Statistics Practice Test 1

The mean of the numbers a, b, 8, 5, 10 is 6
The sum of numbers = a + b + 8 + 5 + 10 = 30
a + b + 23 = 30
a + b = 7 ......(i)
Variance = 6.80 ${\mathit{a}}^2+{\mathit{b}}^2-12\left(\mathit{a}+\mathit{b}\right)+93=34$
${\mathit{a}}^2+{\mathit{b}}^2-12\left(7\right)+93=34$
${\mathit{a}}^2+{\mathit{b}}^2-84+93=34$
${\mathit{a}}^2+{\mathit{b}}^2=34-9$
${\mathit{a}}^2+{\mathit{b}}^2=25$
${\left(\mathit{a}+\mathit{b}\right)}^2-2\mathit{a}\mathit{b}=25$
${\left(7\right)}^2-2\mathit{a}\mathit{b}=25$
$-2\mathit{a}\mathit{b}=25-49$
$-2\mathit{a}\mathit{b}=-24$
$2\mathit{a}\mathit{b}=24$
$\mathit{a}\mathit{b}=12$
$\mathit{b}=\frac{12}{\mathit{a}}$
Substituting this value in equation (i) we get
$\mathit{a}+\left(\frac{12}{\mathit{a}}\right)=7$
${\mathit{a}}^2+12=7\mathit{a}$
${\mathit{a}}^2-7\mathit{a}+12=0$
${\mathit{a}}^2-4\mathit{a}-3\mathit{a}+12=0$
$\mathit{a}\left(\mathit{a}-4\right)-3\left(\mathit{a}-4\right)=0$
$\mathit{a}=4,3$
Value of a and b is 3, 4 respectively.