Let the elements in set A be {x 1 , x 2 , x 3 , x 4 , x 5 }

Now given mean is= 5

Now subtracting 3 from each term we get,

New mean as (x 1 - 3, x 2 - 3..., x 5 - 3)= 5 - 3 = 2

So, sum of elements will be 2 x 5 = 10

Also given variance,

Var(X)= 12

Now we know that subtracting 3 from each term will not change the variance,

So, Var(x 1 - 3, x 2 - 3,... x 5 - 3)= 12

Now let elements in set 5 be {y 1 ,y 2 ….y 5 }

Given mean (y 1 ,y 2 ...y 5 ) =8

Now adding each element by 2 we get,

New mean (y 1 + 2,y 2 + 2,... y 5 + 2)= 10

So, sum of elements will be 10x5 = 50

Also given Var(y 1 , y 2 ... y 5 )= 20

Similarly new variance,

Var(y 1 + 2, y 2 + 2 ... y 5 + 2)= 20

Now finding, combined mean we get,

And combined variance

Hence, the sum of combined mean and variance will be 32 + 6 = 38

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