* do-file for Supplementary exercise 4.71 of IPS7e

version 17 /* works also with versions 13-16 */
set obs 5
egen x=fill(540(5)560)
* type probabilities into the var2 column
rename var2 px
* direct implementation of formula
generate prod=x*px
total(prod)
* same thing in one command, puts the mean value in a new column
egen meancol=total(x*px)
* now for variance and standard deviation
egen varcol=total(px*(x-550)^2)
generate sdcol=sqrt(varcol)
* same thing for temperature in degrees F
generate xF=1.8*x+32
egen meanxF=total(xF*px)
egen varxF=total(px*(xF-1022)^2)
generate sdxF=sqrt(varxF)
browse

* the nicest approach is however to use the probabilities as weights
* frequency weights must be integers, so we convert to percentages
generate perc=int(100*px)
sum x [fweight=perc]
sum xF [fweight=perc]