What is the standard deviation of 1, 2, 3, 4, and 5?

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Answer 1 · 2017-01-24T21:43:27

#sqrt(10)/2#

The formula for standard deviation is

#s=sqrt((sum(x-barx)^2)/(n-1))#

In this case #n=5#

and #barx=1/nsum_(k=1)^nx_k=1/5sum_(k=1)^5k=(1+2+3+4+5)/5=15/5=3#

then the sum of squares #sum_(k=1)^n(x-barx)_k^2# is

#sum_(k=1)^5(x-3)_k^2=(-2)^2+(-1)^2+0^2+1^2+2^2#

#=4+1+0+1+4=10#

Then we plug in

#s=sqrt((sum(x-barx)^2)/(n-1))=sqrt(10/4)=sqrt(10)/2#