BUSINESS STATISTICS EXERCISES

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CHAPTER 2: SUMMARISING DATA EXERCISE 1: The table below shows the daily sales (VND 1,000) of internet cafe in Nov/2009 as: 700 940 765 860 870 890 950 650 750 850 855 780 760 735 600 780 920 690 620 730 830 860 750 1000 740 800 750 680 880 790 a Represent the data using grouped frequency distribution with classes and same class width b Determine the percentage of days with daily sales equal to and more than VND 800,000 c Represent the data arranged by appropriate diagram EXERCISE 2: Here are the raw data of total export value (USD million) of 30 enterprises in Hanoi in 2010: 65 45 56 42 57 a Rearrange the data 65 57 70 65 69 58 74 40 57 50 77 52 72 52 65 67 80 65 45 66 68 61 78 66 65 b Represent the arranged data diagrammatically in an appropriate way c Comment on the presentation CHAPTER 3: STATISTICAL MEASURES EXERCISE Here are the sales of bicycles (number of bicycles) over 40 weeks in a shop, as follows: 44 77 40 80 68 44 50 49 56 68 56 48 74 54 78 58 46 79 64 71 62 52 74 63 58 73 64 46 56 69 62 48 66 58 51 70 47 67 52 58 Question: Create the frequency distribution with classes? h=? Determine the average number of bicycles sold in a week; Mode; Me; σ of the number of bicycles sold? Give a conclusion for the characteristics of this distribution (Moderately Left Skewed? Moderately Right Skewed? Or Symmetric?) EXERCISE The table below shows the age of workers in a company: Age No of workers 20-24 25-29 30-34 35-39 40-44 973 1122 414 257 258 Age No of workers 45-49 50-54 55-59 From 60 and over 369 592 825 210 Question: Determine the average age of workers? Standard deviation of age? If you are a HR manager of this company and want to make a policy that reaches the demand of workers There are groups of demand after research: -Group 1: People from ages 20-34: Need for increasing salary -Group 2: People from ages 35-49: Need for increasing time for relax and entertainment -Group 3: People from ages 50 and over: Need for increasing more benefits after retirement Which group you choose to satisfy their demand? Why? EXERCISE The table below shows the average income of workers in companies, which have produced the same type of products : over 12 months of 2009 (Unit: million VND) A B C 3.3 2.8 1.8 2.1 2.1 2.1 2.2 2.4 2.4 2.3 2.3 1.8 2 2.1 2.2 2.2 2.1 2.3 2.4 2.3 2.2 2.3 2.3 2.4 2.4 2.5 2.3 2.8 2.8 2.6 Calculate the average monthly income of a worker in each company Determine the median of monthly income of workers in each company Determine the standard deviation of monthly income of workers in every company Which company should we apply for, if other conditions are similar (mobile phone support…)? EXERCISE Determine the average income and variance of income in both groups in a manufacture and give a conclusion: Group Income No of workers (1000 VND) (people) 1200 1500 2100 2200 2500 10 Group Income (1000 VND) 1500 1800 2100 2200 2500 No of workers (People) 11 EXERCISE The average weight of students in a class is 55 kg with the standard deviation as 6kg The average height of students is 165 cm with the standard deviation as cm Students in the class are similar in term of weight or height? EXERCISE Research on the average price and standard deviation of price of types of stocks over a period Comment on the variability/ dispersion of those two stocks Type Average (vnd/share) Price Standard (vnd/share) A 20000 4000 B 300000 40000 Deviation EXERCISE Find the weekly stock price of Wal-Mart for the last six months (go to http://moneycentral.msn.com) You can ask for the six-month chart and export to a spreadsheet Calculate the mean and the standard deviation of the stock prices Get the corresponding data for Tesco and calculate the mean and the standard deviation The coefficient of variation (CV) is defined as the ratio of the standard deviation over the mean Calculate the CV of Wal-Mart and Tesco stock prices If the CV of the weekly stock prices is taken as an indicator of risk of the stock, how WalMart and Tesco stock compare in term of risk? Get the corresponding data of the Dow Jones Industrial Average (DJIA) and compute its CV How Wal-Mart and Tesco stocks compare with the DJIA in term of risk? CHAPTER 4: REGRESSION AND CORRELATION ANALYSIS EXERCISE Here is an estimated multiple regression model: Yx1x2x3 = b0 + b1x1 + b2x2 + b3x3 Where: - Y: number of products sold in the month (1000 units) X1: number of people in the area (1000 people) X2: unemployment rate of the area (%) X3: expenditure of advertisement (million VND) Question: a Determine the population multiple regression model to find out b0, b1, b2, b3 b Assume that we have already determine: b0 = -3.4 , b1 = 0.52, b2 = 0.66, b3 = 0.33 Determine the status of those figures and their meaning c Based on the result found out in b, forecast the sales of that product in the area, whereas the number of people is 25,650 people; the unemployment rate is 5%; and the expenditure of advertisement is 30.5 million VND EXERCISE American Express Company has long believed that its cardholders tend to travel more extensively than others – both on business and for pleasure As part of a comprehensive research effort undertaken by a New York market research firm on behalf of American Express, a study was conducted to determine the relationship between travel and charges on the American Express card The research firm selected a random of 25 cardholders from the American Express computer file and recorded their total charges over a specified period The data are as follow: Travel miles Charges Travel (USD) miles Charges Travel (USD) miles Charges Travel (USD) miles Charges Travel (USD) miles Charges (USD) 1211 1802 2026 2305 2699 3371 3643 5298 4533 6059 1345 2405 2133 3016 2806 3998 3852 4801 4804 6426 1422 2005 2253 3385 3082 3555 4033 5147 5090 6321 1687 2511 2400 3090 3209 4692 4267 5738 5233 7026 1849 2332 2468 3694 3466 4244 4498 6420 5439 6964 CHAPTER V: TIME SERIES ANALYSIS EXERCISE A firm’s sales for a product line during the 12 quarters of the past three years were as follows: YEAR QUARTER SALES (1000 USD) 1 YEAR QUARTER SALES (1000 USD) 600 2600 1550 2900 1500 3800 1500 4500 2400 4000 3100 4900 Estimate a trend line and forecast each quarter of the fourth year using least square method and fourquarter moving average method EXERCISE Calculate the trend value using moving average method with three and nine-week period, as followed: WEEK ACTUAL WEEK DEMAND ACTUAL WEEK DEMAND ACTUAL DEMAND 800 11 1700 21 2400 1400 12 1500 22 2600 1000 13 2300 23 2000 1500 14 2300 24 2500 1500 15 2000 25 2600 1300 16 1700 26 2200 1800 17 1800 27 2200 1700 18 2200 28 2500 1300 19 1900 29 2400 10 1700 20 2400 30 2100 EXERCISE Zeus Computer Chips, Inc., used to have major contracts to produce the Pentium-type chips The market has been declining during the past three years because of the dual-core chips, which it cannot produce, so Zeus has the unpleasant task of forecasting next year The task is unpleasant because the firm has not been able to find replacement chips for its product lines Here is demand over the past 12 quarters: 2005 Actual demand 2006 Actual demand 2007 Actual demand I 4800 I 3500 I 3200 II 3500 II 2700 II 2100 III 4300 III 3500 III 2700 IV 3000 IV 2400 IV 1700 Forecast the four quarters of 2008 using least square method to estimate the trend line? (Technique for calculating seasonal variation is Additive model) Forecast the four quarters of 2008 using four-quarter moving average to extract the trend? ... Company has long believed that its cardholders tend to travel more extensively than others – both on business and for pleasure As part of a comprehensive research effort undertaken by a New York market
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