U.S. companies lose  billion 63.2 per year from workers with insomnia. According to 2013 a  article in The Wall Street Journal, workers lose an average of 7.8  days of productivity per year due to lack of sleep. The following data show the number of hours of sleep attained during a recent night for a sample of  20 workers. 7 5 10 7 7 8 8 5 9 6 7 7 9 6 8 8 9 5 10 7 a. What is the mean number of hours of sleep for this sample (to  decimals)? b. What is the variance? Standard deviation (to  decimals)? Variance   Standard deviation

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 + ...