Question

I am trying to determine if the dice that I have is fair, so I will toss the dice 300 times and measure how many times each side appears. Here are my results:

Side : Frequency

1 : 43

2 : 49

3 : 56

4 : 45

5 : 66

6 : 41



Looking at the data, is the dice considered “fair” meaning that each side has an equal chance of appearing?

Did I throw the dice enough times to make this determination?

Why aren’t all of the sides equal to each other?

Answer 1

You have to decide the criteria for fairness: one standard deviation, two standard deviations?
To calculate the standard deviation of those numbers:

Work out the Mean (the simple average of the numbers): Mean 50

Then for each number: subtract the Mean and square the result.:
49,1,36,25,256,81

Then work out the mean of those squared differences.74.6

Take the square root of that and we are done! sigma=8.6
under criteria of one standard deviation, it is biased to give a 5