The Standard and Poor's index of stocks (called the S&P 500) is based on n = 504. The year-to-date return for these 504 stocks were measured and the results are shown below: summary (sp500$return) ## Min. 1st Qu. Median ## -68.92 -15.09 Mean 3rd Qu. -6.76 -5.29 Max. 3.17 50.85 sd (sp500$return) ## [1] 13.702 length (sp500$return) ## [1] 504 hist (sp500$return, breaks =20, col="gray") barplot (table (sp500$sector), las-2, cex.names=0.8) 2 20 Histogram of sp500$return -60 -20 20 sp500$return 701 60- 50- 40- 30 20- 10- 0 Discretionary a) (5 pts.) Describe the distribution of return. Please use at most 3 sentences. b) (5 pts.) Describe the distribution of sector. Please use at most 3 sentences. 7 c) (6 pts.) What would happen to the mean, median, and standard deviation if both the single largest and single smallest observations were removed from return? Would they increase, decrease, or stay the same? Explain your answers. d) (6 pts.) Your friend thinks that there is an association between stock return and sector. What summary statistic(s) would you measure to investigate this association? What visual would you consider? e) (6 pts.) Your friend thinks that there is an association between stock return and the size of the company (as measured by number of employees). What summary statistic(s) would you measure to investigate this association? What visual would you consider?