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pp.34-50 fall 2009

# pp.34-50 fall 2009 - 34 Summary Statistics Recall that...

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Summary Statistics Recall that descriptive statistics consists of tabular and graphical displays of data and summary statistics. Summary statistics are numerical values computed from data set. They provide information about some aspect of the data set. The most common summary statistics are averages , measures of location , and measures of dispersion . Averages. There are many different averages that can be computed for data sets. The most common are the (arithmetic) mean, the weighted mean, the median and the mode. Mean The most frequently used average is the (arithmetic) mean. Typically, when people say “the average” they mean the mean. Mean—the arithmetic center of a set of quantitative, interval/ratio level data. The mean is the balancing point (the center of gravity) for the data set. The population mean, “mu” is computed using the formula: N x μ = 34

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where: μ is the population mean (mu) x is the individual value in data set N = population size The convention is the use Greek letters to represent the aspect of a population that is of interest (the parameter). Parameter—a descriptive measure of a population. Example: The number of freshman that reside in each of the 6 dormitories of Greer University are: 302, 291, 280, 178, 135, 117 The mean is number of students in a dorm at this University is: N x = μ = 17 . 217 6 1303 6 117 135 178 280 291 302 = = + + + + + Another example: The following are weekly earnings for all nine loan officers of a local branch of a large bank: \$775 \$815 \$790 \$845 \$910 \$785 \$715 \$825 \$690 Calculate the mean weekly earnings, μ . N x = μ = 9 7150 = \$794.44 35
You can also calculate the mean for sample data. The sample mean is used as an estimate of the population mean: The sample mean is: n x x = where: x = x-bar, is the sample mean x = individual value of a quantitative variable n = sample size Statistic—a descriptive measure computed from a sample. Used to estimate a population parameter. Example : A random sample of five grocery stores charged the following for a Snickers candy bar: 4 45 0 89 5 x \$0.89+\$0.77+\$1.05+\$0.79+\$0.95 \$ . x = = = \$ . n 5 = The sample mean price for a Snickers bar is \$0.89. Another example : A student concerned about the price of new college text book is selected a random sample of 16 new textbooks from the college bookstore. The priced for each was recorded. The data, in dollars, have already been sorted in the table below: 105 110 117 129 36

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105 113 119 135 110 115 119 140 110 115 125 250 x = 2017/16 = 126.06 On average, a new college textbook costs \$126.06. After the mean, the median is probably the most often used average. Median —the middle value in a set of ordered data.
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