Samples of Size 2 Samples of Size 5 1400 1000 1200 1000 800 800 600 600 400 400 200 200 30 40 50 30 44 Sample Mean Waist Size (inches) Sample Mean Waist Size (inches) Samples of Size 10 Samples of Size 20 1500 2000 1000 1500 1000 500 500 32 36 40 34 40 Sample Mean Waist Size (inches) Sample Mean Waist Size (inches) Number of Samples Number of Samples Number of Samples Number of Samples

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 + ...