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Concordia University Department of Economics ECON 221/4 – Sections AA, B, E Instructors: M. DaPalma, V. Terekhov, G. Tsoublekas Winter 2007 - ASSIGNMENT 2 – ANSWERS 1. The distribution of grades of the 1 st Assignment in the class of Statistics is shown below: [The calculations and the graph for this exercise must be done on Excel. As soon as you get the data on class intervals and frequencies that are shown below, you will create a table on Excel with the necessary detailed column calculations that will be used as a basis to answer sub-questions (a), (d) and (e). You will paste your table here.] (20 points) a) Construct a cumulative frequency distribution, and a cumulative relative frequency distribution. (4 points) b) Using Excel, draw a histogram of the frequencies and paste it in the space provided below. (4 points) c) On the basis of the shape of the histogram, make an assessment about symmetry in the data, its probable cause, and the implication for the mean of the group. (4 points) There is no symmetry in the data. The histogram shows that the distribution is skewed to the left (negative skew). The cause for this pattern may be with the existence of certain outliers in the observations (extremely low values). The implication of this pattern is that the mean gives a pessimistic view of the data.

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d) Using the appropriate formula for grouped data, calculate the mean score of this class. Use the table provided above for your computations. (4 points) Using the data calculated above, Mean = m i * f i / n = 3150 / 42 = 75 e) Using the appropriate formulas for grouped data, calculate the variance and the standard deviation. Use the table provided above for your computations. (4 points) Using the data calculated above, Variance = s 2 = (m i –mean) 2 f i / ( n-1) = 11200 / 41 = 273.17 Standard Deviation = 273.17 = 16.53 2. An insurance company has estimated that 30% of all automobile accidents were partly caused by bad weather conditions and that 20% of all automobile accidents involved bodily injury. Further, of those accidents that involved bodily injury, 40% were partly caused by bad weather conditions. (20 points) a. Construct the table or tree of joint probabilities. (4 points) Partly Caused by Weather Conditions Involved Bodily Injury Total Yes (YBI) No (NBI) Bad Weather (BW) Good Weather (GW) 0.08 0.12 0.22 0.58 0.30 0.70 Total 0.20 0.80 1.00 b. What is the probability that a randomly chosen accident both was partly caused by weather conditions and involved bodily injury? (3 points) P (BW YBI) = P (BW) * P (YBI
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