Question for Statistic

Practice Problems 1-KEY 1. The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. Day Stock Price 1 84 2 87 3 84 4 88 5 85 6 90 7 91 8 83 9 82 10 86

For the above sample, compute the following measures. a. b. c. The mean = ∑X/n = 860/10 = 86 The median = (85+86)/2 = 85.5 The variance = ∑ X - X 2/ n-1 = {(84-86)2 + (87-86)2 + (84-86)2 + (88-86)2 + (85-86)2 + (90-86)2 + (91-86)2 + (83The standard deviation = √8.89 = 2.98 The coefficient of variation = 2.98/86 * 100% = 3.47%

86)2 + (82-86)2 + (86-86)2 } / (10 -1) = 8.89 d. f.

2. In 2008, the average age of students at GUST was 22 with a standard deviation of 3.96. In 2009, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer. CV2008 = 3.96/22 * 100% = 18% CV2009 = 4.08/24 * 100% = 17% So, 2008 shows more dispersed distribution 3. A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of examinations are selected at random and scored. The results are shown below. Grade For the above data, determine a. The mean = ∑X/n = 664/8 = 83 b. c. The median = (85+87)/2 = 86 The standard deviation = √variance ariance = ∑ X - X 2/ n-1 = {(93-83)2 + (65-83)2 + (80-83)2 + (97-83)2 + (85-83)2 + (87-83)2 + (97-83)2 + (60 - 83)2 } / (8 -1) = 196.29 S0, standard deviation = √196.29 = 14.01 d. The coefficient of variation = 14.01/83 * 100% = 16.88% 93 65 80 97 85 87 97 60

4. The following data represent the daily supply (y in thousands of units) and the unit price (x in dollars) for a product. Daily Supply (y) Unit Price (x) 5 2 7 4 9 8 12 5 10 7 13 8 16 16 16 6

1

a.

e an in er re = 11 X = 7

e a

e c variance

r

ea

ve a a. = ∑

-

X - X / n-1

(y) 5 7 9 12 10 13 16 16

(x) 2 4 8 5 7 8 16 6

-6 -4 -2 1 -1 2 5 5

X-X -5 -3 1 -2 0 1 9 -1

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X-X 30 12 -2 -2 0 2 45 -5 80