Given mean and variance of 8 observations are 9 and 9.25

Six observations are 6,7,10,12,12,13

Let the other two observations are x and y.

So 8 observations are : 6,7,10,12,12,13 ,x ,y

Now

       Mean =  (6+7+10+12+12+13+x+y)/8

=> 9 = (6+7+10+12+12+13+x+y)/8

=> 9*8 = 6+7+10+12+12+13+x+y

=> 72 = 60 + x+ y

=> x + y = 72-60

=> x + y = 12...................1

Again Given varience = 9.25

=> (1/8)*∑ (xi - mean)² = 9.25          (1<=i<=8)

=> ∑ (xi - mean)² = 9.25*8

=> ∑ (xi - mean)² = 74

=> {(6-9)² +(7-9)² + (10-9)² + (12-9)² + (12-9)² + (13-9)² + (x-9)² + (y-9)² } = 74

=> {(-3)² +(-2)² + (1)² + (3)² + (3)² + (4)² + x² + 81 - 18x + y² + 81 -18y } = 74

=> {9 + 4 + 1 + 9 + 9 + 16+ x² + y² + 81 + 81 -18(x+y) } = 74

=> {48 + x² + y² + 162 -(18*12)} = 74        (since x+y =12)

=> {48 + x² + y² + 162 -216} = 74

=> x² + y² + 210 - 216 = 74

=> x² + y² - 6 = 74

=> x² + y² = 74 + 6

=> x² + y² = 80................2

Squaring equation 1, we get

(x+y)² = 144

=> x² + y² + 2xy = 144

=> 80 + 2xy = 144

=> 2xy = 144-80

=>2xy = 64

=> xy = 64/2

=> xy = 32.............3

Now (x-y)² = x² + y² - 2xy

                  = 80 - 2*32

                  = 80 - 64

                  = 16

=> x-y = √16

=> x-y = 4, -4

case 1: when x-y = 4 and x+y = 12

After solving it, we get x = 8, y= 4

case 2: when x-y = -4 and x+y = 12

After solving it, we get x = 4, y= 8

So two numbers are 4 and 8