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business
statistical techniques in business

Questions and Answers of Statistical Techniques in Business

In one month the total costs (to the nearest pound) of the calls made by 23 male mobile phone owners were:17 17 14 16 15 24 12 20 17 17 13 21 15 14 14 20 21 9 15 22 19 27 19 Find the mean monthly
Find the median of the data in Example 3.2.Array 17 22 28 31 31 31 32 32 33 37 37 39 39 39 40 42 44 45 In this case there are 18 observations, that is, n = 18, so:Median position = (18 + 1)/2 = 9.5th
Find the median of the data in Example 3.1.Array 16 16 17 17 17 17 17 18 18 18 19 19 20 21 28
The ages of the 18 checkout operators working in a supermarket are:39 17 44 22 39 45 40 37 31 33 39 28 32 32 31 31 37 42 What is the mode?
The ages of the 15 staff working at a fast food restaurant are:17 18 21 18 16 19 17 28 16 20 18 17 17 19 17 What is the mode?
2.20 Select which of the statements listed below on the righthand side describe the words listed on the left-hand side.(a) histogram (i) can only take a limited number of values(b) time series (ii)
2.19 The quarterly sales (in £000) of greeting cards in a supermarket were:Produce a time series plot to show these figures. Year Quarter 1 2 3 4 12 12.0 14.8 9.6 19.2 13.1 16.3 9.2 20.8
2.18 The sales of organic vegetables (in £000) by a fruit and vegetable wholesaler over 10 years were:Construct a time series plot to present this set of data. Year 1992 1993 1994 1995 1996 1997
2.17 A catalogue shop sells ten brands of television sets with 14-inch screens. The prices of these (to the nearest pound), and the number of each sold are:(a) Plot a scatter diagram to represent
2.16 The levels of expenditure on domestic fuel (in $000 millions)and the populations (in millions) of 9 countries are:(a) Plot a scatter diagram to portray these figures.(b) Describe the
2.15 The prices (in pounds) of 27 second-hand ‘supermini’ cars on sale at a garage are:(a) Compile a stem and leaf display for these figures using thousands as stem digits.(b) Modify your display
2.14 The hourly wages (in pounds) of 32 jobs advertised by a‘temp’ agency are:(a) Compile a stem and leaf display to present these figures using the figures in pounds (4, 5, 6, 7) as stem digits
2.13 The monthly membership fees (in pounds) for 17 fitness centres in local authority leisure centres are:(a) Compile a stem and leaf display to show these figures and the set of data in the
2.12 The monthly membership fees (in pounds) for 22 health clubs are:(a) Compile a stem and leaf display of these data.(b) The clubs whose fees appear in bold do not have a swimming pool. Highlight
2.11 One branch of a bank has 849 customers who have credit balances in a certain type of current account. The sizes of the balances in these accounts (to the nearest pound) have been arranged in the
2.10 A video rental shop has 312 different feature films that are available for hire overnight. The number of times these videos were rented out during a month is presented in the following grouped
2.9 The rent per person (to the nearest £) for 83 flats and houses advertised on the notice boards at a university was recorded and the following grouped frequency distribution produced:(a) Plot a
2.8 The rates of growth in revenue (%) of 25 leading companies over a year were:(a) Compile a grouped frequency distribution for these figures.(b) Construct a histogram to portray the distribution.
2.7 The number of a particular brand of PC sold during a week in each of the 37 outlets of a chain of computer dealers were:(a) Present this set of data in the form of a grouped frequency
2.6 The speeds (in miles per hour) of 24 vehicles travelling along a road that has a 30 mph speed limit were:(a) Construct a grouped frequency distribution for this set of data.(b) Plot a histogram
2.5 The ages of 28 applicants for a graduate management trainee post are:(a) Produce a frequency distribution for these figures.(b) Plot a bar chart to represent the frequency distribution. 21 23 21
2.4 The number of people in 35 passenger cars travelling along a road during the morning rush hour were:(a) Compile a frequency distribution for this set of data.(b) Construct a bar chart to
2.3 A machine vending company operates three hot drinks machines, one at a bus station, another at a train station, and the third at a leisure centre. The number of coffee, tea, and chocolate drinks
2.2 A bus company operates services to and from the East, North, South, and West of a city. A recent report from the Chief Executive contains the following summary of their operations. All figures
2.1 Which of the variables below are:(i) Qualitative(ii) Discrete quantitative(iii) Continuous quantitative?(a) Duration of telephone calls (b) Mode of travel to work (c) The alcohol content of beers
The sales (in £s) of cold and flu remedies in a pharmacy over two years were:Produce a time series plot to show this set of data. Year Quarter 1 2 3 4 12 6375 2791 2964 8283 2 6941 2309 3128 8537
The number of employees of a computer games company over nine years were:Produce a time series chart to show this set of data. Year Employees 1992 1993 1994 1995 1996 1997 1998 1999 2000 7 15 38 112
The midday temperature (in degrees Celsius) and the amount of barbecue fuel (in kg)sold at a convenience store on 13 days are:Temperature (°C) 15 17 18 18 19 20 21 22 24 25 27 27 28 Fuel sold (kg)
Produce a histogram to portray the data in Example 2.23.To do this we can use each stem line in the stem and leaf display as a class, which will be represented as a block in the histogram. The first
The prices in £s of 16 different mountain bikes are:448 423 284 377 502 459 278 268 374 344 256 228 380 286 219 352 Produce a stem and leaf display to show this set of data.There are a number of
Produce a stem and leaf display for the audience figures for the second TV series in Example 2.21.
The audiences (in millions) for the 26 programmes in the second series of the TV show in Example 2.19 are:3.6 4.4 2.8 4.5 3.5 3.7 5.7 3.8 4.4 5.8 3.4 2.8 3.6 4.1 3.8 2.9 5.7 2.5 3.6 5.1 5.5 3.6 5.2
The scheduled time of transmission of five of the programmes whose audiences are listed in Example 2.19 was changed at short notice. The sizes of the audiences for these five programmes are shown in
The audience figures for the 26 programmes in a TV series (in millions) are:Produce a stem and leaf display for this set of data. 4.0 3.8 4.2 2.9 2.5 3.5 2.6 3.6 5.0 3.5 4.9 2.9 3.3 4.8 1.0 3.2 5.1
The size of cash payments made by 119 customers at a petrol station are summarized in the following grouped frequency distribution. Plot a cumulative relative frequency graph.
Plot a cumulative frequency graph for the data in Example 2.12
Produce a cumulative frequency graph using the cumulative frequencies from Example 2.15.
Find the cumulative frequencies of each class in the grouped frequency distribution in Example 2.11.
The ages of savers opening accounts at a bank are given in the grouped frequency distribution below. Produce a histogram to depict this distribution.Here not only do the classes have different
Construct a histogram to display the grouped frequency distribution in Example 2.11.See Figure 2.7.
Spot-checks of the amount of nail varnish in bottles labelled as containing 10 millilitres have produced the following figures (in millilitres):Arrange these figures in a grouped frequency
The numbers of e-mail messages sent by 22 office workers are:Produce a grouped frequency distribution to present this set of data. 50 14 25 8 10 5 98 13 31 552 33 52 12 12 45 15 7 6 75 17 22 12 64
The ‘Accommodation to Let’ column in the classified advertisements pages of a local newspaper contains details of 20 houses available to rent. The number of bedrooms in these properties are:2 3 5
Produce a cluster bar chart to show the data from Example 2.4.
Produce a component bar chart to portray the data from Example 2.4
Produce a bar chart to show the data from Example 2.3.
The table below shows the number of medals in different sporting categories that competitors from a particular country won in an international games event. Number of medals won by type of sport Type
Four large retailers each operate their own loyalty scheme. Customers can apply for loyalty cards and receive points when they present them whilst making purchases. These points are accumulated and
Suppose we want to find out how many retail outlets in a city sell trainers.We might survey the streets or consult a telephone directory in order to compile a list of outlets, but the list itself may
A motor magazine provides descriptions of cars that contain the following data:Type of car – hatchback/estate/MPV/off-road/performance;Number of doors;Fuel type – petrol/diesel;CO2 emission rate
Holders of a certain type of credit card are described as ‘wealthy’.To verify this we could use socio-economic definitions of class to categorize each cardholder, or we could count the number of
1.15 In one month consumers purchased 58 749 517 litres of bottled still mineral water. Of this total, sales of the three largest suppliers, in litres, were:(a) Specify the total sales and the sales
1.14 A regulatory authority assesses the performance of railway operators on the proportion of trains that arrive late at their destinations. If more than one in twenty trains are late the operator
1.13 Ray Vonman wants to make 5 litres of punch for a party. The recipe he intends to use requires 3 parts vodka to 1 part vermouth to 1 part lime cordial to 3 parts orange juice to 2 parts lemonade.
1.12 A UK businessman working in a former Soviet republic discovers that he can buy a new car from a local factory for 500 000 units of local currency, soom. The official exchange rate is 120 soom to
1.11 A credit card company charges interest of 2.15 per cent per month on outstanding balances. A customer has no outstanding balance at the beginning of September. During September he spends £279
1.10 A single graduate is offered a job at a salary of £18 000 per annum. She would like to know how much pay she will receive per month after tax and National Insurance. She has obtained the
1.9 The promotional brochure produced by a Health Club informs us that ‘75 per cent of our members are under 30, and 60 per cent of our members who are under 30 are female’. If the Club has 900
1.8 A visitor to Britain from Bahrain wants to buy some articles of clothing in a department store in London. He selects a man’s jumper costing £29.99, a lady’s cardigan that costs£34.99, and a
1.7 An electricity supplier charges domestic consumers a fixed quarterly fee of £8.50 for maintaining the supply and 6.08 pence for each unit of electricity consumed. The total amount is then taxed
1.6 The central feature of a new shopping centre is a square platform composed of one-metre square marble tiles.(a) If the designer wants the platform to measure 14 metres by 14 metres, how many
1.5 A motoring journalist is studying the technical specification of a new car not yet available in the UK. The fuel economy is expressed in continental European style; according to the document the
1.4 You have to fly from London to Tashkent. The plane is due to depart at 21.30 and the airline insists that you check in two hours before take off. You estimate that it will take an hour and a half
1.3 A till-roll from a cash register in a chemist’s shop shows the following transactions:Medicines £4.85 Cosmetics £2.65 Cosmetics £8.54 Cosmetics £7.20 Medicines £2.36 If the variable X is
1.2 Match each of the symbols on the left to the definitions listed on the right.(a) X (i) the number of observed values(b) (ii) the third in a set of observed values of the variable X(c) x (iii) a
1.1 Match the definitions listed below on the right to the words listed on the left.(a) statistics (i) something that occurs by chance(b) Statistics (ii) a subset of a population(c) random (iii) a
What are the relevant commands to use in a Spreadsheet package and/or a statistical package to store the costs of the items listed in Example 1.16, and to produce the total cost of the order?
A bank pays interest of 4.1358 per cent on savings accounts. Express this figure to:(a) three decimal places(b) two decimal places(c) one decimal place(a) 4.136 per cent(b) 4.14 per cent(c) 4.1 per
A record company sold 367 527 copies of an album. Round this figure so that it is expressed to:(a) five significant figures(b) four significant figures(c) three significant figures(a) 367 530 the 7
You walk into a fast food restaurant which is so empty that there is a member of staff waiting to take your order. You know what you want but you don’t know how much it will cost. As you give your
A car dealer promises a new member of the sales team commission of 5 per cent of the profits made on the cars she sells. If the profit margin on the cars sold is 40 per cent and the new member of the
A contractor wants to put in an estimate for laying a lawn area 13 metres by 13 metres at the corporate headquarters in Example 1.13. The cost of turf is £4.20 per square metre. He estimates the job
A new ornamental garden featuring a square lawn area is to be laid out at a corporate headquarters complex. If there are 170 square metres of turf available, what will the dimensions of the lawn be?
The floor covering of the dance space in a live music venue has to be replaced. If the dance floor is 4.2 metres long by 4.2 metres wide, how much new floor covering will be needed?
A visitor to Britain sees a sign saying ‘City Centre 7 miles’. She asks you how far that is in kilometres.A kilometre is equivalent to 0.6214 of a mile, so to reply to her question you need to
Eight residents sharing a house receive a gas bill for £361. If they agree to share the cost equally, how much will each resident need to contribute?
A business traveller returning from Oslo has 3200 Norwegian krone that she wishes to change into pounds. If the rate available at a bureau de change is £0.08 per krone, how many pounds will she get
A property company receives an inquiry about a property from a US client. The rent is£2400 per month. If the exchange rate is $1.60 to the pound, what is the rent in US dollars?
If the traveller described in Example 1.6 begins her journey at 11am, what time will she arrive at her destination, and how would this time be expressed using the 24-hour clock?
A business traveller drives for 12 minutes to reach her local railway station where she boards a train that takes 33 minutes to reach the London terminus. It takes her 24 minutes by tube to reach
The sharp-eyed manager of the store in Example 1.4 spots that the voucher is out of date.What effect will this have on the total amount the customer should be charged?
A customer visits a store and buys 4 CDs that cost £13, £16, £8, and £11. He also claims a £5 discount for using a promotional voucher. What is the total amount that he should be charged?
The gross weekly pay of a shop worker is £200. If her stoppages are £28 tax, £9 National Insurance, and £12 pension contribution, what is her weekly take-home pay?
In the situation described in Example 1.1, we could show that the total time taken for a customer arriving at a cash machine to get their cash (which we could represent by ‘T’)is the sum of the
To withdraw money from a cash machine a customer must insert a card, key in a PIN number, specify the amount, and wait for the money to be issued. If these tasks take 10, 12, 7 and 8 seconds, what is
5.77.* To construct a confidence interval for a proportion π, it is not necessary to substitute πˆ for the unknown value of π in the formula for the true standard error of πˆ .A less
3.81.* The least squares property of the mean states that the data fall closer to ¯y than to any other numberc, in the sense that the sum of squares of deviations about the mean is smaller than the
According to Statistical Abstract of the United States, 2015, the mean salary (in dollars) of secondary school teachers in the United States varied among states with a five-number summary of(a) Find
2.40.∗ Aninterval scale for which ratios are valid is called a ratio scale. Such scales have a well-defined 0 point, so, for instance, one can regard the value 20 as twice the quantity of the value
In a recent Miss America beauty pageant, television viewers could cast their vote on whether to cancel the swimwear parade by phoning a number the network provided.About 1 million viewers called and
An interviewer plans to stand at an entrance to a popular shopping mall and conduct interviews. True or false:Because we cannot predict who will be interviewed, the sample obtained is an example of a
A recent General Social Survey asked subjects if they supported legalizing abortion in each of seven different circumstances. The percentage who supported legalization varied between 45% (if the
An analysis7 of published medical studies involving treatments for heart attacks noted that in the studies having randomization and strong controls for bias, the new therapy provided improved
If we use random numbers to take a simple random sample of 50 students from the 3500 undergraduate students at the University of Rochester,(a) It is impossible to get the random number 1111, because
A simple random sample of size n is one in which(a) Every nth member is selected from the population.(b) Each possible sample of size n has the same chance of being selected.(c) There must be exactly
To sample residents of registered nursing homes in Yorkshire, UK, I construct a list of all nursing homes in the county, which I number from 1 to 110. Beginning randomly, I choose every 10th home on
With a total sample of size 100, we want to compare Native Americans to other Americans on the percentage favoring legalized gambling. Why might it be useful to take a disproportional stratified
In a systematic random sample, every subject has the same chance of selection, but the sample is not a simple random sample. Explain why.
A content analysis of a daily newspaper studies the percentage of newspaper space devoted to news about entertainment.The sampling frame consists of the daily editions of the newspaper for the
In each of the following situations, evaluate whether the method of sample selection is appropriate for obtaining information about the population of interest. How would you improve the sample

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