The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11,16 and 20. What are the other two observations?

Step-by-step solution

x =14, Var (x)=13.2 Observations =11,16,20, a, b x = 11+16+20+a+b 5 =14a+b=23 ....(1) var (X)= x_i^2 n -( x )^213.2= 11^2+16^2+20^2+a^2+b^2 5 -(14)^266=777-980+a^2+b^2a^2+b^2=269 .....(2) By (1) & (2). we get a=13, b=10