A restaurant specializes in pizza that is baked in a wood-burning oven. The sales of food and drink in this restaurant vary from day to day. Past records indicate that the daily sales follow a distribution with a mean of $900 and a standard deviation of $300. The mean sales for the seven days in a week are computed each week. Each week is considered a sample of size n = 7 days.   What would we expect the weekly sample mean sales amounts to fluctuate around (in dollars)? • How much variability would you expect in the weekly sample mean sales figures? • Find the standard deviation of the sampling distribution of the sample mean, and interpret this standard deviation.

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 + ...