How can you compare the results to randomly generated data?
See solution.
Practice makes perfect
We are given that a 12-sided die was invented to overcome the imbalance of standard playing dice. Let's take a look at the results of rolling this die.
Based on the table and the graph, we can see that number 6 came up more often than the number 1. Therefore, one possible conjecture we could make is the following.
When rolling a 12-sided die, we can also observe the imbalance between the frequency of rolling 1 and 6.
To test our conjecture, we can think of an experiment. If we were wrong and die was balanced, then the histogram based on randomly generated results would look roughly the same as the one we drew. Let's assign integers from 1 to 12 to each possible number we can roll, including the fact that each number from 1 to 6 appears twice.
Rolled Number
Integers
1
1,2
2
3,4
3
5,6
4
7,8
5
9,10
6
11,12
Now, using a random number generator we could generate 27 090 numbers between 1 and 12 and draw a histogram of the results. Notice that the more numbers we generate, the more accurate of a distribution we could draw.
This time the bars are approximately the same height and we do not observe that 6 came up more often than 1. Therefore, the designed 12- sided die is also possibly imbalanced. If we think about it more it makes sense because sides with 6 dots will be still the lightest sides.
