Suppose you roll a fair, six-sided die 100 times and then make a histogram of your results. Which of the following would most likely be a characteristic of the histogram you would obtain?
A, Skewed-right
B, Symmetric, with a central peak
C, Skewed-left
D, Uniform

Option D is correct.

The characteristic distribution obtained would be uniform.

Explanation:

A fair die is a type of die where all the faces have equal chances of showing up. So, theoretically, if a fair die is thrown a certain number of times (n), the number of times each face/number would show is n/6 or amazingly close to that; which in turn is a uniform distribution where the data is spread out evenly. Each column of the histogram will have almost equal heights.

A skew distribution will have most of the data points clustering around either the far left or far right of the distribution.

A symmetric distribution with a central peak indicates that the data spreads out from the far right with increasing frequency up till the middle of the distribution, which has the highest frequency, then the data starts reducing in frequency as we move away from this central peak towards the far right of the distribution.

Those are clearly not the type of distribution to theoretically expect from a fair die.

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