# investigation of pennies' ages

# first construct the data string data1
data1 <- c(rep(0,49), rep(1,51), rep(2,50), rep(3,85), rep(4,47)) 
data1 <- c(data1, rep(5,61), rep(6,29), rep(7,29), rep(8,32)) 
data1 <- c(data1, rep(9,21), rep(10,36), rep(11,38), rep(12,30))
data1 <- c(data1, rep(13,27), rep(14,24), rep(15,34), rep(16,38))    
data1 <- c(data1, rep(17,37),rep(18,24), rep(19,32), rep(20,26)) 
data1 <- c(data1, rep(21,23), rep(22,27), rep(23,22), rep(24,19)) 
data1 <- c(data1, rep(25,10), rep(26,10), rep(27,12), rep(28,13)) 
data1 <- c(data1, rep(29,8), rep(30,12), rep(31,5), rep(32,6))
data1 <- c(data1, rep(33,6), rep(34,1), rep(35,11), rep(36,2))
data1 <- c(data1, rep(37,4), rep(38,2), rep(39,1), rep(40,3)) 
data1 <- c(data1, rep(46,1), rep(58,1), rep(59,1))

# now get descriptives
summary (data1) 
hist(data1, main="Distribution of Pennies Ages", xlab="years old", 
          ylab="count”")

# now take samples n=2, 5, 10, 20, and 50
# first, initialized subscripted variables in for loops
samp2 <- c() ; samp5 <- c() ; samp10 <- c()
samp20 <- c() ; samp50 <- c()

# now generate samples
for (i in 1:100) {
     samp <- sample(data1, 2, replace=FALSE)
samp2[i] <- mean(samp)
}
for (i in 1:100) {
     samp <- sample(data1, 5, replace=FALSE)
samp5[i] <- mean(samp)
}
for (i in 1:100) {
     samp <- sample(data1, 10, replace=FALSE)
samp10[i] <- mean(samp)
}
for (i in 1:100) {
     samp <- sample(data1, 20, replace=FALSE)
samp20[i] <- mean(samp)
}
for (i in 1:100) {
     samp <- sample(data1, 50, replace=FALSE)
samp50[i] <- mean(samp)
}

hist(samp2, main="sampling distribution for n=2", xlab="mean",
          ylab="count")
hist(samp5, main="sampling distribution for n=5", xlab="mean",
          ylab="count")
hist(samp10, main="sampling distribution for n=10", xlab="mean",
          ylab="count")
hist(samp20, main="sampling distribution for n=20", xlab="mean",
          ylab="count")
hist(samp50, main="sampling distribution for n=50", xlab="mean",
          ylab="count")