The Uniform Distribution · Try It 1

The data that follow are the number of passengers on 35 different charter fishing boats. The sample mean = 7.9 and the sample standard deviation = 4.33. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. State the values of a and b. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.

$$\begin{array}{ccccccc}\text{1}& \text{12}& \text{4}& \text{10}& \text{4}& \text{14}& \text{11}\\ \text{7}& \text{11}& \text{4}& \text{13}& \text{2}& \text{4}& \text{6}\\ \text{3}& \text{10}& \text{0}& \text{12}& \text{6}& \text{9}& \text{10}\\ \text{5}& \text{13}& \text{4}& \text{10}& \text{14}& \text{12}& \text{11}\\ \text{6}& \text{10}& \text{11}& \text{0}& \text{11}& \text{13}& \text{2}\end{array}$$

OpenStax, Statistics · §5.2 The Uniform Distribution · Try It 1