220TestOct2010 (1).doc

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Statistical Sciences
Augustin Vukov

STA220H Term Test Oct 27, 2010 Last Name: _________________ First Name:_________________ Student #:_______________ Tutorial Day: Monday or Tuesday (circle one) Tutorial Time:_______ Tutorial Room:___________ TAs Name: _________________ Time allowed: 105 minutes. Aids: one sided handwritten aid sheet + non-programmable calculator Check that you have all the consecutively numbered pages of this test, up to the last page which says END at the bottom. A standard normal table is attached at the end of this test. Best marks go to best answers, as a general rule, particularly where some explanation is requested, so try to be complete but also clear and concise; a bunch of nonsense will actually decrease your grade. Explanations should be in the context of the actual study. Be sure to proportion your time carefully among the questions and limit your time spent on any single question. The correct answer for a difficult or lengthy question may not be worth any more marks than for a simple or short one. Easy questions are just as likely to be at the end, as at the beginning of the exam. Show your work and answer in the space provided (or indicate clearly where to look), and in ink or remarks will not be allowed. Use back of pages for rough work. Marks are shown in brackets at the end of the question parts, and are distributed as follows: Question 1 2 3 4 5 6 7 Total Max 18 28 13 9 9 10 13 100 Good luck!! 1 1) The midterm exam grades of a history course were used to create the following stem and leaf plot. Stem-and-leaf of grade N = 40 Leaf Unit = 1.0 1 2 5 1 3 1 4 3 5 26 7 6 1359 12 7 00338 (11) 8 01122335789 17 9 00111233445677899 a) Find the first (lower) and third (upper) quartiles for the distribution. [2] b) Are there any exam scores that would be picked out as suspected outliers according to the 1.5 IQR rule? Which ones? Show your work. [3] c) Give a good thorough description of the distribution of midterm scores. Start with a numerical summary appropriate for data such as these. Then, with numbers and words, give a clear picture of the distribution (to say someone who wont see that graph above), talking about centre and spread and other relevant features. [5] d) Suppose you tried calculating the mean with your calculator and got 89. If you compare with the median, you know you must have erred. Why? [1] 2 e) The instructor wanted the highest grade to be 100 instead of 99, and so decided to add one point to everyones score. How would this affect the standard deviation of the distribution? [1] f) Removing the lowest grade would have a smaller effect on the IQR than on the standard deviation, since the IQR is a more___________________ (fill in blank) measure of spread than the standard deviation. [1] g) For these data, what would the normal quantile (probability) plot look like? Draw a rough sketch of its shape below (if there are outliers, show them properly in the plot). Label clearly the x axis and the y axis, and write at least two numbers on each axis in their roughly correct positions. [4] h) Which of the following statements are true? Circle all correct statements. [1] i) The mean and the standard deviation would provide a complete description of the data since each of these measures uses the complete set of data values. ii) Taking the logarithms would produce a more symmetric distribution. iii) Standardizing all the data values would make the distribution more bell- shaped. iv) None of the above statements are true. 3
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