Teorema limit pusat

Pengantar Statistika di R

Maggie Matsui

Content Developer, DataCamp

Melempar dadu 5 kali

die <- c(1, 2, 3, 4, 5, 6)

# Lempar 5 kali
sample_of_5 <- sample(die, 5,
                      replace = TRUE)
sample_of_5

1 3 4 1 1

mean(sample_of_5)

2.0

dadu enam sisi

# Lempar 5 kali dan ambil rerata
sample(die, 5, replace = TRUE) %>% mean()

4.4

sample(die, 5, replace = TRUE) %>% mean()

3.8

Ulangi 10 kali:

sample_means <- replicate(10, sample(die, 5, replace = TRUE) %>% mean())

sample_means

3.8 4.0 3.8 3.6 3.2 4.8 2.6 3.0 2.6 2.0

Distribusi penarikan dari rerata sampel

histogram 10 rerata sampel

replicate(100, sample(die, 5, replace = TRUE) %>% mean())

2.8 3.2 1.8 4.6 4.0 2.8 4.4 2.4 3.4 2.8 4.2 3.4 ... 2.2 3.8 3.6 3.8 4.4 4.8 2.4

histogram 100 rerata sampel

sample_means <- replicate(1000, sample(die, 5, replace = TRUE) %>% mean())

histogram 1000 rerata sampel

Distribusi penarikan suatu statistik semakin mendekati normal saat jumlah uji meningkat.

histogram 10, 100, dan 1000 rerata sampel; lebih banyak sampel membentuk kurva lonceng

* Sampel harus acak dan independen

replicate(1000, sample(die, 5, replace = TRUE) %>% sd())

Distribusi 1000 simpangan baku sampel dari 5 lemparan dadu

sales_team <- c("Amir", "Brian", "Claire", "Damian")

sample(sales_team, 10, replace = TRUE)

"Claire" "Brian"  "Brian"  "Brian"  "Damian" "Damian" "Brian"  "Brian" 
"Amir"   "Amir"

sample(sales_team, 10, replace = TRUE)

"Amir"   "Amir"   "Claire" "Amir"   "Amir"   "Brian"  "Amir"   "Claire" 
"Claire" "Claire"

Distribusi proporsi sampel juga tampak normal

# Perkirakan nilai harapan dadu
mean(sample_means)

3.48

# Perkirakan proporsi "Claire"
mean(sample_props)

0.26

Distribusi penarikan rerata sampel dengan garis putus-putus di tengah

Pengantar Statistika di R