Consider a family with a mother, father, and two children. Let A1 = {mother has influenza}, A2 = {father has influenza}, A3 = {first child has influenza}, A4 = {second child has influenza}, B = {at least one child has influenza}, C = {at least one parent has influenza}, and D = {at least one person in the family has influenza}. 1 What does A1 ∪ A2 mean? 2 What does A1 ∩ A2 mean? 3 Are A3 and A4 mutually exclusive? 4 What does A3 ∪ B mean? 5 What does A3 ∩ B mean? 6 Express C in terms of A1, A2, A3, and A4. 7 Express D in terms of B and C. 8 What does ?̅ 1 mean? 9 What does ?̅ 2 mean?

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 + ...