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Unique Paper Code 7502

Revised 0 of 26

Business StatisticsDecember 2025

B.Com (Programme) · 5 questions · 1 part still being checked

Duration: 3 HoursMaximum Marks: 90

Reworded by Kunji from the printed paper. The original paper belongs to the University of Delhi. See DU's question bank.

Before you start

Numbers and theory. 15 numerical parts and 8 theory parts. Numericals take longer to lay out, so give them your freshest time.
Pace. Two minutes a mark: about 36 minutes for each 18-mark question, with nothing spare in 3 hours. Pick your side of each OR before you start writing.
Keep score. Every part opens a worked answer checked against the books. Turn the key when you have revised it; the boxes at the top fill in, on this device.

1.

18 marks
· ~36 min

(a)Is the arithmetic mean an average for every purpose?asked 2×"Different averages serve different purposes, but the arithmetic mean is an ideal average that can serve every purpose" Comment(3)

(b)Revised mean, standard deviation and coefficient of variation after late returnsasked 2×For an industry, the mean profit of 80 firms is found to be ₹55 crores with a coefficient of variation of 40%. During the survey, 5 firms could not report profits before the data were compiled. Their profits were…(6)

(c)Age limits after retrenchment and the average age before and afterasked 2×The age distribution of 2,000 employees employed in a large textile mill is given below : Owing to heavy losses, the management decides to bring the strength down to 40% of the present number as per the scheme below:…(9)

OR

(d)Average, SD and CV of two dealers' daily sales, and the effect of a constant changeasked 2×Taraa Ltd., which manufactures electric scooters, recorded the daily sale of two authorized dealers over ten days of the festive season, as given below: Calculate and comment on : (i) Average number of electric scooters…(9)

(e)

First four central moments, skewness and kurtosis of consumers' incomesBeing checked

(6)

(f)Purpose of the coefficient of variation; variance compared with itasked 2×What purpose is served by the coefficient of variation? Distinguish between variance and the coefficient of variation.(3)

2.

18 marks
· ~36 min

(a)Two projects: probability that Chennai also misses, and that at least one succeedsasked 2×At present a company is running two projects, one in Pune and the other in Chennai. The probability that the Pune is successful is 0.3, while the Chennai project is successful with probability 0.6. (i) If the Pune…(5)

(b)Acceptance sampling of chipsets: accept, second sample or reject (binomial)asked 2×On average, a machine produces 10% defective chipsets. When the quality manager visits to inspect, a batch is accepted if a sample of 7 chipsets drawn from it contains no defective chipsets, and rejected if the sample…(9)

(c)Mutually exclusive events and independent eventsasked 2×Distinguish between mutually exclusive events and independent events, with the help of examples.(4)

OR

(d)Bayes' theorem: who was selected, given that the structure changedasked 2×A, B, and C are candidates for the post of director at a private firm, and their chances of selection are in the ratio 4:3:3. The probabilities that they will make changes in the organization structure are 0.4, 0.7, and…(6)

(e)Poisson probabilities of accidents on a motorway stretchasked 2×An insurance company is studying the risk of accidents on a particular stretch of motorway so as to adjust its premium rates. Accidents occur on this stretch at the rate of 4 per month. Find the probability that in a…(9)

(f)When a Poisson distribution approximates the binomialasked 2×Under what conditions can a Poisson distribution reasonably approximate the binomial distribution?(3)

3.

18 marks
· ~36 min

(a)Regression of sales on advertising: equations, r², an estimate and the standard errorasked 2×A retail company wishes to analyze how advertising expenditure affects its monthly sales revenue. The marketing team collected data for the past ten months on the advertising budget (in thousand rupees) and the matching…(10)

(b)Number of pairs from the probable error, and the limits of the correlation coefficientasked 2×In a factory, the correlation coefficient worked out for a sample containing a certain number of observations on two items produced is 0.85 while the probable error is 0.047. Find out the number of pairs of observations…(4)

(c)The standard error of estimate and its importance in regressionasked 2×Explain the concept of the standard error of estimates. Also discuss its importance in regression analysis.(4)

OR

(d)Spearman's rank correlation of consultants' productivity and client satisfaction, with tied ranksasked 2×Crest Consulting, a management consulting firm, is studying how consultant productivity scores relate to client satisfaction ratings within its project teams. The firm supplies the productivity scores and…(9)

(e)Means, correlation and standard error from two regression linesasked 2×A company wishes to analyse the link between Employee Training Hours (X) and Employee Productivity Score (Y). The two regression lines below summarize their findings : 5Y-4X-280=0 and 6Y-5X-330=0 (i) Determine the…(9)

4.

18 marks
· ~36 min

(a)Straight-line trend by least squares, monthly conversion, shift of origin and detrendingasked 2×Evergreen Electronics Ltd. has recorded its revenue for each year (in crores) from 2017 to 2024, as shown below : You have to : (i) Fit a straight-line trend to the revenue data by the method of least squares. (ii)…(14)

(b)Coefficient of determination and standard error of estimate from explained and unexplained variationasked 2×In a regression equation of Y on X based on 11 observations, the explained and unexplained variations were found to be 18 and 27 respectively. Find out the coefficient of determination and the standard error of estimate…(4)

OR

(c)Second-degree parabolic trend of production and a forecast for 2027asked 2×The production of a commodity in 2019-2024 is shown below : You are required to : (i) Fit a parabolic trend of second degree, (ii) Compute the trend values for each of the years 2019 through 2024. (iii) Predict the…(9)

(d)Identifying the component of a time series in five situationsasked 2×Which component of a time series would you mainly associate with each of the following; give reasons: (i) An abrupt supply chain disruption at a semiconductor manufacturer that halts production for one month. (ii)…(5)

(e)Coefficient of determination: meaning, use in decisions, and whether it is always positiveasked 2×Explain briefly the following : (i) What is the coefficient of determination? How is it important in statistical decision making? (ii) "The coefficient of determination is always positive." Do you agree? Back your view…(4)

5.

18 marks
· ~36 min

(a)Laspeyres, Paasche and Fisher price indices from base prices and expenditures, and the ideal indexasked 2×In a survey related to inflation, a national agency collected the following data for five commodities : Find out the price index by : (i) Laspeyres's Method, (ii) The method of Paasche, (iii) Fisher's Index Method. (iv)…(9)

(b)Normal distribution of hospital bills: numbers and probabilitiesasked 2×Sanjeevani care, a hospital specialized in heart surgery, admitted 5,000 patients in the year 2023-24. The average payment made by a patient was ₹3,00,000, with a variance of ₹40,00,00,000. Assuming that the…(9)

OR

(c)Cost-of-living index and the salary rise needed to compensateasked 2×Silver Pay Solutions Pvt. Ltd., a leading FinTech company based in Pune, wants to review its employees' cost of living in order to consider a salary hike. The HR department has gathered data on the average monthly…(9)

(d)Selling at least one of two products, and both products if the sales were independentasked 2×On any given day a sales representative can sell Product A with probability 0.5, and the same representative can sell Product B on that day with probability 0.4. The probability that the representative sells both…(4)

(e)Where the Poisson distribution applies; the axiomatic approach to probabilityasked 2×Explain briefly the following : (i) In what situations can the Poisson distribution be used? Explain with suitable examples. (ii) Discuss the axiomatic approach to probability.(5)

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