The arithmetic mean of the observations 10,8,5, a, b is 6 and their variance is 6.8 , then a b is equal to

Step-by-step solution

Given observations are 10,8,5, a, b . Arithmetic Mean, aligned & A.M. = 10+8+5+a+b 5 =6 & 23+a+b=30 aligned Here, (x_i- x )^2=a^2+b^2+93-12(a+b) Variance, aligned & 1 n (x_i- x )^2=6.8 & a^2+b^2+93-12(a+b) 5 =6.8 & a^2+b^2+93-12 7=6.8 5 & a^2+b^2+93-84=34 [ a+b=7] aligned aligned & [ (a+b)^2=a^2+b^2+2 a b ] & (7)^2=25+2 a b & [using Eqs. (i) and (ii)] & 49=25+2 a b & a b=12 aligned