中心极限定理

R 统计学入门

Maggie Matsui

Content Developer, DataCamp

掷骰 5 次

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

# Roll 5 times
sample_of_5 <- sample(die, 5,
                      replace = TRUE)
sample_of_5

1 3 4 1 1

mean(sample_of_5)

2.0

六面骰子

# Roll 5 times and take mean
sample(die, 5, replace = TRUE) %>% mean()

4.4

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

3.8

重复 10 次：

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

样本均值的抽样分布

10 个样本均值的直方图

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

100 个样本均值的直方图

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

1000 个样本均值的直方图

统计量的抽样分布，试验次数越多越接近正态分布。

10、100、1000 个样本均值的直方图，样本数越多分布越像钟形

* 样本应当随机且独立

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

1000 组 5 次掷骰样本标准差的分布

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"

样本比例的分布也近似正态

# Estimate expected value of die
mean(sample_means)

3.48

# Estimate proportion of "Claire"s
mean(sample_props)

0.26

样本均值的抽样分布，中央有虚线

R 统计学入门