find the standard deviation of first n natural numbers Share with your friends Share 1 Manbar Singh answered this The first n natural numbers are :1,2,3,4,..........n.Mean of first n natural numbers, x = 1+2+3+......+nn = 1n × nn+12 = n+12Now, variance, σ2 = ∑i=1nxi2n - x 2=12+22+....n2n - n+122=1n×nn+12n+16 - n+1n+14=n+12n+16 - n+1n+14=n+12n+16 - n+14=n+14n+2-3n-312=n+1n-112=n2-112So, variance, σ2 = n2-112Now, standard deviation, σ = n2-112 = 12n2-13 1 View Full Answer
