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!

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