1. Each winter (Dec.Feb.), the National Capital Commission in Ottawa monitors the ice conditions on the Rideau Canal Skatewav and decides on the duration that skating is safe to occur. The following table presents historical data for the number of days that skating was permitted on the Canal in winters between 1971/1972 and 1984/1935. (Total 16 marks) Year 71/72 72/73 73/74 74/75 75/73 76/77 77/73 73/79 73/33 30/31 31/32 32/33 33/34 34/35 3 of skang 90 78 65 62 67 71 77 64 62 61 66 45 50 44 days a} Calculate the mean, standard deviation, and coefficient of skewness (SK of your choice} of the data set. What was the reason for your choice of SK? (5 ma rks} b) Compute the 80th percentile of the sample. What does it mean? (4 marks} c) Provide a cumulative relative frequency polygon (report-quality\") of the number of skating days along with a table that summarizes the grouped data (bins, frequencies, etc.}. {5 marks) *Report-quality: clean, scaled, and with all information (axis, titles, units, etc.) Find/show the 80th percentile on the plot and compare its approximate value to what you calculated in question 1 part b. (2 marks) 2. The following table presents data for the number of days that skating was permitted on the (Total 14 marks) Canal in winters between 2003/2004 and 2016/2017. Year o31o4 04105 05105 0610? 01108 08109 09110 10111 11112 12113 13114 14115 15115 1511? #of skating 45 78 62 45 40 63 43 56 38 41 70 58 33 35 days a) Are there any outliers in the data set? What numbers are they? What about extreme outliers? You must show all your manual calculations (IQR, etc.) to answer the question. [12 marks) b) Calculate a coefficient of skewness (of your choice). Explain your reason why you decided which SK to calculate. (2 marks) a) Plot a box and whisker chart in Excel (show all the values on the chart) for the data set of Question 2 (2003/2004 to 2016,1201?) Does the chart confirm your answer of C12 about outliers? (5 marks) b) Plot a box and whisker chart in Excel (including all the values) for the dataset of 01 (71in to 84,185). Investigating the chart visually, do you think the data set is symmetrical or skewed? Is your visual interpretation in-line with your result of SK in C11? (5 marks) c) Investigating both Box and Whisker charts from (11 {older data set} and 02 (more recent data set), how do you compare the two groups of data? Do you think the number of skating days has meaningfully changed in recent years? (1 Bonus mark)