Four dice, each numbered in the usual way from 1 to 6, are colored white, red, green and blue respectively. after casting them a boy scored in the following way. to the white numbered he adds twice the red and blue numbered and then subtract the green numbered. assume that the boy casts the dice large number of times; calculate the mean and variance of scores.

Suppose that the numbers that the boy being cast from the dice are 3 4 5 6.
 3 stands for white, 4 stands for red, 5 stands for green and 6 stands for blue.
  We need to interpret the statement given above.   The set of numbers is 3 4 4 6 6 5.
First, we need to get the mean of this set. Add all the numbers and divide by the total number that the set has. 
 3+4+4+6+6+5=  28 / 6
                        = 4.67    The mean is 4.67
For the variance, we will use the mean above ( 4.67 )

1. Squared the mean and subtract how many numbers are present in the set. 
   4.67x4.67= 21.8089 /6 = 3.64 set aside this result
2. Next squared all the numbers present in the set and add the result 

  3x3= 9 , 4x4= 16, 4x4=16, 6x6=36, 6x6=36, 5x5=25

9+16+16+36+36+25= 138 

3. Subtract the result of #2 with #1
          138 - 3.64=  134.36 set this aside

4. Subtract 1 from the total numbers you have in your set

 6 - 1= 5 

5. Divide the result we have in #3 with the result of #4

  134.36 / 5= 26. 872

So the variance is 26.872