BBM 211: BUSINESS STATISTICS QUESTION SEVEN a) Distinguish between descriptive Statistics and inferential Statistics (4 marks) b) What do you understand .by 'Central Tendency"? Under what conditions is the median more suitable than other measures of central tendency? (5 marks) c) A number of particular articles have been classified according to their weights. After drying for two weeks, the same articles have again been weighed and similarly classified. It is known that the median weight in the first weighing was 20.83 gm while in the second weighing it was 17.35 gm. Some frequencies a and b in the first weighing and x and y in the second are missing. It is known that a = 1/3x and b = 1/2 y. Find out the values of the missing frequencies. (6marks) Class First Weighing Second Weighing Frequencies Frequencies 0-5 a Z 5-10 b 10-15 11 40 15-20 52 50 20-25 75 30 25-30 22 28 d) Why is the standard deviation the most widely used measure of dispersion? Explain. (3 marks) e) Describe the process of planning a statistical enquiry with special reference to its scope and purpose. (7marks) QUESTION EIGHT a) What's the purpose of classifications in statistics? (4 marks) b) Determine the classes of the following distribution given class marks and use it to calculate the first four measures of averages, mode, median, average and relative dispersion from. (1 1marks) Class Marks 11 18 25 32 39 46 53 No. of students 12 18 40 15 2 QUESTION NINE a) Define Kurtosis and Moments. (2marks) b) What are the different types of skewness and their features? (6 marks) c) Calculate coefficients of skewness using the four methods and kurtosis and comment on the answers: (7 marks) Weekly Sales Number of Companies 10-12 12 12-14 18 14-16 35 16-18 42 18-20 50 22-24 30 24-26 8QUESTION THIRTEEN: (25 marks) a) Differentiate between Descriptive statistics and inferential statistics. (2 marks) b) a) Briefly state any five limitations of statistics in decision making. (5marks) c) The data below shows the monthly earnings of 100 employees of XYZ Company. compute the following: Monthly Earnings (kshs.) No. of 000 workers 10-15 5 5-20 12 20-25 15 25-30 18 30-35 20 35-40 14 40-45 11 45-50 5 100 Calculate the Karl Pearson's Coefficient of Skewness and comment on the result (5 marks) d) Distinguish between correlation and regression as used in statistics. (2 marks) e) In two factories A and B engaged in the same industry, average weekly wages and standard deviation are as follows: Factory Average weekly S.D of No. of wage Wages ($) wages earners A 460 50 100 490 40 80 Required: i) Which factory shows greater variability in the distribution of wages? (4marks) ii) What is the mean of all the workers in two factories taken together? (2marks) f) Highlight 4 areas in which statistics can be applied (4 marks) QUESTION FOURTEEN: (15 marks) a) Differentiate between the following terms as used in statistics giving examples in each case: i. Quantitative and Qualitative variables (4 marks) ii. Continuous and Discrete variables (4 marks) b) State 3 advantages of using Questionnaire as data collection instrument (3 marks) c) Present the following information in a suitable tabular form supplying the figures not directly give. "In 1999 out of a total 2,000 workers in a factory 1,550 were members of a trade union. The number of workers employed was 250 out of which 200 did not belong to any trade." "in 2000 the number of union workers was 1,725 of which 1,600 were men. The number of non-union workers was 380 among which 155 were women. (4marks) QUESTION FIFTEEN: (15 marks) a) Briefly explain the following i). Cyclical variation (2 marks) ii). Seasonal variation (2 marks) b) A consultant wishes to determine the relationship between gross profit of firms in the chemical industry and the number of employees. He selects a random sample of 10 firms and obtains the following data: Company Gross Profit (in thousands of dollars) Number of Employees 2800 140 1300 65 1230 130 1600 115 4500 390 5700 670 3150 205 540 40 3400 480 10 6700 220 Using Pearson's correlation coefficient comment on the relationship between gross profit and number of employees (1 1 marks)QUESTION SIXTEEN: (15 marks) a) Define a simple random sample. (2 marks) b) Eight different brands of DVD players (labelled A to H) were assessed by a panel of experts in terms of their overall ease of use and reliability. The panel assigned the following rankings: DVD player Ease of use Reliability H 8 8 Calculate Spearman's rank correlation coefficient and interpret the result. (5 marks) c) The following data gives the test scores and sales made by 9 salesmen during the last one year: Test scores: 14 19 24 21 26 22 15 20 19 Sales (kshs in millions)31 36 48 37 50 45 33 41 39 Calculate the regression equation of test scores on sales. (8 marks) QUESTION SEVENTEEN: (15 marks) a) Define the following terms as used in probability; 1) Mutually exclusive ii) Dependent events (4 marks) b) In a company of 400 employees, 250 use a computer and 100 use a telephone as part of their work. The probability that an employee chosen at random neither uses neither a computer nor a telephone is 1/5. Determine: i). The number of employees who use both a computer and a telephone as part of their work. ii) . The probability that an employee chosen at random uses a telephone and does not use a computer iii) The probability that an employee chosen at random does not use a computer, given a use a telephone. (1 1 marks) QUESTION EIGHTEEN: (15 marks) a) The following data shows the sales of a firm from the years 1982 to 1992. Year Sales (000s) 1982 1340 1983 1360 1984 1370 1985 1350 1986 1410 1987 1460 1988 1480 1989 1490 1990 1510 1991 1530 1992 1520 i) Assuming a four - yearly cycle, calculate the 4 yearly centered moving averages. ii) Comment on the trend. (7 marks) C) The following data shows the age of 117 students in a city college. Age (in years) 17-19 19-21 21-23 23-25 25-27 27-29 29-31 No. of students 2 12 22 20 14 4 Construct an ogive from the data and use it to estimate; i). The median ii). The number of students aged between 21 to 26 years. (8 marks)BBM 211: BUSINESS STATISTICS QUESTION NINETEEN a) Distinguish between descriptive Statistics and inferential Statistics (4 marks) b) What do you understand .by 'Central Tendency"? Under what conditions is the median more suitable than other measures of central tendency? (5 marks) c) A number of particular articles have been classified according to their weights. After drying for two weeks, the same articles have again been weighed and similarly classified. It is known that the median weight in the first weighing was 20.83 gm while in the second weighing it was 17.35 gm. Some frequencies a and b in the first weighing and x and y in the second are missing. It is known that a = 1/3x and b = 1/2 y. Find out the values of the missing frequencies. (6marks) Class First Weighing Second Weighing Frequencies Frequencies 0-5 5-10 y 10-15 40 15-20 50 20-25 30 25-30 28 75 d) Why is the standard deviation the most widely used measure of dispersion? Explain. (3 marks) e) Describe the process of planning a statistical enquiry with special reference to its scope and purpose. (7marks) QUESTION TWENTY a) What's the purpose of classifications in statistics? (4 marks) b) Determine the classes of the following distribution given class marks and use it to calculate the first four measures of averages, mode, median, average and relative dispersion from. (11marks) Class Marks 4 11 18 25 32 39 46 53 No. of students 5 12 18 40 15 3 2 QUESTION TWENTY ONE a) Define Kurtosis and Moments. (2marks) b) What are the different types of skewness and their features? (6 marks) c) Calculate coefficients of skewness using the four methods and kurtosis and comment on the answers: (7 marks) Weekly Sales Number of Companies 10-12 12 12-14 18 14-16 35 16-18 42 18-20 50 22-24 30 24-26 8QUESTION TWENTY TWO a) Distinguish clearly between correlation and regression as concept used in statistical analysis. (3 marks) b) Explain what is meant by Karl Pearson's coefficient of correlation? (2marks) c) Find the Pearsonian correlation coefficient between sales (in thousand units) and expenses (in thousand shillings) of the following 10 firms: Firm 2 3 5 6 10 Sales 50 55 60 65 65 60 50 Expense 11 13 14 16 16 15 15 14 13 Let sales of a firm be denoted by X and expenses be denoted by Y. (5 marks) d) The following table gives the ages and blood pressure of 9 women. Age (X) 56 42 36 47 49 47 60 72 63 Blood Pressure(Y) 147 125 118 128 145 140 155 160 149 Find the correlation coefficient between X and Y. Determine the least square regression equation of Y on X. (3 marks) (ii) Estimate the blood pressure of a woman whose age is 45 years. (2 marks) QUESTION TWENTYTHREE a) Define the the term "probability' and explain how probability relates to uncertainty cases. (3 marks) b) Among the sales staff engaged by a company 60% are males. In terms of their professional qualifications, 70% of males and 50% of females have a degree in marketing. Find the probability that a sales person selected at random will be; i) A female with degree in marketing (2 marks) ii) A male without degree in marketing. (2 marks) iii) Either a male or female with degree in marketing. (2 marks) iv) Either of the gender has no degree (2 marks) c) Discuss the axioms of probability. (4 marks) QUESTION TWENTY FOUR a) Describe each of the following: i. Base period ii. Price relatives iii. Fixed-base index numbers iv. Chain-base index numbers (6 marks) b) Given are the following price-quantity data of fish, with price quoted in Ksh per kg and production in kg. Year 1980 1981 1982 1983 1984 1985 Price 15 17 16 18 22 20 Productio 500 550 480 610 650 600 n Construct: i. The price index for each year taking price of 1980 as base, (5 marks) ii. The quantity index for each year taking quantity of 1980 as base. (4 marks)