Distribution of the Sample Mean

install.packages("mosaic")

HomeRun <- read.csv("https://sullystats.github.io/Statistics6e/Data/CMC3_2020/HomeRuns_2019_traditional.csv")
head(HomeRun, n=4)

##          Player Exit_Velocity Launch_Angle Pitch_Speed Distance Opposing_Team
## 1  Nomar Mazara         109.7           27        94.7      505           CWS
## 2   Miguel Sano         113.5           25        92.3      496           CWS
## 3   Pete Alonso         110.9           30        86.6      489           MIN
## 4 Rangel Ravelo         111.5           26        84.1      487           COL

library(mosaic)
gf_histogram(~Distance,data=HomeRun,binwidth=10,color="black",fill="blue",xlab="Distance (in feet)",ylab="Frequency",title="Distance of a Home Run in 2019")

favstats(~Distance,data=HomeRun)

##  min  Q1 median  Q3 max     mean       sd    n missing
##  307 382    401 418 505 400.3023 26.01616 6653       0

mean(~Distance,data=sample(HomeRun,9))   # Find the mean of a sample of size 9

## [1] 400.2222

SamplingDist <- bind_rows(do(5000)*c(mean = mean(~Distance,data=sample(HomeRun,9))))
head(SamplingDist,n=4)

##       mean
## 1 403.5556
## 2 397.8889
## 3 408.6667
## 4 387.7778

gf_histogram(~mean,data=SamplingDist,binwidth=5,color="black",fill="blue",xlab="Mean Distance (in feet)",ylab="Frequency",title="Distribution of the Sample Mean Distance of a Home Run in 2019 with n = 9")