Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8,308 1,474 1,872 8,879 2,459 11,413 508 14,138 6,552 1,950 2,818 1,256 10,498 7,578 4,119 4,441 739 2,227 3,653 (a) Provide a five-number summary (in million dollars). 5,894 8,305 minimum 508 million dollars first quartile 1911 million dollars median 4119 million dollars third quartile 8306.5 million dollars maximum 14138 million dollars (b) Compute the lower and upper limits (in million dollars). lower limit upper limit 0 17899.75 million dollars million dollars (c) Do the data contain any outliers? All of the values are within the limits, therefore there are no outliers. (d) The largest company on this list has sales of $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error? This number would have shown up as an outlier. Consider a sample with data values of 20, 26, 28, 15, 30, 34, 27, and 26. Compute the range. 19 Compute the interquartile range. 6 Compute the sample variance. (Round your answer to two decimal places.) 34.50 Compute the sample standard deviation. (Round your answer to two decimal places.) 5.87 Need Help? Read It Master It Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determine the minimum percentage of the data within each of the following ranges. (Round your answers to the nearest integer.) (a) 20 to 40 75 % (b) 15 to 45 88.9 (c) 23 to 37 (d) 16 to 44 (e) 14 to 46 % % % % The Panama Railroad Company was established in 1850 to construct a railroad across the isthmus that would allow fast and easy access between the Atlantic and Pacific Oceans. The following table provides annual returns for Panama Railroad stock from 1853 through 1880. Return on Panama Railroad Company Return on Panama Railroad Company Year Stock (%) Year Stock (%) 1853 1 1867 23 1854 -9 1868 20 1855 19 1869 -11 1856 2 1870 -51 1857 3 1871 -42 1858 36 1872 39 1859 21 1873 42 1860 16 1874 12 1861 -5 1875 26 1862 43 1876 9 1863 44 1877 -6 1864 48 88 1878 25 1865 7 1879 31 1866 11 1880 30 (a) Create a graph of the annual returns on the stock. A stock exchange earned an annual average return of 13.4% from 1853 through 1880. Can you tell from the graph if the Panama Railroad Company stock outperformed the stock exchange? It is not possible to tell from the graph if the Panama Railroad Company stock outperformed the stock exchange. (b) Calculate the mean annual return (in %) on Panama Railroad Company stock from 1853 through 1880. (Round your answer to one decimal place.) 13.6 % Did the stock outperform the stock exchange mentioned in part (a) from 1853 through 1880? The stock underperformed the stock exchange from 1853 through 1880.