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

1. (a) State, giving the reasons, the average to be used in the following situations: (i) To determine the average size of the pair of shoes to be sold in the shop, (ii) To determine the average wages in a company, (iii) To find the average beauty among the participants in a fashion show, (iv) To find out per capita income in different cities. (4) a) If the first four moments about the value 5 are -4, 22, -117 and 560, determine the corresponding moments about the mean. (5) (c) Mr. Devavrat, a prospective corporate buyer, compared polyethene bags produced by two companies and tested bursting pressure of the bags and recorded results as follows: Busting Pressure Ob.) Number of bags Company A Company 8 You are required to find out : (i) Average bursting pressure for each company, (ii) Which company bags have more uniform pressure? (iii) If the prices are the same, which company's bags would be preferred by the buyer? (9) (d) A leading retail chain is conducting a performance review of its outlets to identify variation in sales and to classify outlets into different performance segments. The management is particularly interested in understanding the distribution of sales among the lower-performing, average-performing, and top-performing outlets for better strategic decision-making. The following data shows the monthly sales (in { lakh) across 100 outlets : Monthly Sales € ]aTh) Number of Outlets You are required to : (i) Determine the sales level below which 25°/o of the outlets fall. (ii) Identify.the sales level above which only the top-perfoming 25% outlets are placed. (iii) Briefly comment on whether the sales distribution is concentrated or widely spread among the middle-performing outlets. (9) (e) Calculate Karl Pearson's coefficient of skewness for the following distribution: profits (€ ltd) 20 40 60 80 100 a,ess than) Number Of companies 16 40 loo 128 140 ® Identify the suitable measure of dispersion for each of the following cases giving reasons thereof: (i) An investor is comparing two mutual funds that have different average returns and wants to assess which fund is more consistent relative to its returns. (ii) A logistics company anal.yses delivery times which vary slightly but consistently, with no major delays or extreme values. (in) Two sales teams have different average sales figures. Management wants to compare which team is mo're consistent in performance. 2. (a) A well-established automobile components manufacturing company produces premium headlights for leading car brands using three automated production machines; Machine A, Machine 8, and Machine C. These machines contribute differently to the total production, where Machine A produces 40%, Machine