r - Calculating SD of compass directions using Circular -

my goal calculate mean , standard deviation series of compass degrees. since may cross 360/ 0 mark, can't use standard mean or sd calculation.

i've been using circular packing in r, seems give me correct means (though negative values used when crossing 360 mark opposed positive). sd values way small. thoughts on might wrong, or better way calculate mean , sd compass directions?

the below code attempt test calculations of mean , sd on various compass directions, , compare standard mean , sd calculation (they should agree unless cross 360/ 0 mark)

library(circular)  tester<-c(20,40,60) tester<-c(340,360,20) tester<-c(340,0,20) tester<-c(300,320,340) tester<-c(160,180,200)  tocirc<- circular(tester, type="angles", units="degrees",rotation="clock")  mean(tocirc) sd(tocirc) mean(tester) sd(tester) 

when load circular, has separate sd function calculates standard deviation circular data differently.

#data tester<-c(160,180,200) tocirc<- circular(tester, type="angles", units="degrees",rotation="clock")   sd(tocirc) #[1] 0.2864803  #the above equivalent  r = rho.circular(tocirc) #resultant length sqrt(-2*log(r)) #then sd #[1] 0.2864803 

if want use sd of base after loading circular, use sd.default

sd.default(tocirc) #[1] 20  #which equal sd.default(tester) #[1] 20 

or calculate yourself

tester<-c(340,360,20) sine = sum(sin(tester * pi/180)) #sin of each angle, convert radian first cosine = sum(cos(tester * pi/180)) #cos of each angle, convert radian first  tester_mean = (atan2(sine, cosine) * 180/pi) %% 360  mu = (tester - tester_mean + 180) %% 360 - 180 #difference of each angle mean tester_sd = sqrt(sum(mu^2)/(length(tester) - 1)) #standard deviation  tester_mean #[1] 0 tester_sd #[1] 20