1. Below are the final grades of 30 introductory statistics students. 53; 57; 57; 63; 65; 66; 67; 68; 68; 70; 71; 73; 73; 73; 74; 74; 74; 74; 75; 76; 76; 76; 77; 80; 81; 83; 83; 86; 90; 95 a) Calculate the mean. Now, to avoid the tedious calculation of the deviance for each individual data point, the same grades have been grouped by decile. Use the sample mean from part a) to fill in the table. Decile Frequency Midpoint Deviations Deviations Frequency x Deviations m (m - if) (m - If)2 fx (m - if)2 50-59 3 60-69 6 70-79 14 80-89 4 90-99 2 Total: Efx (m - x;)? = Using the results from the table, calculate b) the sample variance, $2. c) the sample standard deviation, s.2. The Australian Open tennis tournament is currently being played, and two Canadian tennis players have made it to the quarterfinals. Dennis Shapovalov is facing the clay court master and 6th ranked player in the world Rafael Nadal, while Felix Auger-aliassime is matched against the top seeded player of the tournament, Daniil Medvedev. Assuming both Canadian players manage to upset their higher ranked opponents, we will have one Canadian in each semifinal match. Let's also assume that Gael Monfils and Stefanos Tsitsipas overcome their opponents to join the Canadians in the semifinals. Finally, assume all remain- ing players are equally talented resulting in equal probabilities of winning the match to advance to the final. Monfils (FRA) Monfils (FRA) Berrettini (ITA) Finalist 1 Shapovalov (CAN) Shapovalov (CAN) Nadal (ESP) Finals Sinner (ITA) Tsitsipas (GRE) Tsitsipas (GRE) Finalist 2 Auger-alliassime (CAN) Auger-alliassime (CAN) Medvedev (RUS) a) List all possible pairs of finalists. b) What is the probability that at least one Canadian will apear in the finals? c) What is the probability that it will be an all-Canadian final? d) What is the probability that no Canadians make the final