Final answer:
The standard deviation of rolling three dice can be found by calculating the mean of the rolls and finding the average of the squared differences between each roll and the mean.
Step-by-step explanation:
The standard deviation of rolling three dice can be calculated by first finding the mean of the rolls and then determining the average of the squared differences between each roll and the mean. To find the mean, we add up all the faces rolled and divide by the total number of rolls. For example, if we roll three dice and get 2, 4, and 6, the mean is (2 + 4 + 6)/3 = 4.
Next, we calculate the squared differences between each roll and the mean: (2-4)^2, (4-4)^2, and (6-4)^2. These differences are 4, 0, and 4, respectively.
Finally, we find the average of these squared differences, which is (4 + 0 + 4)/3 = 2. The standard deviation is then the square root of this average, so the standard deviation of rolling three dice is √2 ≈ 1.414.