MATH1711_08 - Durham University EXAMINATION PAPER date exam...

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Durham University EXAMINATION PAPER date May/June 2008 exam code MATH1711/01 description Data Analysis Modelling & Simulation Time allowed: 3 hours Examination material provided: Graph paper. Normal distribution table. Instructions: Credit will be given for the best SIX answers. All questions carry the same marks. Use a separate answer book for each Section. Approved electronic calculators may be used. ED01/2008 Durham University Copyright continued
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page number 2 exam code MATH1711/01 SECTION A Use a separate answer book for this Section. 1. The following data show the number of lives lost in major tornadoes in the United States of America between 1900 and 1988 (Source: U.S. Environmental Data Ser- vice). No. of Deaths Frequency up to 24 10 25–49 21 50–74 20 75–99 13 100–149 7 150–199 2 200–249 4 250 and over 2 79 (a) Draw a histogram to show the proportion of tornadoes in each class, carefully labelling the axes. You may assume that no tornado has killed as many as 400 people. (b) Which classes contain the median and lower and upper quartiles? Explain your answer. (c) Use the frequency table and your histogram calculations to draw as accurately as you can a box-plot for the data. Show your working. (d) The distribution of the number of deaths is clearly not Gaussian. Suggest a transformation of the data which might make the distribution more Gaussian. Draw a histogram of the transformed data. Was your choice of transformation successful? (e) What are the advantages of transforming data so that the distribution is Gaus- sian? ED01/2008 Durham University Copyright continued
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page number 3 exam code MATH1711/01 2. As part of a study reported in the Journal of Nonverbal Behaviour (1996), a sample of 36 introductory psychology students was randomly divided into six groups, each group being assigned to view one of six slides showing a person making a facial ex- pression. The six expressions were angry, disgusted, fearful, happy, sad and neutral. After viewing the slide, a student rated the degree of dominance they inferred from the expression on a scale ranging from - 15 to +15. Data are listed and summarised in the table below: Expression Dominance Values x s Angry 2 · 1 0 · 6 0 · 5 0 · 4 1 · 6 - 0 · 1 0 · 85 0 · 83 Disgusted 0 · 4 0 · 7 - 0 · 1 - 0 · 2 0 · 9 1 · 9 0 · 60 0 · 77 Fearful 0 · 8 - 2 · 9 - 0 · 7 0 · 8 - 0 · 8 - 1 · 6 - 0 · 73 1 · 43 Happy 1 · 7 0 · 0 1 · 0 1 · 4 1 · 4 0 · 6 1 · 02 0 · 63 Neutral 1 · 7 - 0 · 6 - 0 · 6 0 · 3 - 0 · 6 - 2 ·
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