Using R to work through Sokal and Rohlf's Biometry: Chapter 6 (The Normal Probability Distribution), section 6.6

Previously in this series: Chapter 6 (The Normal Probability Distribution), sections 6.3-6.5.

Section 6.6 Skewness and Kurtosis

#Box 6.1 shows how to compute g1 (skewness) and g2 (kurtosis) from a frequency distribution.
#This is unlike to be how one would do it with your own table of data, 
#but it is a helpful exercise in understanding how these moment statistics work and coding.
#This section assumes you have loaded the birthweights data from the last post.

mean.bw<-sum(birthweights[-16, "frequencies"]*(birthweights[-16, "classmark"]))/samplesize
yfreq<-(
    birthweights[-16, "classmark"]-mean.bw #This is deviation from the mean (see pg 51, section 4.7)
  )

(g1<-(
        samplesize*
        sum(birthweights[-16, "frequencies"]*yfreq^3)
      )/
    (
      (samplesize-1)*(samplesize-2)*birthweights.sd^3
      )
)


(g2<-(
  (
  (samplesize+1)*samplesize*sum(birthweights[-16, "frequencies"]*yfreq^4)
   )/
  (
    (samplesize-1)*(samplesize-2)*(samplesize-3)*(birthweights.sd^4)
    )
  )-
  (
    (
      3*(samplesize-1)^2
      )/
      (
        (samplesize-2)*(samplesize-3)
        )
    )
)

#As an interesting side note, if you use the value of the mean given in the book,
birthweights.mean
#which is rounded to four decimal places, the calculation for cubing 

#(and raising to the power of 4) both were off.  The power of three one was off by 118!