Linked Questions

2 votes
1 answer
10k views

How does the Central Limit Theorem show that the Binomial Distribution is approximately Normal for a large value of n? [duplicate]

This is my understanding of what the Central Limit Theorem (CLT) is: if you take a number of samples, each containing a large number of observations, and calculate their respective sample means, then ...
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  • 189
1 vote
1 answer
2k views

What does the y-axis of a normal distribution represent? [duplicate]

In a normal distribution ,as far as I know distribution represents frequency of sth.But then how come ...
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  • 111
1 vote
0 answers
697 views

What does "properly normalized" mean in CLT? [duplicate]

What does "properly normalized" mean in CLT? https://en.wikipedia.org/wiki/Central_limit_theorem In probability theory, the central limit theorem (CLT) establishes that, in some situations, when ...
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  • 3,207
1 vote
1 answer
125 views

Central Limit Theorem - intuitive explanation without deep math [duplicate]

The Central Limit Theorem says that the distribution of the sample mean is approximately normal. Is there any intuitive explanation for why this should be so? I know it can be proven with deep math, ...
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  • 6,003
1 vote
0 answers
198 views

normalization coefficient in the central limit theorem [duplicate]

why do we use normalization coefficient in the central limit theorem? For CLT we use $\sqrt{n}$ as the normalization factor, but why do we need it?
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  • 139
1 vote
0 answers
153 views

Central Limit Theorem [duplicate]

Possible Duplicate: What intuitive explanation is there for the central limit theorem? I am in an introductory statistics course, and I am having trouble understanding the Central Limit Theorem. ...
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  • 11
1 vote
1 answer
107 views

The central limit theorem, What it means [duplicate]

For instance I have a hypothetical data like the one below ...
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1 vote
0 answers
61 views

Central limit theorem on distributions with support other than $\mathbb{R}$ [duplicate]

Let $X_1,\dots,X_n \overset{iid}\sim exp(1)$. But then $\bar{X}$ is supposed to approach a normal distribution? I agree that the skewness will slow such convergence, but that isn't my issue. The ...
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  • 32.2k
1 vote
0 answers
46 views

Is the mean of n independent Bernoulli random variables normal? [duplicate]

I'm trying to figure out the difference between an A/B split test and an ANOVA test and I came across this article. It suggests that the mean of $n$ independent Bernoulli random variables is normally ...
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  • 500
1 vote
0 answers
19 views

Normal distribution in nature: additive result of multiple variables? [duplicate]

We found normal distribution is so common in nature, such as many measurement of species (weight, height or size). From the point of central Limit Theorem, Can I intuitively understand this as the ...
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  • 789
529 votes
23 answers
283k views

Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
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  • 5,535
93 votes
10 answers
21k views

What is meant by a "random variable"?

What do they mean when they say "random variable"?
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  • 2,078
52 votes
6 answers
5k views

Debunking wrong CLT statement

The central limit theorem (CLT) gives some nice properties about converging to a normal distribution. Prior to studying statistics formally, I was under the extremely wrong impression that the CLT ...
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  • 32.2k
47 votes
4 answers
14k views

Where does $\sqrt{n}$ come from in central limit theorem (CLT)?

A very simple version of central limited theorem as below $$ \sqrt{n}\bigg(\bigg(\frac{1}{n}\sum_{i=1}^n X_i\bigg) - \mu\bigg)\ \xrightarrow{d}\ \mathcal{N}(0,\;\sigma^2) $$ which is Lindeberg–Lévy ...
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  • 5,849
34 votes
7 answers
4k views

How do you convey the beauty of the Central Limit Theorem to a non-statistician?

My father is a math enthusiast, but not interested in statistics much. It would be neat to try to illustrate some of the wonderful bits of statistics, and the CLT is a prime candidate. How would you ...

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