In September 2007, U.S home prices fell at a record pace, and price declines in Los Angeles and Orange Counties in California outpaced other major metropolitan areas ( Los Angeles Times November 28, 2007). The report was based on the standard and poor's/Case-Shiller index that measures the value of single - family homes based on their sales histories. According to this index, the prices in San Diego dropped by an average of 9.6% from a year earlier. Assume that the survey was based on recent sales of 34 houses in San Diego that also resulted in a standard  deviation of 5.2%. Can we conclude that the mean drop of all home prices in San Diego is greater than the 7% drop in Los Angeles?.

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 + ...