The standard deviation and mean of five observations are 0 and 9 respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10 , then their standard deviation is

Step-by-step solution

Let the five observations are x₁, x₂, x₃, x₄, x₅ . So, mean = x₁+x₂+x₃+x₄+x₅ 5 =9 (given) x₁+x₂+x₃+x₄+x₅=45 and standard deviation = _ i=1 ^5 (9-x_i )^2 5 =0 (given) _ i=1 ^5 (9-x_i )^2=0 x_i=9 i Now, let observation x₅ is changed with y , so array lrr mean = x₁+x₂+x₃+x₄+y 5 =10 & (given) & x₁+x₂+x₃+x₄+y=50 & & 45-x₅+y=50 & (from Eq. (i)) & x₅+5=y y=14 & x₅=9 array (given) Now, the changed standard deviation is aligned & (10-x₁ )^2+ (10-x₂ )^2+ (10-x₃ )^2 + (10-x₄ )^2+(10-y)^2 5 = & 1+1+1+1+16 5 = 20 5 = 4 =2 align