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The following data represent the social ambivalence scores for a simple random sample of 15 people as measured by a psychological test. (The higher the score, the stronger the ambivalence.) 7,14,10,16,15,12,11,3,12,9,19,12,12,16,8. (a) Calculate the mean of the above data set. (b) Calculate the Mean Deviation of the above data set. (c) Find the range, R, of the above data set and use the range approximation method to approximate the standard deviation of the above values. Rule: Where n is the sample size, the sample standard deviation may be approximated by Forn = 5 data set, S m % For n = 10 data set, S N % Forn = 15 data set, S N ITRS For n = 25 data set, S m % For a large data set, S N g (d) Calculate the variance and then find the actual standard deviation of the above data set. (e) What proportion of the scores actually lie on the interval x 1 2S ? (1) Find the mode of the above data set. (9) Find the five-number summary of the above data set. (h) Draw a box-and-whisker plot for the above data set. What are the outliers, if any, of the above data? The number of companies offering flexible work schedules has increased as companies try to help employees cope with the demands of home and work. One flextime schedule is to work four 10-hour shifts. A survey provided the following information for 215 firms located in two cities in Quebec. Flextime Schedule City Available Not Available Total A 35 74 109 B 21 85 106 Totals 56 159 215 A company is selected at random from this pool of 215 companies. (Write your answers in fraction form.) (a) What is the probability that the company is located in city A? (b) What is the probability that the company is located in city B and offers flextime work schedules? (c) What is the probability that the company does not have flextime schedules? (d) What is the probability that the company is located in city B, given that the company has flextime schedules available? (e) What is the probability that the company has flextime schedules available given that the company is located in city B