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R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> pdf("philrain.pdf")
> 
> philrain <- read.fwf("C:\\data\\philrain.dat", width=c(8,8,8,8), 
+ col.names=c("year","ymonth","smonth","rain"))
> 
> philrain <- data.frame(philrain)
> attach(philrain)
> 
> ymonth <- factor(ymonth)
> 
> # Summary Statistics for Rainfall
> mean(rain)
[1] 367.6796
> median(rain)
[1] 340
> var(rain)
[1] 36776.90
> sd(rain)
[1] 191.7731
> min(rain)
[1] 19
> quantile(rain,c(0.25,0.5,0.75))
   25%    50%    75% 
232.75 340.00 468.00 
> max(rain)
[1] 1582
> 
> # POPULATION Mean and Variance saved to variables
> MU.rain <- mean(rain)
> SIGMA2.rain <- (length(rain)-1)*var(rain)/length(rain)
> 
> 
> # Summary Statistics for rainfall by Month of Year
> tapply(rain,ymonth,mean)
       1        2        3        4        5        6        7        8 
336.2889 300.5333 348.2000 365.0889 405.9111 417.6000 384.3333 429.2000 
       9       10       11       12 
362.3556 340.0889 351.9556 370.6000 
> tapply(rain,ymonth,sd)
       1        2        3        4        5        6        7        8 
175.8682 130.1317 149.7016 181.7714 192.9197 199.0010 183.8897 286.9646 
       9       10       11       12 
248.8752 177.4534 146.0495 155.4938 
> 
> # Plots of Rainfall
> # Histogram
> hist(rain,breaks=seq(0,1600,100))
> # Boxplot by Month of Year
> plot(ymonth,rain)
> # Time series
> plot(rain,type="o",xlab="Month", ylab="Rainfall (1/100 inches)",main="Philadelphia Monthly Rain -- 1825-1869")
> abline(h=mean(rain))
> 
> mean <- numeric(10000)
> var <- numeric(10000)
> # 10000 Random Samples of size n=30 (Sampling without replacement)
> for (i in 1:10000) {
+ ransamp <- sample(rain,30)
+ mean[i] <- mean(ransamp)
+ var[i] <- var(ransamp)
+ }
> 
> # Summary statistics for sample Mean and Variance
> mean(mean)
[1] 367.7721
> var(mean)
[1] 1162.386
> sd(mean)
[1] 34.09378
> mean(var)
[1] 36751.92
> var(var)
[1] 235190435
> sd(var)
[1] 15335.92
> 
> min(mean)
[1] 257.4333
> max(mean)
[1] 496.7667
> min(var)
[1] 9099.264
> max(var)
[1] 126039.4
> 
> 
> 
> 
> # Histogram of Sampling Distribution of Y-bar with Normal Super-Imposed 
> hist(mean,breaks=seq(200,550,10),xlab="ybar",main="Sampling Distribution of Y-bar")
> lines(225:515,10000*dnorm(225:515,MU.rain,sqrt(SIGMA2.rain/30)))
> 
> # Histogram of (n-1)S^2/SIGMA^2  with Chi-squared Super-Imposed
> hist(29*var/SIGMA2.rain,breaks=seq(0,200,2),xlab="S2",main="Sampling Distribution of Scaled S2")
> lines(seq(0,200,2),10000*dchisq(seq(0,200,2),29))
> 
> 
> 
> dev.off()
null device 
          1 
>