Which of the following data has minimum variance?

Step-by-step solution

Option (a) Data 1,2,3,4,5 aligned & Variance = _ i=1 ^n (x_i-x_ avg )^2 n-1 = 1 4 [ (x_i-x_ avg )^2 ] & x_ avg = 1+2+3+4+5 5 =3 & Variance =1 / 4 & [(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2 ] & = 1 4 [4+1+0+1+4]= 10 4 =2.5 aligned aligned & Option (b) Data 1,1,2,3,6 & x_ avg = 1+1+2+3+6 5 = 13 5 =2.6 & Variance = 1 4 [(1-2.6)^2+(1-2.6)^2+ . & =4.3 & Option (c) Data 1,1,2,3,5 & Variance =2.8 & Option (d) Data 1,1,2,2,5 & Variance =2.7 & Minimum Variance is of 1,2,3,4,5 ; i.e. 2.5 . aligned