Question

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

• A. a = 0, b = 7
• B. a = 5, b = 2
• C. a = 1, b = 6
• D. a = 3, b = 4

Answer 1

Answer: (D)

mean $=\frac{\sum x_i}{n}$
$=\frac{a+b+8+5+10}{5}=6$
$a+b+23=30$
$a+b=7$
variance $=\frac{\sum {\left(x_i-\bar{x}\right)}^2}{n}$
$=\frac{(a-6{)}^2+(b-6{)}^2+4+1+16}{5}=6.8$
$(a-6{)}^2+(b-6{)}^2+21=34$
$(a-6{)}^2+(b-6{)}^2=13$
$(a-6{)}^2+(1-a{)}^2=13$
$a^2-12a+36+1-2a+a^2=13$
$2a^2-14a+24=0$
$a^2-7a+12=0$
$(a-4)(a-3)=0$
$a=4$ or 3
and $b=3$ or 4