a) The box and whisker plot below summaries the number of computers fixed per day by a technician in one month 3 4 5 6 7 B 9 '1 CI 11 12 13 1 4 1 5 16 1? Determine the range [2] Calculate the quartile deviation of the number of computers xed per day. Interpret this value [2] Comment on the skewness of this distribution. [2] b) The stem and leaf below show the amount of magnesium found in a brand of bottled water in milligrams. Exhibit 1 StemandLeaf Display: Amount of Magnesium Leaf Unit = 0.1 N=a 3 1 345 ' ' 2 O O 2 7 8 8 8 8 (:3) 3 0113334577899 b 4 122245777 12 5 23344 7 6 11237 2 7 45 What advantage does preparing a stem and leaf diagram have over grouping a data set using a grouped frequency distn'bution? [1] Find the value of a and b [2] What is the largest value in the dataset? [1] What the is median of the data displayed? [1] What is the mode of the distribution? [1] a) The following data shows how many employees showed up to work every day for two weeks 12 18 O9 10 13 11 i. Calculate the interquartile range ii. Calculate the mean iii. Calculate the sample standard deviation 08 ll [2] [2] [3] b) The following table shows the time students from a college took to complete a marathon. Time (minutes) 3844 Frequency 14 Frequency Density i) Find the value of a and b. ii) Calculate the mean time iii) Calculate the mode iv) Calculate the variance [2] [2] [3] [3] a) In a private school students can choose only of French, Spanish or Music as their Elective. In a group of students, the number of males and females studying Spanish, French or Music are given in a table below Spanish French Music 23 12 26 -_ i) Find the probability that a randomly chosen student a) studies music [2] b) studies music or is female [3] c) is male, given that they do not study Spanish [3] ii) Determine whether the events 'a randomly chosen student is a male' and 'a randomly chosen student is studying Music' are independent, justifying your answer. [3] iii) Two students are randomly selected, without replacement, what is the probability that the first student studies Spanish and the second student studies French. [3] a) For the following determine if it quantitative or qualitative. If it is quantitative, determine whether it is continuous or discrete. [7] i. The address of all clients at a salon. ii. The weight of meat sold by a butcher iii. The number of children who graduate from a college iv. The cost of a new television at courts b) A small-town mechanic says that 8% his customers come in for an oil change. When 1000 samples were drawn from his records, it was found that 6.5% of these came in for an oil change. i. What is the target population? [2] ii. Does the value 8% refer to the parameter or to the statistic? [1] iii. Is the value 6.5% a parameter or a statistic? [1] c) State which sampling method used in the following scenarios i. Select the first 19 customers who enter building. [1] ii. Select 40 students in each district in proportion of how many students are in each district [1] iii. Randomly select 30 customers by assigning each customer a number, then selecting customers based on which number appears in a random numbers table. [1] iv. Take note of every fifth car passing over a bridge. [1] d) State one similarity and one difference between quota sampling and stratied random sampling. [2]