Business Statistics — DU B.Com (P) Previous Year Question Papers

1. (a) State the empirical relationship between mean, median and mode for symmetrical and asymmetrical distributions. Under what circumstances median (3) is considered to be a better average than Arithmetic Mean? (b) You are given frequency distribution of wages (in 000 rupees) paid to the workers in a factory as under : Calculate Mean Deviation about Median. (6) (c) A car manufacturing company facing a dispute with labour decided to make changes in compensation policies after deliberation with the labour union. The following table exhibits information before and after settlement: Before dispute After dispute Mean wages 650 700 Median Wages 680 650 Standard Deviation 50 40 You are required to compare the position before and after the dispute settlement in terms of : (i) Total Wages, (il) Modal Wages, (iii) Coefficient of variation, (iv) Skewness, and (V) Also comment on whether employees got benefits out of this settlement or not. (9) (d) A toy manufacturing firm recorded the daily production data for two machines over a period of ten days, as shown below: (i) You are required to calculate and comment on Mean and Standard (i) Which machine manufactures toys more consistently? (iii) How will the statistics change if all the observations of Machine A are decreased by 10, and all the observations of Machine B are increased by 30? Show the revised results. (9) (e) A survey provides data on the monthly income (in thousand rupees) of consumers as follows: Monthly Income (000 2) 40 - 42 43 - 45 46 - 48 49 - 51 52 - 54 Number of Consumers 32 22 31 44 21 You are required to calculate the following statistical measures : (i) First four moments about the mean. (ii) Moment coefficient of skewness. (iii) Moment coefficient of kurtosis. (9) 2. (a) An investor uses either mutual funds or stocks to manage his portfolio. The probability of his investment losing value if he invests in mutual funds is 0.1, and the probability of his investment losing value if he invests in stocks is 0.2. What is the probability that his investment lost value? (4) (b) A company produces electrical components utilizing three non-overlapping work shifts. It is observed that 50%, 30%, and 20% of the components are produced during shifts 1, 2, and 3, respectively. Furthermore, 6%, 10%, and 8% of the components produced in shifts 1, 2, and 3, respectively, are defective. Determine: (i) What percentage of all components is defective? (i) Given that a defective component is found, what is the probability that it was produced in shift 3? (5) (c) A company receives 80% of its shipments from its supplier without any damage. The quality control inspector examines 16 shipments from this supplier. Determine the average number (mean) and the standard deviation of shipments that arrive undamaged. (4) (d) A manufacturing plant experiences an average of two equipment failures per week. What is the probability of: (i) exactly three equipment failures in a given week, -