Frank’s Barber Shop is a popular local barber shop. He estimates that the time required to serve a customer on each visit has a uniform distribution between 15 minutes and 45 minutes. Simulate the service times for five customers by using the following five random numbers: 0.6905, 0.1740, 0.0443, 0.5975, 0.1178. Calculate the average of the five service times and compare it to the mean of the service-time distribution. Use Excel to generate 500 random observations and calculate the average. Compare this average to the mean of the service-time distribution

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...