Use the following to answer questions 20 and 21:  In a large population of adults, the mean IQ is 112 with a standard deviation of 20.  Suppose 200 adults are randomly selected for a market research campaign. The sampling distribution of the sample mean IQ is: a)  exactly normal, mean 112, standard deviation 20. b)  approximately normal, mean 112, standard deviation 0.1. c)  approximately normal, mean 112, standard deviation 1.414 d)  approximately normal, mean 112, standard deviation 10. The probability that the sample mean IQ is greater than 110 is: a)  079                 b)  0.46                    c)  0.54                      d)  0.921

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 + ...