Assessment 1 – calculations and short written responses (20%)INSTRUCTIONSPerform the required calculations, present your findings, and prepare short written responses to the following...

Assessment 1 – calculations and short written responses (20%)INSTRUCTIONSPerform the required calculations, present your findings, and prepare short written responses to the following questions.Question 1 (4 marks)One of the variables most often included in surveys is income. Sometimes the question is phrased, ‘what is your income (in thousands of dollars)?’ In other surveys, the respondent is asked to ‘Place an X in the circle corresponding to your income group’ and given a number of ranges to choose from.a) In the first format, explain why income might be considered either discrete or continuous (1 mark).b) Which of these two formats would you prefer to use if you were conducting a survey? Why (1.5 marks)?c) Which of these two formats would probably bring you a greater rate of response? Why (1.5 marks)?Question 2 (11 marks)One of the major measures of the quality of service provided by any organisation is the speed with which the organisation responds to customer complaints. A large family-owned department store selling furniture and flooring, including carpet, has undergone major expansion in the past few years. In particular, the flooring department has expanded for installation crews to an installation supervisor, a measurer and 15 installation crews. During a recent year the company got 50 complaints about carpet installation. The following data represent the number of days between recipient of the complaint and resolution of the complaint. a) Construct frequency and percentage distributions (1 mark).b) Construct histogram and percentage polygons (1 mark).c) Construct a cumulative percentage distribution and plot the corresponding ogive (1 mark).d) Calculate the mean, median, first quartile and third quartile (2 marks).e) Calculate the range, interquartile range, variance, standard deviation and coefficient of variation (2 marks).f) Construct a box-and-whisker plot. Are the data skewed? If so, how (2 marks)?g) On the basis of a to f, if you had to report to the manager on how long a customer should expect to wait to have a complaint resolved, what would you say? Explain (2 marks).Question 3 (5 marks)The datafile gives nutrition content (number of calories and total fat, in grams) per 250ml of a random sample of 20 fresh milk available in Australia.a) Calculate the covariance (1 mark).b) Calculate the coefficient of correlation (1 mark).c) Which do you think is more valuable in expressing the relationship between calories and fat content – the covariance or the coefficient of correlation? Explain (1.5 marks).d) What conclusions can you reach about the relationship between calories and fat content (1.5 marks)?