The central limit theorem

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

Rolling a die five times

Roll	Result
1	1
2	3
3	4
4	1
5	1

 

$Mean(Results) = 2 $

Rolling a die five times

Roll	Result
1	4
2	4
3	5
4	3
5	6

 

$Mean(Results) = 4.4 $

Roll	Result
1	1
2	3
3	1
4	5
5	6

 

$Mean(Results) = 3.2 $

10 sets of five die rolls

• Roll a die five times
• Record the mean
• Repeat 10 times

Set	Mean
1	3.8
2	4.0
3	3.8
4	3.6
5	3.2
6	4.8
7	2.6
8	3.0
9	2.6
10	2.0

Sampling distributions

Sampling distribution of the sample mean

100 sample means

1000 sample means

10000 sample means

100000 sample means

One million sample means

Central limit theorem

The sampling distribution of a statistic becomes closer to the normal distribution as the size of the sample increases.

* Samples should be random and independent

Standard deviation and the CLT

Proportions and the CLT

Roll	Result
1	2
2	1
3	4
4	2
5	6

 

• $\frac{1}{5}$ or 20% are a 4

Set	Mean
1	4
2	4
3	1
4	4
5	3

 

• $\frac{3}{5}$ or 60% are a 4

Sampling distribution of proportion

Mean of the sampling distribution

Benefits of the central limit theorem

Let's practice!

Introduction to Statistics