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# tutorial1sol - Stat 211 Tutorial 1 Solutions 1 A closing...

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Stat 211 - Tutorial 1 Solutions 1. A closing price (in dollars) at Dec 31, 2011 of 30 stocks in a portfolio are given below: 52.78 48.27 49.82 55.85 54.60 52.87 52.85 54.48 50.73 51.46 55.88 40.72 51.69 47.59 57.19 54.83 50.21 49.54 52.29 53.14 51.12 52.39 54.59 52.48 49.04 53.34 50.49 49.03 54.97 52.16 You are also given that the sum of the above values is 1556.40 and the sum of their squares is 81041.7816. (a) i. Calculate the mean/average closing price and the standard deviation of the prices. Solution: Denote the data by x 1 , x 2 , . . . , x 3 0 . Mean = ¯ x = 30 i =1 x i 30 = 1556 . 40 30 = \$51 . 88 Variance = s 2 = 30 i =1 x 2 i - 30¯ x 2 30 - 1 = 81041 . 7816 - 30(51 . 88) 2 29 = 10 . 1983 Standard Deviation = s = 10 . 1983 = \$3 . 1935 ii. Determine the range, median, and the 1st and 3rd quartiles. Hence, deter- mine the interquartile range. Solution: Range = Largest Value - Smallest Value = 57 . 19 - 40 . 72 = \$16 . 47 Sort the 30 data points: (The data will already be sorted for you in an exam) 52.78 55.88 51.12 48.27 40.72 52.39 49.82 51.69 54.59 55.85 47.59 52.48 54.6 57.19 49.04 52.87 54.83 53.34 52.85 50.21 50.49 54.48 49.54 49.03 50.73 52.29 54.97 51.46 53.14 52.16 Median (or 50th percentile) : i = (50 / 100) · 30 = 15 = Median = Average of the 15th and 16th sorted values = 52 . 29 + 52 . 39 2 = 52 . 34 1

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1st Quartile (or 25th percentile) : i = (25 / 100) · 30 = 7 . 5 = Q 1 = 8th sorted value = 50 . 21 3rd Quartile (or 75th percentile) : i = (75 / 100) ·
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tutorial1sol - Stat 211 Tutorial 1 Solutions 1 A closing...

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