The following table gives a sample of the percentage of current users of alcohol and cigarettes in the 18- to 25-year-old age group in the United States for some recent selected years. Find the average, sample variance, and sample standard deviation of each. (Round your answers to four decimal places.) Alcohol 68 69 71 77 76 74 Cigarettes 29 16 17 22 21 25 Alcohol: mean     sample variance     sample standard deviation     Cigarettes: mean     sample variance     sample standard deviation     Which group of users is varying more? - cigarettes - alcohol     - cannot be determined

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 + ...