#central-limit-theorem — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #central-limit-theorem, aggregated by home.social.
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“It’s the bell curve again”*…
Joseph Howlett on how the central limit theorem, which started as a bar trick for 18th-century gamblers, became something on which scientists rely every day…
No matter where you look, a bell curve is close by.
Place a measuring cup in your backyard every time it rains and note the height of the water when it stops: Your data will conform to a bell curve. Record 100 people’s guesses at the number of jelly beans in a jar, and they’ll follow a bell curve. Measure enough women’s heights, men’s weights, SAT scores, marathon times — you’ll always get the same smooth, rounded hump that tapers at the edges.
Why does the bell curve pop up in so many datasets?
The answer boils down to the central limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is so unintuitive and surprising,” said Daniela Witten, a biostatistician at the University of Washington. Through it, the most random, unimaginable chaos can lead to striking predictability.
It’s now a pillar on which much of modern empirical science rests. Almost every time a scientist uses measurements to infer something about the world, the central limit theorem is buried somewhere in the methods. Without it, it would be hard for science to say anything, with any confidence, about anything.
“I don’t think the field of statistics would exist without the central limit theorem,” said Larry Wasserman, a statistician at Carnegie Mellon University. “It’s everything.”
Perhaps it shouldn’t come as a surprise that the push to find regularity in randomness came from the study of gambling…
Read on for the fascinating story of: “The Math That Explains Why Bell Curves Are Everywhere,” from @quantamagazine.bsky.social.
Howlett concludes by observing that “The central limit theorem is a pillar of modern science, ultimately, because it’s a pillar of the world around us. When we combine lots of independent measurements, we get clusters. And if we’re clever enough, we can use those clusters to find out something interesting about the processes that made them”– which follows from the story he shares.
Still, we’d do well to remember that there are limits to its applicability, both descriptively (as Nassim Nicholas Taleb points out, “because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty”) and prescriptively (as Benjamim Bloom argues, “The bell-shaped curve is not sacred. It describes the outcome of a random process. Since education is a purposeful activity….the achievement distribution should be very different from the normal curve if our instruction is effective).
For (much) more, see Peter Bernstein‘s wonderful Against the Gods: The Remarkable Story of Risk
* Robert A. Heinlein, Time Enough for Love
###
As we noodle on the normal distribution, we might send curve-shattering birthday greetings to Norman Borlaug; he was born on ths date in 1914. An agronomist, he developed and led initiatives worldwide that contributed to the voluminous increases in agricultural production we call “the Green Revolution.” Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom, and the Congressional Gold Medal; he’s one of only seven people to have received all three of those awards.
#agriculture #BellCurve #centralLimitTheorem #culture #GreenRevolution #history #Mathematics #normalDistribution #NormanBorlaug #Science #statistics -
“It’s the bell curve again”*…
Joseph Howlett on how the central limit theorem, which started as a bar trick for 18th-century gamblers, became something on which scientists rely every day…
No matter where you look, a bell curve is close by.
Place a measuring cup in your backyard every time it rains and note the height of the water when it stops: Your data will conform to a bell curve. Record 100 people’s guesses at the number of jelly beans in a jar, and they’ll follow a bell curve. Measure enough women’s heights, men’s weights, SAT scores, marathon times — you’ll always get the same smooth, rounded hump that tapers at the edges.
Why does the bell curve pop up in so many datasets?
The answer boils down to the central limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is so unintuitive and surprising,” said Daniela Witten, a biostatistician at the University of Washington. Through it, the most random, unimaginable chaos can lead to striking predictability.
It’s now a pillar on which much of modern empirical science rests. Almost every time a scientist uses measurements to infer something about the world, the central limit theorem is buried somewhere in the methods. Without it, it would be hard for science to say anything, with any confidence, about anything.
“I don’t think the field of statistics would exist without the central limit theorem,” said Larry Wasserman, a statistician at Carnegie Mellon University. “It’s everything.”
Perhaps it shouldn’t come as a surprise that the push to find regularity in randomness came from the study of gambling…
Read on for the fascinating story of: “The Math That Explains Why Bell Curves Are Everywhere,” from @quantamagazine.bsky.social.
Howlett concludes by observing that “The central limit theorem is a pillar of modern science, ultimately, because it’s a pillar of the world around us. When we combine lots of independent measurements, we get clusters. And if we’re clever enough, we can use those clusters to find out something interesting about the processes that made them”– which follows from the story he shares.
Still, we’d do well to remember that there are limits to its applicability, both descriptively (as Nassim Nicholas Taleb points out, “because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty”) and prescriptively (as Benjamim Bloom argues, “The bell-shaped curve is not sacred. It describes the outcome of a random process. Since education is a purposeful activity….the achievement distribution should be very different from the normal curve if our instruction is effective).
For (much) more, see Peter Bernstein‘s wonderful Against the Gods: The Remarkable Story of Risk
* Robert A. Heinlein, Time Enough for Love
###
As we noodle on the normal distribution, we might send curve-shattering birthday greetings to Norman Borlaug; he was born on ths date in 1914. An agronomist, he developed and led initiatives worldwide that contributed to the voluminous increases in agricultural production we call “the Green Revolution.” Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom, and the Congressional Gold Medal; he’s one of only seven people to have received all three of those awards.
#agriculture #BellCurve #centralLimitTheorem #culture #GreenRevolution #history #Mathematics #normalDistribution #NormanBorlaug #Science #statistics -
“It’s the bell curve again”*…
Joseph Howlett on how the central limit theorem, which started as a bar trick for 18th-century gamblers, became something on which scientists rely every day…
No matter where you look, a bell curve is close by.
Place a measuring cup in your backyard every time it rains and note the height of the water when it stops: Your data will conform to a bell curve. Record 100 people’s guesses at the number of jelly beans in a jar, and they’ll follow a bell curve. Measure enough women’s heights, men’s weights, SAT scores, marathon times — you’ll always get the same smooth, rounded hump that tapers at the edges.
Why does the bell curve pop up in so many datasets?
The answer boils down to the central limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is so unintuitive and surprising,” said Daniela Witten, a biostatistician at the University of Washington. Through it, the most random, unimaginable chaos can lead to striking predictability.
It’s now a pillar on which much of modern empirical science rests. Almost every time a scientist uses measurements to infer something about the world, the central limit theorem is buried somewhere in the methods. Without it, it would be hard for science to say anything, with any confidence, about anything.
“I don’t think the field of statistics would exist without the central limit theorem,” said Larry Wasserman, a statistician at Carnegie Mellon University. “It’s everything.”
Perhaps it shouldn’t come as a surprise that the push to find regularity in randomness came from the study of gambling…
Read on for the fascinating story of: “The Math That Explains Why Bell Curves Are Everywhere,” from @quantamagazine.bsky.social.
Howlett concludes by observing that “The central limit theorem is a pillar of modern science, ultimately, because it’s a pillar of the world around us. When we combine lots of independent measurements, we get clusters. And if we’re clever enough, we can use those clusters to find out something interesting about the processes that made them”– which follows from the story he shares.
Still, we’d do well to remember that there are limits to its applicability, both descriptively (as Nassim Nicholas Taleb points out, “because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty”) and prescriptively (as Benjamim Bloom argues, “The bell-shaped curve is not sacred. It describes the outcome of a random process. Since education is a purposeful activity….the achievement distribution should be very different from the normal curve if our instruction is effective).
For (much) more, see Peter Bernstein‘s wonderful Against the Gods: The Remarkable Story of Risk
* Robert A. Heinlein, Time Enough for Love
###
As we noodle on the normal distribution, we might send curve-shattering birthday greetings to Norman Borlaug; he was born on ths date in 1914. An agronomist, he developed and led initiatives worldwide that contributed to the voluminous increases in agricultural production we call “the Green Revolution.” Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom, and the Congressional Gold Medal; he’s one of only seven people to have received all three of those awards.
#agriculture #BellCurve #centralLimitTheorem #culture #GreenRevolution #history #Mathematics #normalDistribution #NormanBorlaug #Science #statistics -
“It’s the bell curve again”*…
Joseph Howlett on how the central limit theorem, which started as a bar trick for 18th-century gamblers, became something on which scientists rely every day…
No matter where you look, a bell curve is close by.
Place a measuring cup in your backyard every time it rains and note the height of the water when it stops: Your data will conform to a bell curve. Record 100 people’s guesses at the number of jelly beans in a jar, and they’ll follow a bell curve. Measure enough women’s heights, men’s weights, SAT scores, marathon times — you’ll always get the same smooth, rounded hump that tapers at the edges.
Why does the bell curve pop up in so many datasets?
The answer boils down to the central limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is so unintuitive and surprising,” said Daniela Witten, a biostatistician at the University of Washington. Through it, the most random, unimaginable chaos can lead to striking predictability.
It’s now a pillar on which much of modern empirical science rests. Almost every time a scientist uses measurements to infer something about the world, the central limit theorem is buried somewhere in the methods. Without it, it would be hard for science to say anything, with any confidence, about anything.
“I don’t think the field of statistics would exist without the central limit theorem,” said Larry Wasserman, a statistician at Carnegie Mellon University. “It’s everything.”
Perhaps it shouldn’t come as a surprise that the push to find regularity in randomness came from the study of gambling…
Read on for the fascinating story of: “The Math That Explains Why Bell Curves Are Everywhere,” from @quantamagazine.bsky.social.
Howlett concludes by observing that “The central limit theorem is a pillar of modern science, ultimately, because it’s a pillar of the world around us. When we combine lots of independent measurements, we get clusters. And if we’re clever enough, we can use those clusters to find out something interesting about the processes that made them”– which follows from the story he shares.
Still, we’d do well to remember that there are limits to its applicability, both descriptively (as Nassim Nicholas Taleb points out, “because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty”) and prescriptively (as Benjamim Bloom argues, “The bell-shaped curve is not sacred. It describes the outcome of a random process. Since education is a purposeful activity….the achievement distribution should be very different from the normal curve if our instruction is effective).
For (much) more, see Peter Bernstein‘s wonderful Against the Gods: The Remarkable Story of Risk
* Robert A. Heinlein, Time Enough for Love
###
As we noodle on the normal distribution, we might send curve-shattering birthday greetings to Norman Borlaug; he was born on ths date in 1914. An agronomist, he developed and led initiatives worldwide that contributed to the voluminous increases in agricultural production we call “the Green Revolution.” Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom, and the Congressional Gold Medal; he’s one of only seven people to have received all three of those awards.
#agriculture #BellCurve #centralLimitTheorem #culture #GreenRevolution #history #Mathematics #normalDistribution #NormanBorlaug #Science #statistics -
“It’s the bell curve again”*…
Joseph Howlett on how the central limit theorem, which started as a bar trick for 18th-century gamblers, became something on which scientists rely every day…
No matter where you look, a bell curve is close by.
Place a measuring cup in your backyard every time it rains and note the height of the water when it stops: Your data will conform to a bell curve. Record 100 people’s guesses at the number of jelly beans in a jar, and they’ll follow a bell curve. Measure enough women’s heights, men’s weights, SAT scores, marathon times — you’ll always get the same smooth, rounded hump that tapers at the edges.
Why does the bell curve pop up in so many datasets?
The answer boils down to the central limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is so unintuitive and surprising,” said Daniela Witten, a biostatistician at the University of Washington. Through it, the most random, unimaginable chaos can lead to striking predictability.
It’s now a pillar on which much of modern empirical science rests. Almost every time a scientist uses measurements to infer something about the world, the central limit theorem is buried somewhere in the methods. Without it, it would be hard for science to say anything, with any confidence, about anything.
“I don’t think the field of statistics would exist without the central limit theorem,” said Larry Wasserman, a statistician at Carnegie Mellon University. “It’s everything.”
Perhaps it shouldn’t come as a surprise that the push to find regularity in randomness came from the study of gambling…
Read on for the fascinating story of: “The Math That Explains Why Bell Curves Are Everywhere,” from @quantamagazine.bsky.social.
Howlett concludes by observing that “The central limit theorem is a pillar of modern science, ultimately, because it’s a pillar of the world around us. When we combine lots of independent measurements, we get clusters. And if we’re clever enough, we can use those clusters to find out something interesting about the processes that made them”– which follows from the story he shares.
Still, we’d do well to remember that there are limits to its applicability, both descriptively (as Nassim Nicholas Taleb points out, “because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty”) and prescriptively (as Benjamim Bloom argues, “The bell-shaped curve is not sacred. It describes the outcome of a random process. Since education is a purposeful activity….the achievement distribution should be very different from the normal curve if our instruction is effective).
For (much) more, see Peter Bernstein‘s wonderful Against the Gods: The Remarkable Story of Risk
* Robert A. Heinlein, Time Enough for Love
###
As we noodle on the normal distribution, we might send curve-shattering birthday greetings to Norman Borlaug; he was born on ths date in 1914. An agronomist, he developed and led initiatives worldwide that contributed to the voluminous increases in agricultural production we call “the Green Revolution.” Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom, and the Congressional Gold Medal; he’s one of only seven people to have received all three of those awards.
#agriculture #BellCurve #centralLimitTheorem #culture #GreenRevolution #history #Mathematics #normalDistribution #NormanBorlaug #Science #statistics -
Simulating and Visualising the Central Limit Theorem
https://blog.foletta.net/post/2025-07-14-clt/
#HackerNews #Simulating #Visualising #CentralLimitTheorem #Statistics #Education
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Simulating and Visualising the Central Limit Theorem
https://blog.foletta.net/post/2025-07-14-clt/
#HackerNews #Simulating #Visualising #CentralLimitTheorem #Statistics #Education
-
Simulating and Visualising the Central Limit Theorem
https://blog.foletta.net/post/2025-07-14-clt/
#HackerNews #Simulating #Visualising #CentralLimitTheorem #Statistics #Education
-
Simulating and Visualising the Central Limit Theorem
https://blog.foletta.net/post/2025-07-14-clt/
#HackerNews #Simulating #Visualising #CentralLimitTheorem #Statistics #Education
-
Simulating and Visualising the Central Limit Theorem
https://blog.foletta.net/post/2025-07-14-clt/
#HackerNews #Simulating #Visualising #CentralLimitTheorem #Statistics #Education
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Considering referring to the central limit theorem as the CLiT in my intro stats classes. WAIT, hear me out:
1. It's critical for almost everything you really want to do in basic inferential stats; without it, nothing works right.
2. When students learn about it, they're surprised it was there all along.
3. Students need to be guided directly to it many times before they remember its importance.
4. We need fresh ideas to increase women's engagement in STEM fields...
#statistics #centrallimittheorem #normal #distribution #NotSerious #OrIsIt #teaching #professor #highered #STEM
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Considering referring to the central limit theorem as the CLiT in my intro stats classes. WAIT, hear me out:
1. It's critical for almost everything you really want to do in basic inferential stats; without it, nothing works right.
2. When students learn about it, they're surprised it was there all along.
3. Students need to be guided directly to it many times before they remember its importance.
4. We need fresh ideas to increase women's engagement in STEM fields...
#statistics #centrallimittheorem #normal #distribution #NotSerious #OrIsIt #teaching #professor #highered #STEM
-
Considering referring to the central limit theorem as the CLiT in my intro stats classes. WAIT, hear me out:
1. It's critical for almost everything you really want to do in basic inferential stats; without it, nothing works right.
2. When students learn about it, they're surprised it was there all along.
3. Students need to be guided directly to it many times before they remember its importance.
4. We need fresh ideas to increase women's engagement in STEM fields...
#statistics #centrallimittheorem #normal #distribution #NotSerious #OrIsIt #teaching #professor #highered #STEM
-
Considering referring to the central limit theorem as the CLiT in my intro stats classes. WAIT, hear me out:
1. It's critical for almost everything you really want to do in basic inferential stats; without it, nothing works right.
2. When students learn about it, they're surprised it was there all along.
3. Students need to be guided directly to it many times before they remember its importance.
4. We need fresh ideas to increase women's engagement in STEM fields...
#statistics #centrallimittheorem #normal #distribution #NotSerious #OrIsIt #teaching #professor #highered #STEM
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學習大數據分析和人工智慧前，先對兩者的基礎之一 — 統計學 — 做一個新科技反饋回統計學中央極限定理的驗證。中央極限定理是很多理工科理論和應用的基礎，但我們提出
1. 母體分配影響中央極限定理中的樣本數量，形成不同母體分配會有不同的最少樣本數
2. 尋找原因：影響第一點的原因來自中央極限定理只提到一二階動差，事實是三和四階動差同時影響樣本數
3. 自主用數字證明，提出反例證實中央極限定理未曾考量到的因素
有興趣的朋友可以使用軟體或購買書籍，自主測試中央極限定理的問題，以及為何我們提出中央極限定理的條件需要增加
https://meiyulee.github.io/leetalk/2023/09/01/clt-mistake
#統計學 #中央極限定理 #統計 #生物統計 #計量經濟學 #statistics #probability #機率論 #概率論 #econometrics #biostatistics #centrallimittheorem
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學習大數據分析和人工智慧前，先對兩者的基礎之一 — 統計學 — 做一個新科技反饋回統計學中央極限定理的驗證。中央極限定理是很多理工科理論和應用的基礎，但我們提出
1. 母體分配影響中央極限定理中的樣本數量，形成不同母體分配會有不同的最少樣本數
2. 尋找原因：影響第一點的原因來自中央極限定理只提到一二階動差，事實是三和四階動差同時影響樣本數
3. 自主用數字證明，提出反例證實中央極限定理未曾考量到的因素
有興趣的朋友可以使用軟體或購買書籍，自主測試中央極限定理的問題，以及為何我們提出中央極限定理的條件需要增加
https://meiyulee.github.io/leetalk/2023/09/01/clt-mistake
#統計學 #中央極限定理 #統計 #生物統計 #計量經濟學 #statistics #probability #機率論 #概率論 #econometrics #biostatistics #centrallimittheorem
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學習大數據分析和人工智慧前，先對兩者的基礎之一 — 統計學 — 做一個新科技反饋回統計學中央極限定理的驗證。中央極限定理是很多理工科理論和應用的基礎，但我們提出
1. 母體分配影響中央極限定理中的樣本數量，形成不同母體分配會有不同的最少樣本數
2. 尋找原因：影響第一點的原因來自中央極限定理只提到一二階動差，事實是三和四階動差同時影響樣本數
3. 自主用數字證明，提出反例證實中央極限定理未曾考量到的因素
有興趣的朋友可以使用軟體或購買書籍，自主測試中央極限定理的問題，以及為何我們提出中央極限定理的條件需要增加
https://meiyulee.github.io/leetalk/2023/09/01/clt-mistake
#統計學 #中央極限定理 #統計 #生物統計 #計量經濟學 #statistics #probability #機率論 #概率論 #econometrics #biostatistics #centrallimittheorem
-
學習大數據分析和人工智慧前，先對兩者的基礎之一 — 統計學 — 做一個新科技反饋回統計學中央極限定理的驗證。中央極限定理是很多理工科理論和應用的基礎，但我們提出
1. 母體分配影響中央極限定理中的樣本數量，形成不同母體分配會有不同的最少樣本數
2. 尋找原因：影響第一點的原因來自中央極限定理只提到一二階動差，事實是三和四階動差同時影響樣本數
3. 自主用數字證明，提出反例證實中央極限定理未曾考量到的因素
有興趣的朋友可以使用軟體或購買書籍，自主測試中央極限定理的問題，以及為何我們提出中央極限定理的條件需要增加
https://meiyulee.github.io/leetalk/2023/09/01/clt-mistake
#統計學 #中央極限定理 #統計 #生物統計 #計量經濟學 #statistics #probability #機率論 #概率論 #econometrics #biostatistics #centrallimittheorem
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@Alphastream @slyflourish Reading through the "Understanding the Action Economy" section in Tome of Foes got me back thinking about damage probability distributions. So, I threw this together to illustrate how a monster with one attack compares to one with two attacks across three rounds of combat. Both deal the same average DPR but the monster with two attacks is much more consistent.
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@Alphastream @slyflourish Reading through the "Understanding the Action Economy" section in Tome of Foes got me back thinking about damage probability distributions. So, I threw this together to illustrate how a monster with one attack compares to one with two attacks across three rounds of combat. Both deal the same average DPR but the monster with two attacks is much more consistent.
-
@Alphastream @slyflourish Reading through the "Understanding the Action Economy" section in Tome of Foes got me back thinking about damage probability distributions. So, I threw this together to illustrate how a monster with one attack compares to one with two attacks across three rounds of combat. Both deal the same average DPR but the monster with two attacks is much more consistent.
-
@Alphastream @slyflourish Reading through the "Understanding the Action Economy" section in Tome of Foes got me back thinking about damage probability distributions. So, I threw this together to illustrate how a monster with one attack compares to one with two attacks across three rounds of combat. Both deal the same average DPR but the monster with two attacks is much more consistent.
-
@Alphastream @slyflourish Reading through the "Understanding the Action Economy" section in Tome of Foes got me back thinking about damage probability distributions. So, I threw this together to illustrate how a monster with one attack compares to one with two attacks across three rounds of combat. Both deal the same average DPR but the monster with two attacks is much more consistent.
