your AI shipped a backend that boots. That is the whole problem.",{"_id":294,"publishedAt":295,"slug":296,"sponsored":100,"title":298},"5cf362e1-fe7b-45af-b69c-914731c6a052","2026-06-23T14:00:00.000Z",{"_type":10,"current":297},"the-2026-developer-survey-is-now-open-for-human-developers-only","The 2026 Developer Survey is now open (for human developers only)!",{"data":300,"sourceMap":-1},{"count":301,"lastTimestamp":302},1,"2023-05-25T09:47:33Z"]