A 4 6 5 7 8 9 11 10 12 hours of sleep female students

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greatest values to describe the overlap between the two data sets. a. 4 6 5 7 8 9 11 10 12 Hours of sleep Female students Male students b. 56 58 57 59 60 61 63 62 65 64 Female students Heights (inches) Male students c. Ages of People in Two Exercise Classes 10:00 A . M . Class 8:00 P . M . Class 1 8 9 2 1 2 2 7 9 9 3 0 3 4 5 7 9 7 3 2 2 2 4 0 7 5 4 3 1 5 7 0 0 6 0 7 Key: 1 8 = 18 ACTIVITY: Comparing Two Data Distributions 2 3. IN YOUR OWN WORDS How can you compare data sets that represent two populations? Use what you learned about comparing data sets to complete Exercise 3 on page 452. Recognize Usefulness of Tools How is each type of data display useful? Which do you prefer? Explain. Math Practice
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450 Chapter 10 Probability and Statistics Lesson 10.7 Lesson Tutorials Recall that you use the mean and the mean absolute deviation (MAD) to describe symmetric distributions of data. You use the median and the interquartile range (IQR) to describe skewed distributions of data. To compare two populations, use the mean and the MAD when both distributions are symmetric. Use the median and the IQR when either one or both distributions are skewed. EXAMPLE Comparing Populations 1 The double dot plot shows the time that each candidate in a debate spent answering each of 15 questions. 30 50 40 60 70 80 100 90 120 110 Candidate B Candidate A Times (seconds) a. Compare the populations using measures of center and variation. Both distributions are approximately symmetric, so use the mean and the MAD. Candidate A Candidate B Mean = 1260 15 = 84 Mean = 870 15 = 58 MAD = 244 15 16 MAD = 236 15 16 So, the variation in the times was about the same, but Candidate A had a greater mean time. b. Express the difference in the measures of center as a multiple of the measure of variation. mean for Candidate A mean for Candidate B ———— MAD = 26 16 1.6 So, the difference in the means is about 1.6 times the MAD. 1. WHAT IF? Each value in the dot plot for Candidate A increases by 30 seconds. How does this affect the answers in Example 1? Explain. Exercises 4–6 Study Tip You can more easily see the visual overlap of dot plots that are aligned vertically. Study Tip When two populations have similar variabilities, the value in part (b) describes the visual overlap between the data. In general, the greater the value, the less the overlap.
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Section 10.7 Comparing Populations 451 EXAMPLE Using Random Samples to Compare Populations 2 You want to compare the costs of speeding tickets in two states. a. The double box-and-whisker plot shows a random sample of 10 speeding tickets issued in two states. Compare the samples using measures of center and variation. Can you use this to make a valid comparison about speeding tickets in the two states? Explain. 50 90 70 110 80 60 100 120 130 150 140 160 Cost (dollars) State B State A Both distributions are skewed right, so use the median and the IQR. The median and the IQR for State A, 70 and 20, are less than the median and the IQR for State B, 80 and 30. However, the sample size is too small and the variability is too great to conclude that speeding tickets generally cost more in State B.
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