* Example 5.3.1

* Generate population
clear
set obs 5
gen x = (_n+2)*2
gen Freq = 1
gen Frac = 1/5
list
twoway (bar Freq x, sort fintensity(10) ylabel(#6)), ytitle(Freq (x)) yscale(range(0 6)) xtitle(Distribution of population)

twoway (bar Frac x, sort fintensity(10) ylabel(#2)), ytitle(Relative Freq (x)) yscale(range(0 0.2)) xtitle(Distribution of population)

summarize x, detail

* Generate sampling distribution of sample mean
clear
set obs 25
gen s1 = ceil(_n/5)
gen s2 = mod(_n, 5)
replace s2=5 if s2==0
gen x1=(s1+2)*2
gen x2=(s2+2)*2
gen xMean = 0.5*(x1+x2)
summarize xMean, detail

* Generate the histogram for frequency
histogram xMean, discrete color(blue) fintensity(inten10) freq xlabel(#9) xtitle(Sampling distribution of sample mean) yscale(range(0 6)) ylabel(#6)

* Generate the histogram for density
histogram xMean, discrete color(blue) fintensity(inten10) dens xlabel(#9) xtitle(Sampling distribution of sample mean)

* Calculate the frequency, relative frequency and cumulative frequency in percentage for sample mean
tabulate xMean