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

1 Answer
Jan 24, 2017

sqrt(10)/2102

Explanation:

The formula for standard deviation is

s=sqrt((sum(x-barx)^2)/(n-1))s=(x¯x)2n1

In this case n=5n=5

and barx=1/nsum_(k=1)^nx_k=1/5sum_(k=1)^5k=(1+2+3+4+5)/5=15/5=3¯x=1nnk=1xk=155k=1k=1+2+3+4+55=155=3

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

sum_(k=1)^5(x-3)_k^2=(-2)^2+(-1)^2+0^2+1^2+2^25k=1(x3)2k=(2)2+(1)2+02+12+22

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

Then we plug in

s=sqrt((sum(x-barx)^2)/(n-1))=sqrt(10/4)=sqrt(10)/2s=(x¯x)2n1=104=102