The following relates to Problems 4 and 5. Christchurch, New Zealand experienced a major earthquake on February 22, 2011. It destroyed 100,000 homes. Data were collected on a sample of 300 damaged homes. These data are saved in the file called CIEG315 Homework 4 data.xlsx, which is available on Canvas under Files. A subset of the data is shown in the accompanying table. Two of the variables are qualitative in nature: Wall construction and roof construction. Two of the variables are quantitative: (1) Peak ground acceleration (PGA), a measure of the intensity of ground shaking that the home experienced in the earthquake (in units of acceleration of gravity, g); (2) Damage, which indicates the amount of damage experienced in the earthquake in New Zealand dollars; and (3) Building value, the pre-earthquake value of the home in New Zealand dollars. PGA (g) Damage (NZ$) Building Value (NZ$) Wall Construction Roof Construction Property ID 1 0.645 2 0.101 141,416 2,826 253,000 B 305,000 B T 3 1.163 167,277 370,000 B T 4 0.211 5,759 520,000 B | 5 0.990 173,975 225,000 C 6 0.582 153,408 970,000 C T 7 0.098 1,248 195,000 C T 8 1.074 336,331 395,000 W T Notes: • Do all parts of Problems 4 and 5 using the complete set of 300 homes • • • The "Excel cheat sheet" in the Files section of Canvas website may be useful. All figures should be properly labeled (including a title, x-axis title, y-axis title, appropriate range of values on each axis, appropriate number of decimal places on axis marks, and no legend if there's only one series of data). All tables should be properly labeled (including a title, column headings) The sample statistics (5a and 5b) should have an appropriate number of significant figures (number used in input data). 5. The questions in #5 relate to the quantitative variable, peak ground acceleration (PGA). For this problem, do parts c to e both by hand and using Excel. You should submit both your handwritten calculations and figures, and printouts of your Excel results as well. Part ƒ can be done only by hand. Parts a, b, and g can be done just once. a. Compute the sample mean, sample median. b. Compute the sample variance, sample standard deviation, and sample interquartile range (IQR). c. Draw 3 histograms using frequency as the y-axis. For each figure, use a different bin size: 0.05, 0.1, and 0.3. Briefly comment on the patterns that emerge from the three figures (no more than a few sentences). e. d. Use a bin size of 0.1, draw 2 histograms using relative frequency and density on the y-axes, respectively. (Excel's histogram function provides a figure with the y-axis frequency, and a table of data with columns "Bin" and "Frequency." You will have to modify the data in the "Frequency" column to get the same graph with relative frequency and density on the y-axis.) Draw an empirical CDF using a bin size of 0.1. (This should be a step function, so note that the Excel CDF function is not technically correct. See how it differs from your handwritten solution). f. Draw a boxplot, with whiskers of length equal to 1.5 times the interquartile range (IQR), and outliers plotted as separate points. (Excel does not easily make these, so do this by hand only.) g. In a short paragraph, summarize the data, referring to values and figures in parts a to f as it is useful. Comment on the central value(s), dispersion, and skewness.