PRACTICE QUESTIONS FOR CH 6 INTRODUCTION ANDD COLLECTION OF NUMERICAL DATA FOR PIPFA Exercise 1(p 171): - Look through the following list of surveys and decide whether each is collecting data on attributes, discrete variable or continuous variable. (a) A survey of statistics text book, to determine how many diagrams they contain (b) A survey of cans in a shop, to determine whether or not each has a price sticker. (c) A survey of athletes to find out how long they take to run a mile (d) A survey of the heights of telegraph poles in Pakistan. Exercise 2(p 175): - Compare the postal questionnaire and the interview as methods of collecting data. Example (planning a survey p177): - You are asked to conduct a survey of the spending habits of the population of Pakistan. Write down the point you should think before conduct a survey. Exercise 3(p 179): - What might be a better way of asking Do you often go to the cinema? Exercise 4(p 181): - What types of problem can you envisage arising from the use of multiple choice questions? How can such problems be overcome? Practice question 6.1(SUFIAN LTD): - (a) Explain the importance of careful planning for a statistical survey, and list the matters which should be considered. (b) Sufian Ltd is planning to survey its regular customers, by sending each of them a questionnaire asking about delivery times, the quality of goods and payment terms. Outline the problems with may arise with the survey, and suggest how they might be overcome. Practice question 6.2(COLLECTING DATA): - (a) Compare and contrast the interview and the postal questionnaire as methods of collecting data. (b) Compare quota sampling and random sampling as survey methods. (c) The major survey conducted by most countries is a population census. Outline the main reasons why population censuses are usually conducted only every ten years. Practice question 6.3(SAMPLING METHODS): - (a) (b) (c) Sampling methods are frequently used for the collection of data. Explain the terms simple random sampling, stratified random sampling and sampling and sampling frame. Suggest a suitable sampling frame for each of the following in which statistical data will be collected. (i) An investigation into the reactions of workers in a large factory to new proposals for shift working. (ii) A survey of students at a college about the relevance and quality of the teaching for their professional examinations. (iii) An enquiry into the use of home computers by school children in a large city Explain briefly, with reasons, the type of sampling method you would recommend in each of the three situations given above. Practice question 6.4(MODERNISATION): - The head office of a company is situated in Multan City. The building is in urgent need of modernization and refurbishment. The least on the head office is due to run in 4 years time. The company has a number of options. (a) Apply to have the lease extended (b) Search for an up-to-date office accommodation in Multan City (c) Move out of Multan into a new purpose-built office block. The advantage of option (c) is that the cost of office space is much cheaper outside Multan. Staff would be easier to recruit and rates of pay outside Multan are much lower. It is expected that some office staff would wish to move outside Multan since house prices are cheaper and travelling time and travelling expenses are much lower. Relocation expenses (removal costs, all expenses in buying and selling a property, new carpets and curtains etc) would be met. However, it is thought that the majority of staff would accept redundancy payments which would be more generous than those under the Government scheme. The company decides to send a questionnaire together with a short explanatory letter to all the Multan employee to find out their views on the possibility of a move out of Multan. Draft the explanatory and the questionnaire.
Practice question 6.5(SALE NEWSPAPER): - A local weekly newspaper sells about half a million copies in a week in a region of about 100 square miles. Market research indicates that the readership profile is as follows. Age Annual income Age Annual income Sex Under 25 10 Under 10 10 Male 50 25----34 15 10----15 10 Female 50 35----44 20 15----20 25 45----54 20 20----25 25 Region 55----64 20 25----30 20 Rural 10 65+ 15 Over 30 10 Suburban 30 Total 100 Total 100 Town 60 You are working with a marketing colleague on the design of a sample survey to find out (i) current strengths and weaknesses of the paper and (ii) whether the introduction of colour, leisure and/or business supplements and so on would increase sales and by how much. (a) Considering the information requirements, recommend a method for collecting the data (such as by post, telephone, personal interviews and so on), giving reasons. (b) Design and explain a suitable practical sampling scheme that would achieve the objectives. Do not attempt to write a questionnaire. Practice question 6.6(SOURCE OF SECONDARY DATA): - What are the sources of secondary data?
PRACTICE QUESTIONS FOR CH 7 THE PRESENTATION OF DATA: TABULATION AND CHARTS FOR PIPFA Example (tables p196): - The total number of employees in a certain trades company 1000. They are employed in the departments: production, administration and sales. 600 people are employed in the production department and 300 in administration. There are 110 male juveniles in employment, 110 female juveniles, and 290 adult females. The remaining employees are adult males. In the production department there are 350 adult males, 150 females and 50 male juveniles whilst in the administration department there are 100 adult males, 110 adult females and 50 juveniles males. Draw up a table to show all the details of employment of people in department. Example (a frequency distribution p198): - The output in units of 20 employees during one week was as follows: 65 69 70 71 70 68 69 67 70 68 72 71 69 74 70 73 71 67 69 70 Construct frequency distribution. Example (grouped frequency distribution p198): - The output produced by each of 20 employees during one week was as follows in units: 1087 850 1084 792 924 1226 1012 1205 1265 1028 1230 1182 1086 1130 989 1155 1134 1166 1129 1160 Make a frequency distribution. Exercise 1(p 200): - The commission earnings for May 19X3 of the assistants in a department store were as follows (in rupees). 60 35 53 47 25 44 55 58 47 71 63 67 57 44 61 48 50 56 61 42 43 38 41 39 61 51 27 56 57 50 55 68 55 50 25 48 44 43 49 73 53 35 36 41 45 71 56 40 69 52 36 47 66 52 32 46 44 32 52 58 49 41 45 45 48 36 46 42 52 33 31 36 40 66 53 58 60 52 66 51 51 44 59 53 51 57 35 45 46 54 46 54 51 39 64 43 54 47 60 45 Prepare a grouped frequency distribution classifying the commission earnings into categories of Rs. 5 commencing with Rs. 25 and under Rs. 30. Example (pie charts p204): - The costs of production at Factory A and Factory B during March 19X2 as follows: Factory A Factory B Degrees Degrees Direct materials 70 35 15 20 Direct labour 30 15 125 50 Production overhead 90 45 50 20 Office costs 10 5 25 10 200 100 250 100 Show the costs for the factories in pie charts. Example (a simple bar chart p206): - A company s total sales for the years from 19X1 to 19X6 are as follows: Year 19X1 19X2 19X3 19X4 19X5 19X6 Sales 800 1200 1100 1400 1600 1700 Draw simple bar chart.
Example (a component bar chart p207): - Nestle Ltd., sales for the years from 19X7 to 19X9 are as follows: 19X7 19X8 19X9 Product A 1000 1200 1700 Product B 900 1000 1000 Product C 500 600 700 Total 2400 2800 3400 Draw component bar chart Example (a percentage bar chart p208): - The information in the previous example of sales of Nestle Ltd. Draw percentage component bar chart. Example (a multiple bar chart p208): - The output of Royal Fan Ltd in the years from 19X6 to 19X8 is as follows: 19X6 19X7 19X8 Product X 180 130 50 Product Y 90 110 170 Product Z 180 180 125 Total 450 420 345 Draw multiple bar chart Exercise 2(p 209): - Income for Habib Bank in 19X0, 19X1 and 19X2 is made up as follows: 19X0 19X1 19X2 Interest income 3579 2961 2192 Commission income 857 893 917 Other income 62 59 70 Using the above data, draw the following (a) A simple bar chart (b) A component bar chart (c) A percentage component bar chart (d) A compound bar chart Example (gantt chart p212): - Suppose that budget sales of Crown Ltd are as follows: Month January February March April May June Sales Units 1000 1500 2000 2500 1500 500 Construct Gantt chart. Example (a histogram p215): - The weekly wages of employees of National Salt Ltd are as follows: Wages per employee Number of employees > Rs. 40 Rs. 60 4 > Rs. 60 Rs. 80 6 > Rs. 80 Rs. 90 6 > Rs. 90 Rs. 120 6 > Rs. 120 Rs. 150 3 Draw histogram. Exercise 3(p 216): - The sales force of a company have just completed a successful sales campaign. The performances of individual sales staff have been analyzed as follows, into a grouped frequency distribution: Sales Number of sales staff Up to Rs. 10000 1 > Rs. 10000 Rs. 12000 10 > Rs. 12000 Rs. 14000 12 > Rs. 14000 Rs. 18000 8 > Rs. 18000 Rs. 22000 4 > Rs. 22000 1 Draw a histogram from this information.
Example (a frequency polygon p218): - The following grouped frequency distribution relates to the number of occasions during the past 40 weeks that a particular cost has been a given amount: Cost Rs. Number of occasions > Rs. 800 Rs. 1000 4 > Rs. 1000 Rs. 1200 10 > Rs. 1200 Rs. 1400 12 > Rs. 1400 Rs. 1600 10 > Rs. 1600 Rs. 1800 4 40 Prepare a frequency polygon. Exercise 4(p 220): - Look at the two budgetary control reports below. What should the second report be used for? Who would find the first one useful and why? What are the disadvantages of the first report compared with the second? BUDGETARY CONTROL REPORT JANUARY-JUNE 19X3 Fixed budget at 75 Actual results Variances Revenue costs 51 51 0 Material costs 25 21 4 Labour costs 6 9-3 Production overhead costs 3 2 1 Administrative costs 2 3-1 Selling and distribution costs 4 4 0 40 39 1 Profit 11 12 1 Practice question 7.1(IMRAN LTD): - The management of Imran Ltd wish to present some information about results to employees. It has been decided that a visual form of display would be the best way to communicate the information. The relevant data are as follows. 19X5 19X4 19X3 19X2 Sales cost 5.2 5.1 4.8 4.0 3.5 Direct materials 1.5 1.4 1.2 1.0 0.8 Direct wages 2.3 1.8 1.6 1.3 1.0 Production overhead 0.7 0.7 0.6 0.5 0.4 Other overhead 0.6 0.5 0.4 0.3 0.2 Taxation 0.0 0.3 0.4 0.3 0.3 Profit 0.1 0.4 0.6 0.6 0.8 Product groups, as a percentage of total sales, are as follows. Product group 19X5 19X4 19X3 19X2 W 33 36 38 30 25 X 5 10 12 18 25 Y 46 36 30 30 25 Z 16 18 20 22 25 19X1 19X1 Prepare two different visual displays to show the following (a) Sales by product group (b) A comparison of 19X4 with 19X5, analyzing total sales into costs, taxation and profit, with particular emphasis on direct wages.
Practice question 7.2(INTERPRETATION): - You are a management accountant s assistant, employed by a company operating coach services between backwards and forwards. This company has researched the preferences between coach and car travel of regular travelers on this journey. One hundred regular coach users and two hundred regular car users were interviewed about a journey to forwards. Some of the results were as follow. Question Which is quicker? Which is more economical? Which is more comfortable? Answer Coach Car Coach Car Coach Car users users users users users users Coach 76 18 80 120 16 18 Car 14 156 10 32 71 162 About the same 7 22 9 38 11 16 Don t know 3 4 1 10 2 4 (a) Draw conclusions from the data (b) Illustrate two of these conclusions with suitable charts Practice question 7.3(SOYUZ INSURANCE AND TELL HAL): - (a) By 19X9, the Soyuz Insurance Company had been in business for nine years. It now employs 20770 people, of whom the largest group (36) were sales staff, the next largest group (21) were accountants and the third largest group (18) were actuaries. Other groups of employees made up the rest of the staff. Thing had been very different when the company first began operations in 19X0. Then, it had just 4200 employees, of whom the 1260 actuaries were the biggest group; there were 1176 sales staff and just 840 accountants. By 19X3, the company employed 12740 people, and the growth in numbers had been most noticeable amongst sales staff, of whom there were 4840. There were 3185 actuaries. Accountants had increased substantially in number to 2550. The company s managing director has been very pleased with the growth in business over the past nine years, but has tried to limit the growth in the numbers of staff who are not sales staff, actuaries or accountants. Present the data above in tabular form Explain whether there are any comments you would make about what the information in the table should tell the managing director of the company. (b) The management of Tell Hall Ltd wish to present some information about result to employees. It has been decided that a visual form of display would be the best way to communicate the information. The relevant data are as follows. 19X5 19X4 19X3 19X2 Sales cost 5.2 5.1 4.8 4.0 3.5 Direct materials 1.5 1.4 1.2 1.0 0.8 Direct wages 2.3 1.8 1.6 1.3 1.0 Production overhead 0.7 0.7 0.6 0.5 0.4 Other overhead 0.6 0.5 0.4 0.3 0.2 Taxation 0.0 0.3 0.4 0.3 0.3 Profit 0.1 0.4 0.6 0.6 0.8 Product groups, as a percentage of total sales. Product group 19X5 19X4 19X3 19X2 W 33 36 38 30 25 X 5 10 12 18 25 Y 46 36 30 30 25 Z 16 18 20 22 25 100 100 100 100 100 19X1 19X1 Prepare two different visual displays to show the following. (i) Sales by product group (ii) A comparison of 19X4 with 19X5, analyzing total sales into costs, taxation and profit, with particular emphasis.
Practice question 7.4(PERCENTAGE FREQUENCY): - From the data in the following table construct (a) a relative or percentage frequency distribution (b) a histogram (c) a frequency polygon. Wages (Daily) Rs. Number of Employees 50.00----59.99 08 60.00----69.99 10 70.00----79.99 16 80.00----89.99 14 90.00----99.99 10 100.00----109.99 05 110.00----119.00 02 65 Practice question 7.5(MAN DISTRIBUTION): - (a) Describe the methods to construct: (i) a pie chart (ii) a histogram (b) For the data given below: 0.3 0.9 1.1 1.5 0.8 0.7 1.1 0.8 1.0 1.3 1.6 0.1 0.5 0.7 1.2 1.5 0.8 0.7 0.5 1.1 1.5 0.1 1.4 0.7 0.6 1.3 1.2 1.4 1.8 0.7 0.9 0.3 1.2 1.8 1.0 (i) Construct a frequency distribution taking equal classes of size 4.0 (ii) Calculate mean of the distribution (iii) Calculate mean of the raw data and compare it with the mean of the distribution. Practice question 7.6(PIE DIAGRAM): - Draw a Pie Diagram to present the following data about a family s expenditure: Item Amount Food 10000 Clothing 2000 Education 4000 Utilities 4000 Miscellaneous 5000 Note: exact measurements are not required and the diagram may be drawn freehand.
PRACTICE QUESTIONS FOR CH 8 THE PRESENTATION OF DATA: GRAPHS FOR PIPFA Exercise 1(p 233): - The following table shows the distribution of the levels of turnover of the companies in a certain industry. Turnover Number of companies Over 500----1000 32 Over 1000----1500 58 Over 1500----2000 41 Over 2000----2500 33 Over 2500----3000 28 Over 3000----3500 16 (a) Construct a Lorenz curve from these data. Use mid-point of each calss as the turnover of each company in the class. (b) State what this chart shows. Example (Z charts p234): - The sales figures for a company or 19X2 and 19X3 are as follows: 19X2 sales Rs. m 19X3 sales Rs. m January 7 8 February 7 8 March 8 8 April 7 9 May 9 8 June 8 8 July 8 7 August 7 8 September 6 9 October 7 6 November 8 9 December 8 9 90 97 Draw a Z chart to represent these data. Exercise 2(p 235): - Why does the annual moving total line on a Z chart show the long-term trend, unaffected by seasonal effects such as sales being higher in summer than winter? Example (time series p238): - The following data show the sales of a product in the period 19X6-X8: Year Quarter I 000 Quarter II 000 Quarter III 000 Quarter IV 000 19X6 86 42 57 112 19X7 81 39 55 107 19X8 77 35 52 99 Plot a time series of the above data. Example (scattergraphs p238): - The output at a factory each week for the last ten weeks, and the cost of that output, were as follows: Output (units) 10 12 10 8 9 11 7 12 9 14 Cost (Rs.) 42 44 38 34 38 43 30 47 37 50 Draw scattergraphs.
Practice question 8.1(SEVEN UPP LTD): - Illustrate the following data by means of a histogram and an ogive. The distribution of average weekly wages paid to direct labour employees at the factory of Seven Up Ltd is as follows. Weekly average wage Rs. Number of employees 51 and < 56 5 56 and < 61 8 61 and < 66 12 66 and < 71 16 71 and < 76 21 76 and < 81 25 81 and < 86 20 86 and < 91 14 91 and < 96 6 96 and < 101 3 Practice question 8.2(LORENZ INCOME): - (a) Briefly outline the uses of the Lorenz curve (b) Distribution of annual income before tax 19X8-X9 Range of income Rs. No of people Millions Total income Rs. bn 2500----5000 2.6 10 5000----7500 3.7 23 7500----10000 3.3 29 10000----15000 5.2 64 15000----20000 2.9 50 20000----30000 2.3 54 30000 and over 1.0 48 Total 21.0 278 The figures above are estimates based on a projection of 19X5-X6 data (i) Use a Lorenz curve to examine the distribution of income in 19X8-X9 (ii) Comment on the data and your diagram. Practice question 8.3(INTERPRETATION OF LORENZ CURVE): - (a) (b) List the basic principles to be observed in the construction of a graph. In a cooperative farm, the land was sub divided into plots as follows: Size of plots in hectares 0----10 10----20 20----30 30----40 40----50 Number of plot 320 160 60 40 20 Construct a Lorenz curve and interpret the curve Practice question 8.4(Z CHART): - The manufacturing costs of Prodco Ltd for the period from January 19X6 to December 19X7 are displayed in the table below. Month 19X6 Manufacturing cost Rs. 000 Month 19X7 Manufacturing cost Rs. 000 January 35.8 January 43.9 February 33.6 February 40.1 March 35.5 March 46.0 April 37.5 April 48.7 May 34.2 May 48.9 June 36.3 June 46.0 July 36.0 July 48.3 August 35.4 August 47.9 September 30.4 September 48.2 October 36.1 October 47.0 November 37.5 November 49.4 December December 51.5 (a) Draw a Z chart using the above data. (b) Describe the purpose of such a chart. Use the diagram that you have just drawn to illustrate your answer.
Practice question 8.5(INTERPRETATION): - Draw a semi logarithmic graph of the following data and interpret it. (The figures have been grossly exaggerated in order to illustrate the point). Time 1 2 3 4 5 6 7 Price 6 12 24 35 70 140 280 Practice question 8.6(REPRESENTATIVE SALES): - The sales manager of a firm randomly selected 10 sales representatives. He gathered data on the number of calls and the number of units sold by each representative in one month, which is as follows: Sales Representative Number of calls made Number of units sold 1 14 28 2 35 66 3 22 38 4 29 70 5 6 22 6 15 27 7 17 28 8 20 47 9 12 14 10 29 68 Plot the data in a scatter diagram. Based on the scatter diagram, what observations can you make?