Mean and Standard Deviation

Question

The number of pages in a PDF document you create has a discrete uniform distribution from 5 to 11 pages (including the end points). What are the mean and standard deviation of the number of pages in the document? Round answer 3 decimal points.

Answer 1

In a discrete uniform distribution, the mean can be calculated using the formula:

Mean = (a + b) / 2

For your example, where a = 5 and b = 11, the mean would be:

Mean = (5 + 11) / 2 = 16 / 2 = 8

The standard deviation can be calculated using the formula:

Standard Deviation = sqrt((b - a + 1)^2 - 1) / sqrt(12)

For a = 5 and b = 11, the standard deviation would be:

Standard Deviation = sqrt((11 - 5 + 1)^2 - 1) / sqrt(12) = sqrt((7)^2 - 1) / sqrt(12) = sqrt(48 / 12) = sqrt(4) = 2

So, the mean number of pages is 8, and the standard deviation is 2, rounded to 3 decimal points as requested.