The value of pi the ratio of the circumference of a circle to its diameter is known as π (pi). the value of π is an irrational number, which means that the decimal part goes on forever and there is no fixed sequence of numbers that repeats. people have found the decimal part of π to over a million places. we can statistically study the number. shown here is the value of π to 40 decimal places. construct an ungrouped frequency distribution for the digits. based on the distribution, do you think each digit appears equally in the number? 3.141592653589793238462643383279502 8841971

From the distribution, it seems as though the digits at fairly even frequencies, though we can test our intuition by doing a few calculations.

The mean (or average) frequency can tell us quite a bit here, and we can calculate it by adding together all of the frequencies and then dividing by the number of frequencies (in this case, 10, since we have 10 digits)

Doing that, we find

(1 + 4 + 5 + 7 + 4 + 5 + 2 + 3 + 5 + 5)/10 = 41/10 = 4.1

When we divide the number of digits (40) by 4.1, we find it equals roughly 10, which means that, *on average*, each of the 10 digits appeared about 4 times. With this knowledge in hand, it wouldn’t be too out-there to suggest that this distribution is going to tend to even out more and more as we continue to add further decimal approximations of π

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