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Price of Chevy Cobalts The following data represent the sales price in dollars for nine 2-year- old Chevrolet Cobalts in the Los Angeles area. 14050 13909 12909 10905 9980 8998 7889 7200 5500 Source: cars.com (a) Determine the sample mean and median price. (b) Determine the range, sample standard deviation, and interquartile range. (c) Redo (a) and (b) if the data value 14,050 was incorrectly entered as 41,050. How does this change affect the mean? The median? the range? the standard deviation? the interquartile range? Which of these values is resistant?Determine the range of the homework data from. The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Factoring Polynomials. 48 88 57 109 111 193 71 83 Source: MyMathLab(a) Determine the standard deviation of the homework data from The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Factoring Polynomials. 48 57 109 111 71 83 Source: MyMathLab (b) By hand, determine and interpret the interquartile range of the homework data from Problem. The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 88 57 109 11 93 71 83 Source: MyMathLab (c) Which of these two measures of dispersion is resistant? Why? Problem The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 83 57 109 111 93 71 83 Source: MyMathLab (a) Determine the mean amount of time spent doing Section homework. (b) Determine the median amount of time spent doing Section homework. (c) Suppose the observation 109 minutes is incorrectly recorded as 1009 minutes. Recompute the mean and the median. What do you notice? What property of the median does this illustrate?Skinfold Thickness Procedure One method of estimating body fat is through skinfold thickness measurement. The measurement can use from three to nine different standard anatomical sites around the body. The right side is usually only measured (for consistency). The tester pinches the skin at the appropriate site to raise a double layer of skin and the underlying adipose tissue. but not the muscle. Calipers are then applied 1 centimeter below and at right angles to the pinch and a reading is taken 2 seconds later. The mean of two measurements should be taken. If the two measurements differ greatly, a third should be done and then the median value taken. Explain why a median is used as the measure of central tendency when three measures are taken, rather than the mean.Answer the following based on the histograms shown to the right. (a) Which measure of central tendency would you recommend reporting for the data whose histogram is shown in Figure I? Why? (b) Which one has more dispersion? Explain. 20 200 700 16 Frequency 480 520 IIThe median for the given set of six ordered data values is 28.5. What is the missing value? 7 12 21 41 50Miles per Gallon The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon. Source: www.fueleconomy.gov 34.0, 33.2. 37.0, 29.4, 23.8. 25.9\fConcrete Mix A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The concrete is poured into casting cylinders and allowed to set for 28 days. The concrete's strength is then measured. The following data represent the strength of nine randomly selected casts (in psi). Compute the mean, median, and mode strength of the concrete [n psi)- 3980, 4090, 3200, 3100, 2040. 3830. 4080. 4040. 3780M&Ms The following data represent the weights (in grams) of a simple random sample of 50 M&M plain candies. 0.87 0.88 0.82 0.90 0.90 0.84 0.84 10.87 0.91 091 0.86 0.89 0.88 0.88 0.89 0.79 0.82 0.83 0.90 0.88 0.84 0.93 0.81 0.90 0.88 0.92 0.85 0.84 0.84 0.86 Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M&M?Old Faithful We have all heard of the Old Faithful geyser in Yellowstone National Park. However, there is another, less famous, Old Faithful geyser in Calistoga, California. The following data represent the length of eruption (in seconds) for a random sample of eruptions of the California Old Faithful. 108 | 108 66 105 | 103 103 94 102 99 106 110 113 100 101 107 110 92 108 Determine the shape of the distribution of length of eruption by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the length of eruption?A Dealer's Profit The following data represent the profit (in dollars) of a new-car dealer for a random sample of 40 sales. 781 1038 453 1446 3082 501 451 1826 1348 3001 1342 1889 580 0 2909 2883 480 1864 1064 2978 149 1291 507 261 540 543 87 798 673 2862 1892 1783 2186 398 528 730 2324 2823 1678 4148 Determine the shape of the distribution of new-car profit by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the profit?Political Views A sample of 30 registered voters was surveyed in which the respondents were asked, "Do you consider your political views to be conservative, moderate, or liberal?" The results of the survey are shown in the table Liberal Conservative Moderate Moderate Liberal Moderate Liberal Moderate Conservative Moderate Conservative Moderate Moderate Moderate Liberal Liberal Moderate Liberal Conservative | Moderate Moderate Liberal Conservative Liberal Liberal Conservative Liberal Conservative | Moderate Conservative (a) Determine the mode political view. (b) Do you think it would be a good idea to rotate the choices conservative, moderate, or liberal in the question? Why?\fMr. Zuro finds the mean height of all 14 students in his statistics class to be 68.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 65 inches tall. What is the mean height of the 15 students in the class?You are negotiating a contract for the Players Association of the NBA. Which measure of central tendency will you use to support your claim that the average player's salary needs to be increased? Why? As the chief negotiator for the owners, which measure would you use to refute the claim made by the Players Association?Which histogram depicts a higher standard deviation? Justify your answe Frequency 40 44 48 52 56 60 10 Frequency 30 35 40 -45 50 55 60 65 70 75 (b)Questions about authorship of unattributed documents are one of the many problems confronting historians. Statistical analyses, when combined with other historical facts, often help resolve these mysteries. One such historical conundrum is the identity of the writer known as A MOURNER. A letter appearing in the February 26. 1770, issue of The Boston Gazette and Country Joumal is as follows: The general Sympathy and Concern for the Murder of the Lad by the base and infamous Richardson on the 22d Instant, will be sufficient Reason for your Notifying the Public that he will be buried from his Father's House in Frogg Lane, opposite Liberty-Tree, on Monday next, when all the Friends of Liberty may have an Opportunity of paying their last Respects to the Remains of this little Hero and first Martyr to the noble Cause-Whose manly Spirit (after this Accident happened) appear'd in his discreet Answers to his Doctor, his Thanks to the Clergymen who prayed with him, and Parents, and while he underwent the greatest Distress of bodily Pain; and with which he met the King of Terrors. These Things, together with the several heroic Pieces found in his Pocket, particularly Wolfe's Summit of human Glory, gives Reason to think he had a martial Genius, and would have made a clever Man. A MOURNER. The Lad the writer refers to is Christopher Sider, an 11-year-old son of a poor German immigrant. Sider was shot and killed on February 22, 1770, in a civil disturbance involving schoolboys. patriot supporters of the nonimportation agreement, and champions of the English crown, preceding the Boston Massacre by just a couple of weeks. From a historical perspective, the identity of A MOURNER remains a mystery. However, it seems clear from the letter's text that the author supported the patriot position, narrowing the field of possible writers. Ordinarily. a statistical analysis of word frequencies contained in the contested document compared with frequency analyses for known authors permit an identity inference to be drawn. Unfortunately, this letter is too short for this strategy. Another possibility is based on the frequencies of word lengths. In this case, a simple letter count is generated for each word in the document. Proper names, numbers, abbreviations, and titles are removed from consideration, because these do not represent normal vocabulary use. Care must be taken in choosing comparison texts, since colonial publishers habitually incorporated their own spellings into their essays they printed. Therefore, it is desirable to get comparison texts from the same printer the contested material came from. The following table contains the summary analysis for six passages printed in The Boston Gazette and Country Joumal in early 1770. The Tom Sturdy (probably a pseudonym) text was included because of the use of the phrase "Friends of Liberty." which appears in A MOURNER's letter, as opposed to the more familiar "Sons of Liberty." John Hancock, James Otis, and Samuel Adams are included because they are well-known patriots who frequently wrote articles carried by the Boston papers. Samuel Adams' essay used in this analysis was signed VINDEX, one of his many pseudonyms. The table presents three summaries of work penned by Adams: The first two originate from two separate sections of the VINDEX essay and the last is a compilation of the first two. Summary Statistics of Word Length from Sample Passages by Various Potential Authors of the Letter Signed A MOURNER Tem Sturdy John Hancock James Ofis Samuel Adams-| Samuel Adams- Samuel Adams1 8 Mean Median Mode 2 3 2 2 2 Standard deviation 2.17 275 2 8 270 Sample variance TRA Range 13 9 14 12 16 Minimum 1 I I Maximum 14 10 13 17 17 795 842 1482 Count 121 176 151 Generate a data set consisting of the length of each word used in the letter signed by A MOURNER. Be sure to disregard any text that uses proper names, numbers, abbreviations, or titles