104 CHAPTER 3 Describing, Exploring, and Comparing Data percentage growth rate that is the same as the six consecutive growth rates by computing the geometric mean of 1.0058, 1.0029, 1.0013, 1.0014, 1.0015, and 1.0019. 40. Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below: Quadratic mean = A Σx2 n Find the R.M.S. of these voltages measured from household current: 0, 60, 110, -110, -60, 0. How does the result compare to the mean? 41. Median When data are summarized in a frequency distribution, the median can be found by first identifying the median class, which is the class that contains the median. We then assume that the values in that class are evenly distributed and we interpolate. Letting n denote the sum of all class frequencies, and letting m denote the sum of the class frequencies that precede the median class, the median can be estimated as shown below. (lower limit of median class) + (class width) ° a n + 1 2 b - 1m + 12 frequency of median class¢ Use this procedure to find the median of the frequency distribution given in Table 3-3 on page 95. How far is that result from the median found from the original list of 1000 Los Angeles commute times listed in Data Set 31 “Commute Times” in Appendix B? Key Concept Variation is the single most important topic in statistics, so this is the single most important section in this book. This section presents three important measures of variation: range, standard deviation, and variance. These statistics are numbers, but our focus is not just computing those numbers but developing the ability to interpret and understand them. This section is not a study of arithmetic; it is about understanding and interpreting measures of variation, especially the standard deviation. 3-2 Measures of Variation STUDY HINT Part 1 of this section presents basic concepts of variation, and Part 2 presents additional concepts related to the standard deviation. Part 1 and Part 2 both include formulas for computation, but do not spend too much time memorizing formulas or doing arithmetic calculations. Instead, focus on understanding and interpreting values of standard deviation. PART 1 Basic Concepts of Variation Visualizing Variation See Figure 3-3, which shows histograms and dotplots comparing volumes of cola in cans of (1) regular Coke and (2) Special Cola. (The volumes of regular Coke are real data from Data Set 37 in Appendix B.) Recall from Section 2-3 that a dotplot is a graph of quantitative data in which each data value is plotted as a point (or dot) above a horizontal scale of values, and dots representing equal values are stacked vertically. To visualize the property of variation, refer to Figure 3-3 and note these extremely important observations about the two data sets:
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