Return to Exercise 6 in Chapter 4. The Finance Department in the local authority has estimated that at least 45 people per day on average need to use the local library to justify the cost of keeping it open – costs relate to staff wages, heating, lighting, cost of periodicals and so on. You have been asked to evaluate the data collected on the mean number of people using the library in the context of this minimum figure. Draft a report to the committee (most of whom have low levels of numeracy) evaluating the information available. If you had been given the task of collecting data on the number of users how would you have done this and how would you try to ensure you had a representative sample? Data from Exercise 6 in Chapter 4: The leisure services committee of a local authority has seen its budget decline over the last few years and is currently having to consider closing a number of its leisure facilities – sports halls, small parks, museums and so on. One closure being considered is that of a small branch library in an outlying village. As a preliminary aspect of the decision some data has been collected on the number of people using the library and its facilities: No. of people using the library per day ………………………. No. of days less than 10……………………………………………5 10 < 20…………………………………………………12 20 < 30……………………………………………….28 30 < 40………………………………………………44 40 < 50……………………………………………….50 50 < 75……………………………………………….30 75 or more…………………………………………..8 Calculate suitable measures of average and dispersion for this data. Comment on the usage of the library.
> Go to the St. Louis Federal Reserve FRED database, and find data on recession dating (USREC), the unemployment rate (UNRATE), nonfarm payroll employment (PAYEMS), and the mean duration of unemployment (UEMPMEAN). a) Using the recession dating series (USR
> Go to the St. Louis Federal Reserve FRED database and find the most currently available data on Currency (CURRNS), Total Checkable Deposits (TCDSL), Total Reserves (RESBALNS), and Required Reserves (RESBALREQ). a) Calculate the value of the currency depo
> You have been appointed secretary of a student group which has an annual programme of invited speakers from the business world. The group has suffered from a membership decline over the last few years and you are keen to reverse this trend by planning a
> Table 3.23 shows per capita income in the UK and consumers expenditure on a number of categories. For each category, analyze the relationship between income expenditure using scatter plots. Table 3.23 UK per capita income and per capita consumers' e
> A local authority operates a leisure centre for its citizens, offering a swimming pool, squash courts, badminton and other facilities on a single site. Last year the authority was concerned about the relatively low number of people using the facilities o
> Table 3.20 shows data on the distribution of incomes before and after tax in the UK in 2012/13. Using Lorenz curves analyse the data shown. Table 3.20: Table 3.20 Incomes before and after tax UK 2012/13 All Males Females Range Total Total Total of t
> Table 3.19 shows data on employment rates and unemployment rates for EU countries and for selected other countries for 2013–2014. Analyze the data using appropriate diagrams. Employment rate is the number of people in paid employment as
> Table 3.18 shows selected labour market statistics for spring 2014 for each region of the UK. Draft a report highlighting key patterns. Table 3.18: Table 3.18 UK labour markot statistics Spring 2014 Economically active In Employment Unemployed Econo
> Table 3.17 shows motor vehicle production from 2000 to 2013 for selected countries and the global total. Using appropriate diagrams and any additional calculated statistics, comment on the trends in production over this period. Table 3.17: Table 3.1
> Table 3.16 shows the UK expenditure on bilateral aid from 2009 to 2013 by geographical region of the recipient country. Using appropriate diagrams, draft a short report highlighting key patterns and trends Table 3.16 UK total expenditure on bilatera
> You also obtained supplementary information about the financial costs typically involved in providing health care for people of different ages. On a per capita basis the costs are as shown in Table 3.15. Age group……………………..Estimated spending
> Like many countries, Scotland is facing challenges in terms of providing health care to a demographically changing population. Health care provision and planning is organised largely on a regional basis. Two of the regions have commissioned a short repor
> The company you work for is considering acquiring several of the latest generation desktop computers for use in an office. The company expects the equipment to have a useful life of three years. The finance director has asked you to recommend whether the
> The data below shows quartile and median income for UK taxpayers before and after paying income tax for selected years. Analyze and comment on the data. Total income before tax Total income before tax Lower Upper quartile Lower Upper quartile quart
> A retail organization has recently been investigating customer spending patterns at two of its stores, Store A and Store B, and has obtained the following data: Using these statistics, and any others you can derive, draft a short management report summ
> The data shown in Table 4.15 shows average weekly earnings for all adults, weekly rate of unemployment benefit for single adults and the retail price index for the UK for the period 2000–2014. Using this data comment on any trends in
> The leisure services committee of a local authority has seen its budget decline over the last few years and is currently having to consider closing a number of its leisure facilities – sports halls, small parks, museums and so on. One closure being consi
> Table 4.14 shows the age distribution of males and females in England and Wales at the time of their marriage, from 1981–2011. Using the data calculate for each gender: (a) the mean (b) the median (c) the standard deviation (d) the lowe
> In the Laspeyres index in this chapter we used 2010 as the base year. Choose 2014 as the base year instead and recalculate the Laspeyres series for 2010, 2014 and 2015. Comment on these values compared with the index base 2010.
> For the data in Table 4.11, plot the real and money values over time on the same graph. Comment on the potential for misleading the user of money values. Table 4.11: Table 4.11 Hourly rates and hours worked: Part-time staff 2010 2014 Hourly pay Hour
> A local residential community has been complaining to the chief of police about speeding traffic through their area. Residents have complained that vehicles driving through the community have not been observing the speed limit, which officially is 50 kil
> For the two data sets shown below calculate the mean and standard deviation and comment on the relationship. Set 1………………………………Set 2 10……………………………………….100 20………………………………………200 30……………………………………..300 40…………………………………….400 50…………………………………….500
> A firm is involved in manufacturing high-quality electrical equipment. Each item produced costs £6000 and total annual output is 500 items. At the end of the production process each item is individually tested for quality and safety. If the item is defec
> You have the choice of investing a sum of money in four alternative schemes: (a) one which will pay 10 per cent per annum interest compounded daily; (b) one which will pay 10.25 per cent per annum interest compounded monthly; (c) one which will pay 10.5
> A supermarket sells one particular item in its store on a regular basis. It currently has 750 units of this item in stock and no deliveries are expected until next week. The manager knows that average weekly sales of this item are 625, standard deviation
> An enterprising MBA graduate who has been unable to find gainful employment has taken to visiting an office block in town each lunch time with an array of freshly made sandwiches for sale. The graduate reckons that he has a 90 per cent chance of selling
> An auditor is checking invoices that have been paid to see if they contain any errors. Historically around 7 per cent of all invoices are expected to contain some error. The auditor takes a random batch of ten invoices. Calculate the probability distribu
> On average last year a local leisure centre had 230 customers per day, standard deviation 27, and the distribution of customers was found to be Normal. Determine the probability that on any one day the centre has: (a) more than 270 customers (b) less tha
> A small firm has recently purchased a new PC system comprising a colour monitor, a CPU, a laser printer and a keyboard. The supplier of the equipment states that the chance of any one of the components developing a fault in the first year is 1 per cent.
> A large retail store buys an item from a supplier in batches of 100. Because of the delicate nature of the item some are inevitably damaged in transit between the supplier and the store and the price the store pays to the supplier reflects this. Over the
> The finance department of a large organization has responsibility for monitoring costs in other departments of the organization. A photocopier facility is available for one department’s use and data has been collected which reveals that the number of pho
> Return to the Worked Example in this chapter. After conducting market research we have found that the possibility of a customer in the top 5 per cent group switching to a competitor is 0.85 if we do not offer a price discount and 0.15 if we do. Consider
> Return to the example used in the chapter of two machines filling bottles of shampoo. One machine had a mean of 500 ml, SD 10 ml, the other a mean of 750 ml, SD 15 ml. For each machine calculate the lower and upper amounts (in ml) between which: (a) 90 p
> Return to the example of Machine 2 in the shampoo bottle problem. Assume that management likewise wishes to ensure that the advertised contents satisfy some specific criteria. Determine what the advertised contents should be if management: (a) require no
> Return to the worked example data shown in Table 2.2. (a) Calculate the percentage of total transactions split between credit cards and debit cards and show the results in a suitable diagram. Comment on what you see. How many significant figures do you t
> A small company finds itself in the position of having to complete a contract for a large customer or pay high financial penalties for failing to deliver. The firm finds itself with a problem. The stocks of one particular component used to assemble the p
> A small engineering firm is under increasing pressure from foreign competitors and is considering a number of strategic options. One of these relates to changing over from the existing production process to one which is completely automated. The firm has
> A large multinational oil company is considering its strategy in the North Sea. The UK government has announced that a new drilling site in the North Sea will be offered for sale on a competitive tender basis, the site going to the company making the hig
> A manufacturing firm has decided to capitalize on its existing success by building an extension to its production plant to come on stream by 2018. The firm has evaluated the decision and calculated that its profitability will improve by £650 000 if the e
> Consider the pay-off in Table 6.3 without the probability information. How could you now evaluate suitable decisions? Table 6.3: Table 6.3 Pay-off table: Eastern Europe (£000s) Market growth Zero Low High Pilot programme 10 50 150 Major product lau
> For the pay-off table shown in Table 6.3 construct a decision tree to confirm the decision without perfect information. If the pay-off for pilot/zero growth was now changed to -£10 (000), how would this affect the potential value of perfect
> An organization is trying to evaluate which of two PC computer systems to standardize on within the organization. In terms of price, specification and performance there is little to choose between the two models being considered, Model A and Model B. How
> A local training agency is trying to get government support for its activities – which relate to the provision of industrial and commercial training for the local labour force – on the basis that unemployed workers who are better skilled have a better ch
> A local hospital is trying to assess its performance vis-à-vis national performance. The Department of Health has recently indicated that, nationally, for a particular hospital-based treatment the mean length of stay of patients in hospital was 8.6 days.
> A local authority has a pool of cars available for staff to use on official business. One particular make and model of car, of which the authority has a considerable number, claims to give a miles per gallon (mpg) performance of 52 mpg for simulated out-
> A large organisation is considering replacing part of its vehicle fleet with the latest equipment. Although such a decision is expensive, it is felt that the investment will be worthwhile in terms of generating future cost savings in repairs, maintenance
> A small engineering firm manufactures high-precision components for the aeronautical industry. In order to ensure quality, the production equipment has to be regularly maintained. One particular component in the production equipment must be replaced regu
> In the Worked Example in Chapter 5 we had a distribution of a sample of customers’ electricity consumption. Test whether this distribution is Normal.
> Several years ago a new chief executive was appointed to a group of firms. On appointment the CE expressed concern about the quality of the senior management in one of the major companies in the group. He felt that this group of managers was by and large
> An airline operating between London and Aberdeen knows that a large part of its customer base represents business executives. The airline is considering offering a limousine service to/from the airport to be included in the airline ticket price, which wo
> Recent legislation requires adherence to detailed and complex food-labelling requirements on products sold to consumers. A recent survey examined whether the food labelling on supermarket own-brand products met these requirements. The results were catego
> An international company routinely rotates its senior managers every five to six years around its activities worldwide. Staff are financially compensated for such moves but with many staff buying a house in their new location, there are concerns about re
> A company employs largely part-time staff, and in the past has found staff turnover to be 23 per cent each year (that is 23 per cent of staff in any one year leave the company). This is felt to be too high, with implications for morale, motivation and co
> The Inland Revenue has introduced a self-assessment system for tax payments whereby citizens themselves calculate the amount of tax to be paid on income each year. Naturally, the Inland Revenue checks such self-assessments, although it does not have the
> Return to Exercise 6 in Chapter 4. Calculate the mean and standard deviation if you have not already done so. Given that this data is a sample, calculate the 90 per cent, 95 per cent and 99 per cent confidence intervals around the mean. Provide a managem
> An airline company is considering providing a new daily service between Edinburgh and Copenhagen. The aircraft has a maximum capacity of 200 passengers and each flight incurs a fixed cost of £25 000 (regardless of the number of passengers). In addition,
> A public transport organization has had a reputation for many years of caring little for its customers – the passengers it carries. In particular, the enquiry office has had a particularly poor reputation. New management have decided to try to improve th
> A hospital laboratory has the task of screening blood samples of patients and producing a summary report for clinicians. Because of the limitations of equipment, staff training and time, the laboratory manager knows that there is an error rate involved i
> A large manufacturing firm is concerned about lost production: that is, production capability that was not utilized for a variety of reasons. One of the causes of such lost production has been identified as employees taking time off work because of illne
> A large retail organization is currently investigating a number of areas of its operations with a view to improving performance in terms of efficiency, sales and profits. The organization has been monitoring the monthly sales of one of its more profitabl
> The following exercises all relate to the development of a suitable time-series decomposition model for the data shown. In each case you should adopt the following procedure: (a) Plot the original data as a time-series graph. (b) Determine whether an add
> Consider the two sets of sales data in Table 9.14. Apply the exponential-smoothing model to this data with a variety of values. What do you observe about the accuracy of the model over time in the two series? Table 9.14 Weekly sales Week Sales uni
> Return to the unit sales data used in this chapter. Apply the exponential-smoothing model to this data using values for a of 0.15, 0.2, 0.25 and 0.3. Assess the accuracy of each choice of a and decide which you would use to forecast future values.
> A senior police manager is reviewing manpower allocation of police officers to a number of geographical districts which fall under her responsibility. Data has been collected on a number of variables, as shown in Table 10.22. Crimes The number of reporte
> A training agency is currently reviewing part of its operations. It runs one particular scheme whereby young people who are unemployed are put through a training course which provides them with a variety of IT skills including word-processing, spreadshee
> A large retail organisation has a number of home-furnishing outlets in a particular region, selling products such as carpets, curtains, domestic furniture and fittings. The organisation has been affected badly by the downturn in domestic property sales i
> Next week you have to travel around parts of the country on business and have decided to hire a car from a car-hire company. You have contacted two companies which offer different services. The first company will rent you a car for £45 per day. The secon
> As manager of a local leisure centre you are investigating the frequency of use of the centre by its members. You hope that by understanding some of the key factors that influence how often members use the centre’s facilities you will b
> The corporate planning department in a large brewing company has been trying to develop a medium-term forecasting model relating to the demand for one of their products: a low-alcohol lager. The method used has been based around multiple regression. The
> A small engineering company has been monitoring its total costs over the last few years on a quarterly basis together with the number of employees and production level. In order to assist the company to evaluate alternative strategic and operational opti
> In the worked example we analyzed the relationship between per capita income and consumers’ expenditure on Food & Drink. Table 10.17 shows consumers’ expenditure on a number of other categories. For each category,
> Return to the variables used in Chapter 9, Exercise 3. In that exercise you were required to obtain a trend for each variable using moving averages. For each trend that you obtained, forecast the trend one year into the future using regression. Evaluate
> For the following data calculate the correlation coefficient and plot the data on a scatter diagram. Do you think it measures the strength of the relationship accurately?
> A small electrical repair shop finds it has two main types of work. Customers bring items in for repair: TVs, videos, etc. require major repair; other repairs are classed as minor. At present the shop has more business than it can handle and is trying to
> A small engineering company makes two products for export, A and B. Both products go through a four-stage process: turning, grinding, polishing, finishing. The two products are produced in batches of 100 items and the time taken, in hours, for each batch
> For the problem in Exercise 1 assume the firm now wishes to maximise revenue rather than profit (a) Formulate this problem in terms of determining the revenue-maximising combination of the two products on a weekly basis. (b) Solve the problem graphicall
> A manufacturer is trying to determine the combination of two products, A and B, that should be produced. Each product passes through a three-stage production process: Stages I, II and III. For product A Stage I takes three hours of labour, Stage II four
> A firm finds that the demand for its product can be represented mathematically as: Qd = 1000 - 5P where Qd is the number of units of the product demanded by customers and P is the selling price. (a) Construct a graph for a price between 0 and 200. (b) Co
> A large construction company has recently won the contract for routine inspection and maintenance of the Channel Tunnel linking the UK to France. Obviously, routine maintenance and repair work, unless carefully planned, will have adverse consequences on
> A domestic appliance manufacturer is evaluating its delivery system from the production plant to showrooms around the country. One item used in the transportation of large appliances is a prefabricated polystyrene-foam packing case. These are supplied by
> Following internal reorganisation in a large brewing company, a comprehensive review of stock-control procedures is currently being undertaken. You have been asked to investigate stock control in the context of one of the firm’s products: lowalcohol lage
> A local authority operates over a large geographical area. The Education Department is responsible for ensuring that stocks of a certain item are kept for distribution to schools through the area on request. In order to try to ensure supplies reach the s
> A company requires a particular item from an outside supplier for its production process. Annual demand for the item is 3000 units. Order costs are estimated at £15 and holding costs at 20 per cent of the purchase price of the item, which is £5.50 per un
> Describe the quantitative techniques that are available to assist a manager with stock-control responsibilities in an organisation.
> What are the basic decisions that a manager with stock-control responsibility faces and what are the likely objectives of such a manager in this context?
> For a particular project the information in Table 13.17 has been obtained. (a) Construct a network diagram for this project showing EFTs, LFTs and the critical path. (b) The company concerned has indicated that it would like the project completed in no m
> A firm is making minor alterations to its automated stock-handling system in one of its warehouses. The relevant information relating to this project is shown in Table 13.16. The table shows the activities that must be completed, their expect
> A project comprises the activities shown in Table 13.15, which also shows the duration of each activity. (a) Construct a network diagram for this project and determine the expected completion time together with the critical path. (b) Determine the prob
> A company is thinking of investing £15 000 in a savings fund. The fund runs for a 10-year period and is expected to generate a return each year of 8 per cent of the amount invested. All annual returns remain in the fund until the end of the period. (a) C
> In the project detailed in Table 13.13, activity labels indicate the major activities to be completed in a project. The duration of each activity and cost of each activity have been identified, on both a normal basis and a crash basis. (a) Construct a ne
> A large banking organisation is installing a network of automated teller machines (ATMs) for use by its customers in a large town. These machines are installed in an exterior wall of the bank and allow customers to withdraw cash from their accounts. A nu
> A business organisation is trying to improve staff morale and motivation and has decided to replace the existing staff canteen with a modern cafeteria. The works department has drawn up a detailed list of the various activities that will need to be compl
> A utility company is currently reviewing its manpower requirements in the domestic-appliance servicing department. One feature of the servicing work relates to domestic central-heating systems. For an annual fee, a trained engineer will undertake a safet
> You are currently employed by a high street bank and have been asked to investigate the bank’s policy in one particular area of its operations, that relating to small loans to individual customers. The loans in question are usually shor
> An investigation is being carried out into a local authority’s housing policy. The local authority has a limited supply of housing which it owns and rents out. It receives requests for housing from a number of individuals and families t
> An organisation has recently purchased a company car for one of its senior managers at a cost of £25 000 and is trying to determine the most suitable time for replacement. It is estimated that the car will depreciate by £5000 in the first year, £2000 in
> A local authority is under severe financial pressure and is considering selling some of the land it owns to a building company. The building company is offering to pay £150 000 for the land now or a payment of £40 000 a year for the next five years. (a)
> A hospital has decided to replace an important piece of medical equipment at a cost of £30 000. The expected life of the equipment is five years and it will have a resale value of £4000 at this time. The hospital is trying to decide how to finance the pu
> Return to Exercise 8 in Chapter 4. Test to see whether there is a significant difference between mean customer spend in the two stores. Draft a short report explaining your conclusion in non-technical terms for the store managers. Data from Exercise 8 i
> Historically it has taken a local council an average of 18 weeks to reach a decision about planning applications for building development work submitted by construction companies. The companies have complained that decisions are taking too long and delay
