5:44 File Details ARC Sp24 STAT 300 LEC 12125 Abdul Exercises 3.1 Understanding the Concepts and Skills 3.1 Explain in detail the purpose of a measure of center. 3.2 Name and describe the three most important measures of center. 3.3 Of the mean, median, and mode, which is the only one appro- priate for use with qualitative data? 3.4 True or false: The mean, median, and mode can all be used with quantitative data. Explain your answer. 3.7 Floor Space. The U.S. Department Housing and Urban Development compiles information on new, privately owned single- family houses. According to the document Characteristics of New Housing, in 2012 the mean floor space of such homes was 2505 sq ft and the median was 2306 sq ft. Which measure of center do you think is more appropriate? Justify your answer. 3.8 Net Worth. The Board of Governors of the Federal Reserve System publishes information on family net worth in the Survey of Consumer Finances. In 2010, the mean net worth of families in the United States was $498.8 thousand and the median net worth was $77.3 thousand. Which measure of center do you think is more appropriate? Explain your answer. In Exercises 3.9-3.14, we have provided simple data sets for you to practice the basics of finding measures of center. For each data set, determine the a. mean. 3.9 4, 0,5 3.11 1, 2, 4, 4 3.13 1, 9, 8, 4, 3 b. median. 3.15 Explain what each symbol represents. a. Σ b. n 3.10 3, 5, 7 c. mode(s). 3.12 2,5, 0, -1 3.14 4, 2, 0, 2, 2 3.16 For a particular population, is the population mean a variable? What about a sample mean? 6 3.17 Consider these sample data: X₁ = 1, x₂ = 7, x3 = 4, X45, X5 10. a. Find n. b. Compute Ex¡. c. Determine x 3.18 Consider these sample data: x₁ = 12, x₂ = 8, x3 = 9, X4 = 17. a. Find n. b. Compute Ex₁. c. Determine x. Dashboard Applying the Concepts and Skills In Exercises 3.19-3.26, find the b. median. c. X c. mode(s). a. mean. For the mean and the median, round each answer to one more decimal place than that used for the observations. ◄ Previous 3.19 Amphibian Embryos. In a study of the effects of radiation on amphibian embryos titled "Shedding Light on Ultraviolet Radiation and Amphibian Embryos" (BioScience, Vol. 53, No. 6, pp. 551-561), L. Licht recorded the time it took for a sample of seven different species of frogs' and toads' eggs to hatch. The following table shows the times to hatch, in days. 7 11 6 5 3.20 Hurricanes. An article by D. Schaefer et al. (Journal of Trop- ical Ecology, Vol. 16, pp. 189-207) reported on a long-term study of the effects of hurricanes on tropical streams of the Luquillo Experi- mental Forest in Puerto Rico. The study shows that Hurricane Hugo had a significant impact on stream water chemistry. The following table shows a sample of 10 ammonia fluxes in the first year after 5 11 000 000 Calendar 3.5 Consider the data set 1, 2, 3, 4, 5, 6, 7, 8, 9. a. Obtain the mean and median of the data. b. Replace the 9 in the data set by 99 and again compute the mean and median. Decide which measure of center works better here, and explain your answer. c. For the data set in part (b), the mean is neither central nor typi- cal for the data. The lack of what property of the mean accounts for this result? 3.6 Complete the following statement: A descriptive measure is resistant if.... D 96 66 116 57 3.21 Tornado Touchdowns. Each year, tornadoes that touch down are recorded by the Storm Prediction Center and published in Monthly Tornado Statistics. The following table gives the number of tornadoes that touched down in the United States during each month of one year. [SOURCE: National Oceanic and Atmospheric Administration] 6 CO 3.1 Measures of Center 3.22 Technical Merit. In one Winter Olympics, Michelle Kwan competed in the Short Program ladies singles event. From nine judges, she received scores ranging from 1 (poor) to 6 (perfect). The following table provides the scores that the judges gave her on tech- nical merit, found in an article by S. Berry (Chance, Vol. 15, No. 2, pp. 14-18). To Do 147 147 175 154 88 154 3 2 47 118 204 97 68 86 62 57 98 99 Person 3.23 Billionaires' Club. Each year, Forbes magazine compiles a list of the 400 richest Americans. As of September 19, 2012, the top 10 on the list are as shown in the following table. 5.8 5.7 5.9 5.7 5.5 5.7 5.7 5.7 5.6 S. Robson Walton Michael Bloomberg Bill Gates Warren Buffett Larry Ellison Charles Koch David Koch Christy Walton & family Jim Walton Alice Walton Wealth ($ billions) 66.0 46.0 41.0 31.0 31.0 27.9 3.24 Tablet Computers. Tablet personal computers such as iPad and Kindle Fire are one-piece portable computers that typically offer a touchscreen. Tablets are available in different sizes but generally offer a screen that is greater than 7 inches diagonally. Consumer Reports reviews tablets of different sizes and Internet capabilities. The battery lives, in hours, for a sample of tablets with screen sizes between 9 and 12 inches are provided in the following table. 101 26.8 26.3 26.1 25.0 3.25 The Beatles. The English rock band, The Beatles, was formed in Liverpool in 1960. There are 12 studio albums that are considered part of their core catalogue. In the article, "Length of The Beatles' Songs" (Chance, Vol. 25, No. 1, pp. 30-33), T. Koyama lists the album title, date of release, and number of songs on each album. Here 8.4 5.6 10.9 10.8 11.5 8.0 8.5 12.9 Notifications Next □ Inbox 1