Business Statistics L2 Past Paper Series 2 2002

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2009/2/02/F 1 ASE 2009 2 02 1

SERIES 2 EXAMINATION 2002

BUSINESS STATISTICS

SECOND LEVEL

(Code No: 2009)

WEDNESDAY 17 APRIL

________

Instructions to Candidates

(a) The time allowed for this examination is 2 hours 30 minutes.

(b) Answer4 questions.

(c) All questions carry equal marks.

(d) Your answers should be written in blue or black ink/ballpoint. Pencil may be used only forgraphs, charts, diagrams, etc.

(e) Candidates should note that graph paper is provided within the answer book.

(f) All answers must be clearly and correctly numbered but need not be in numerical order. If noworking is shown, a correct answer may receive full marks but an incorrect answer will receive nomarks. Candidates are therefore advised to indicate how they arrive at their answers.

(g) Candidates must pay due regard to good figures, accuracy and neatness in their work.

(h) Candidates may use calculators provided the calculators give no printout, have no word displayfacilities, are silent and cordless. The provision of batteries and responsibility for their conditionmust rest with the candidate.

(i) A list of formulae appear at the end of the paper.

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QUESTION 1

(a) Explain what is meant by the term rate of inflation.(2 marks)

(b) State the main steps involved in the construction of an index to measure the rate of inflation.(5 marks)

(c) The following data was collected from the wages section of a company:

Employee Status 1997

Number ofEmployees

Weekly

Wage ()

2001

Number ofEmployees

Weekly

Wage ()

Non Manual: Men 100 260 80 344Manual: Men 480 242 240 325

Non Manual: Women 180 193 200 252Manual: Women 400 170 840 206

(i) Calculate a base weighted index which shows the increase in wages between 1997 and

2001.(8 marks)

(ii) Calculate a current weighted index which shows the increase in wages between 1997 and2001.

(8 marks)

(iii) Explain briefly the reasons for the differences in your answers to parts (i) and (ii).(2 marks)

(Total 25 marks)

QUESTION 2

The training manager of a large company has recorded the time taken by 200 new recruits tocomplete a particular task. The following table shows the distribution of times (in minutes):

Time Taken (minutes) Number of Recruits

0 and under 10 1610 and under 20 4420 and under 30 7230 and under 40 36

40 and under 60 2060 and under 90 12

(a) Construct a histogram to represent the data.

(8 marks)

(b) Estimate the modal value from the histogram.

(3 marks)

(c) Calculate the mean and standard deviation of the time taken.

(9 marks)

(d) Calculate the coefficient of variation explaining what it measures.

(5 marks)

(Total 25 marks)


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QUESTION 3

(a) Explain the meaning of the terms independent event and mutually exclusive event.(4 marks)

(b) A batch of 200 components checked by a company showed 4 to be substandard. A sample of3 components is to be selected at random from the batch with replacement.

Find the probability that the sample includes:

(i) no substandard component,

(ii) exactly one substandard component,(iii) more than one substandard component.

(13 marks)

(c) The high cost of inspection has resulted in the company having to consider alternative methods ofsample selection.

Write brief notes to explain the differences between the following pairs:

(i) Systematic and Quota sampling(ii) Multistage and Stratified sampling.

(8 marks)

(Total 25 marks)

QUESTION 4

(a) Explain the difference between primary and secondary sources of data.

(4 marks)

(b) The number of items produced last month by each of the 15 members of a production assembly

team was recorded as follows:

142 101 137 128 124 121 133 77127 108 139 68 112 123 130

Find the value ofeach of the following measures for the data given above:

(i) Range(ii) Quartile deviation

(iii) Mean deviation.(12 marks)

(c) For each of the measures listed, state what is being measured and give one advantage and onedisadvantage for each alternative.

(9 marks)

(Total 25 marks)


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QUESTION 5

The following data shows the turnover and profit levels of 8 companies in the year 2001:

Company Turnover (000)

Profit(000)

A 650 75B 520 90

C 400 16D 780 82

E 1100 135F 330 55G 850 92

H 970 105

(a) Plot the data on a scatter diagram.(4 marks)

(b) Calculate the product moment correlation coefficient between profit and turnover.(12 marks)

(c) Calculate the coefficient of determination and briefly outline what it measures.(4 marks)

(d) Explain how you would attempt to forecast the profit level for another company if you were giventhe turnover. Discuss the likely accuracy of such a forecast.

(5 marks)

(Total 25 marks)


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QUESTION 6

(a) Describe and illustrate diagrammatically the Lorenz Curve as a method of presenting businessdata.

(8 marks)

(b) The following data shows the monthly sales (in units) of a product during the years 2000 and2001:

Month Sales (units)2000

Sales (units)2001

January 102 124February 92 118March 110 130April 136 148

May 144 166June 156 178July 167 194

August 162 186September 123 142October 101 130

November 74 100December 174 213

(i) Draw a Z chart to represent the above data.(11 marks)

(ii) Give three detailed comments on your results.(6 marks)

(Total 25 marks)


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Business Statistics L2 Past Paper Series 2 2002