Suppose Burger King has run a major advertising campaign in the hopes of increasing monthly sales. To investigate the effectiveness of this campaign, Burger King randomly selected seven restaurants and recorded the monthly sales before and after the advertising. The following data represents these sales figures in thousands of dollars. Restaurant 1 2 3 4 5 6 7 After $127 $122 $145 $156 $160 $134 $108 Before $107 $110 $143 $168 $145 $125 $98 If Population 1 is defined as the year 2012 and Population 2 is defined as the year 2011, the mean of the matched-pair differences is ________. Question 7 options: 1) 8.0 2) 9.7 3) 11.9

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 + ...