SECTION 2.5 Measures of Position 113 Extending Concepts Midquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below. Midquartile = Q1 + Q3 2 In Exercises 55 and 56, find the midquartile of the data set. 55. 5 7 1 2 3 10 8 7 5 3 56. 23 36 47 33 34 40 39 24 32 22 38 41 57. Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown. 125 150 175 200 225 250 275 300 325 350 375 400 288 200 224 275 390 177 200 210 220 240 Punk Rock Concert Jazz Concert Song length (in seconds) (a) Describe the shape of each distribution. Which concert has less variation in song lengths? (b) Which distribution is more likely to have outliers? Explain. (c) Which concert do you think has a standard deviation of 16.3? Explain. (d) Can you determine which concert lasted longer? Explain. 58. Credit Card Purchases The credit card purchases (rounded to the nearest dollar) over the last three months for you and a friend are listed. You 60 95 102 110 130 130 162 200 215 120 124 28 58 40 102 105 141 160 130 210 145 90 46 76 Friend 100 125 132 90 85 75 140 160 180 190 160 105 145 150 151 82 78 115 170 158 140 130 165 125 Use technology to draw side-by-side box-and-whisker plots that represent the data sets. Then describe the shapes of the distributions. Modified Box-and-Whisker Plot In Exercises 59–62, (a) identify any outliers and (b) draw a modified box-and-whisker plot that represents the data set. Use asterisks (*) to identify outliers. 59. 16 9 11 12 8 10 12 13 11 10 24 9 2 15 7 60. 75 78 80 75 62 72 74 75 80 95 76 72 61. 47 29 59 83 46 1 46 23 52 53 35 37 49 62. 36 38 47 50 53 54 19 27 30 47 48 50 56 60 90 62 63. Project Find a real-life data set and use the techniques of Chapter 2, including graphs and numerical quantities, to discuss the center, variation, and shape of the data set. Describe any patterns.
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