You are required to answer all questions listed below. This particular assignment weights 30% towards your module mark.
Explain the importance of Statistics to Industry and Business. (You can start by mentioning the types of statistics, use & limitations of statistics, and any other aspect that you feel adds weight within the field of discussion). (8 marks)
You are encouraged to use practical (real-life) examples/data. Please note that your score for this question will depend on the quality of discussion with suitable examples provided.
a) The following dataset records 40 yearly charitable contributions (in ?? dollars, where i=1, 2, ..,40) to the Oxedius Fund for a group of 40 employees at a public university.
6700 2800 4100 2000+y 4700 5100 5600 5900 6300 6900
6400 6500 2400 6900 7000 7100 7500 7700 7800 7900
8000 8000 8000 8000 8000 8100 8100 5000 8300 8400
9000 9200 9300 9900 10100 10300 10500 11200 11500 5800
Note that ? ?? = 300,000
You are required to find the value of y and to calculate the measures of central tendency/dispersion (including but not limited to the sample mean, standard deviation, mode, median, and the inter-quartile range, amongst others). (8 marks) b) What are the desiderata (requirements) of a good average? Compare the mean, the median and the mode in the light of these desiderata? Why averages are called measures of central tendency? Explain with suitable examples. (5 marks)
a) An urn contains ‘b’ blue cards and ‘r’ red balls. One of the cards is drawn at random, but when it is put back, ‘c’ additional cards of the same color are put in the bag.
Then, assume that a second card is drawn at random. Prove the probability that the first card drawn was blue given that the second card drawn was red is given by the formula . (5 marks)
b) A visitor is trapped in a garden maze. He comes across three possible exits, and he needs to decide which one to choose. The first exit takes him to safety after 2 hours of travel. The second exit returns him back to the same place after 3 hours of travel. The third exit leads to a tunnel that returns him again to his departure point after 5 hours. Assuming that the visitor is at all times equally likely to choose any one of the exits, what is the expected length of time until the visitor reaches safety? (4 marks)
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