The mean of the numbers a, b, 8,5 and 10 is 6 and the variance is 6.80 , then the possible values of a and b are

Step-by-step solution

Given data, a, b, 8,5,10 Mean = a+b+8+5+10 5 6= a+b+23 5 a+b=7 ...(i) Variance = (a-6)^2+(b-6)^2+(8-6)^2+(5-6)^2+(10-6)^2 5 6.80= a^2+36-12 a+b^2+36-12 b+4+1+16 5 array ll & 34=a^2+b^2-12 a-12 b+93 & a^2+b^2-12(a+b)=-59 array array rrr & a^2+b^2-12(7) & =-59 & a^2+b^2 =25 array a^2+(7-a)^2=25 [from Eq. (i), b=7-a ] array ll & 2 a^2+49-14 a=25 & 2 a^2-14 a+24=0 array a^2-7 a+12=0(a-4)(a-3)=0 a=4 or a=3 If a=3 b=7-3=4