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1. AND TOURISM N Routledge Taylor amp Francis Group LONDON AND NEW YORK First published by Butterworth Heinemann This edition published 2011 by Routledge 2 Park Square Milton Park Abingdon Oxon OX 14 4RN 711 Vhird Avenue New York SY 10017 USA Routledge is an imprint of the Taylor amp Francis Group an informa business First published 2000 John Buglear 2000 All rights reserved No part of this publication may be reproduced in any material form including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication without the written permission of the copvright holder except in accordance with the provisions of the Copyright Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd 90 Tottenham Court Road London England WIP OLF Applications for the copyright holder s written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data Buglear John Stats to go 1 Tourist trade Statistical methods 2 Hospitality industry Statistical methods I Title 338 4 7910015195 ISBN 0 7506 4556 3 Transferred to digital printing 2005 Composition by Genesis Typesetting Rochester Kent Preface Acknowledgements 1 starting out 1 4 Numbers in the hospitality and tourism industries
2. 1 2 How this book is organized 1 3 Taking the first steps 1 amp Technological support Review questions rresenting data 2 1 Types of data 2 2 Displaying qualitative data 4 3 Displaying quantitative data Review questions Summarizing univariate data 3 1 Measures of location 3 2 Measures of spread Review questions Summarizing bivariate data 4 1 Correlation and regression 4 2 summarizing data collected over time Review questions Assessing risk 51 Measuring probability 5 2 LEfferent types of probabilities 5 3 The rules of probability 5 amp Trea diagrams Review questions lt E WD oC C pha B2 E n Sega H1 i20 122 i25 128 136 136 pananta harrera ar Lr Aa L A LE hk T a a O r L a a a M L l a ep caa aaora Icc 19 Putting probability to work 6 1 Simpie probability distributions 6 2 Binomial distributions 6 3 Poisson distributions 6 4 Expectation 6 5 Decision trees Review questions Simulating populations 7 1 Normal distributions 7 2 The Standard Normal Distribution 7 3 Sampling distributions 7 4 t distributions Review questionis Statistical decision making 5 1 Estimation 8 2 Hypothesis testing Review questions Statistical decision making using bivariate data 9 1 Contingency tests 9 2 Testing and estimating using quantitative bivatiate data Review questions Managing statistical research 10 1 Secondary data 10 2 Primary data 10 3 Presenting your analy
3. ihe product wil be negative However if vou multiply two negative number together the product will be positive 3x 0 7 6 but Axs Division or finding how many Hines one amount goes into another is the process of dividing one nuniber by another It is represented either by the forward siash or the sign If you divide a number bv another number that is greater than one the result will be smaller than the original number The 48 guests atteruling a function are to be offered a glass of wine on arrival if the contents of one battle of wine will fill three and a half glasses how many bottles will be x required We can obtain the answer by dividing the number of guests by the number of glassfuis per bottle a Number of bottles 48 35 13714 to 3 decimal places UE E Vv TTTEEEEEEEEEYUUUUY sd Merting out NI I We ETY SD a a aee I I I rl 7 1 Se ee ee 2 8 8 ee ad Something to note in Example 1 10 is that aithough we can get a very precise result in this case specified to three places of numbers after the decimal point in the situation described the Heure would be rounded up to the nearest whole number 14 If you divide a number by another number that is less than one the result will be larger than the original number A visitor to Britain sees a sign saying Airport 7 mules She asks you how far that is in kilometres A kilometre is equivalent to 0 62 of
4. 83 10 93 Pee es e tnt thn ee be RSS ANN S SN N NN NN nnne SN MITIS MD e NI I ee You get exaciv the same result if you simply add the amount concerned 20 You may find if helpful to imagine the two minus signs cancelling each other out to leave you with an addition Alternatively it may help io think that taking away a negative is always positive Addition and suptraction involving time is something many people find difficuli because time is measured in hours made up of 60 minutes and minutes made up of 60 seconds rather than nice neat numerical parcels of ten The use of the 24 hour clock on top of all this seems to phase most people completely A business traveller drives for 12 minutes fo reach her local railway station where she boards a train that takes 33 minutes to reach its London terminus It taxes her 24 minutes by tube to reach another London terminus where she boards another tain After a journey that takes i hour 5 minutes to reaches her station from where she takes a i Aninute traxi ride o ner destination What is the iotal journey rme votre M eae Ier drea Io get the answer we can express all the times mentioned including the figure tor the second train journey in minutes Total journey tene 124 33 4 24465 10 144 bd The answer may not be satisfactory in this form To convert it into hours and minutes we need to find how many units of 60 minutes there are in 144 mi
5. A 9 minutes 14 09 or 2 09 pm E Multiplication and division s e e 5 Multiplication or Gmies ing represented either by the mes 2 sign x or the asterisk is the process of multiplying two or 2 more numbers together to make a product Hf the number is multiplied by a munber greater than one the resulting product will be greater than the original number 3 ee LITTTITTLLLI MINES II SPI uuu ee Sn a a YY a i Rs LLNL NNI DNI Le Loi Li MEE e A ho daymaker wishes fo convert 240 into US dollars I the rate advertised at the murean de change 15 1 60 to the pound bow many doliara wil his pounds buy You can get the answer by multiplying the total xuimber of pounds oy the exchange rate Dollars he can buy 240 x 1 60 384 in this case the number of dollars is greater than the number of pounds the product represents a numerical increase But if you multiply a number by another nember that is less than one you will get a product that is lower than your first number A business traveller returning from Oslo has 3200 Norwegian krone that she wishes to change into pounds if the rate available at a oureau de change is 0 08 per krone how many pounds will she get for her krone 1o get the answer miulticly the total number of krone by the exchange rate Founde she can buy Kr3200 x 0 08 256 Oe i i re ee eer aT MX ete if you have to multiply a positive number by a negative number
6. AP S SI I ALLEE I E SA 7 LEE AAAA I LFLSLLE I FT LInan FLOS LLSSTSUUTAR EFE LLLI SATAA Aa HL LE Sasa A A A Sadak ELI A A ASA L UTR OP BAA D E A T LI A SAT LLLI LLLI LTLLI LLLI A a LLLALLN LS NEL LLL LRL LL NN Rm n nl e i i A new ornamental garden featuring a square lawn area is to be laid out at a conference centre IF there are 160 square metres of turf available what wilh the dimensions of the lawn be You can find the answer by taking the square root of 160 ine lawn would be 12 65 metres long by 12 65 metres wide cquarne a positive number wil always give you a positive result But because multiplying one negative number by another always gives you a positive product squaring a negative number will always give you a positive result as well So 24 9 and 3 9 ine fact that we always get a positive result wien we square negative nuxnber is worth remembering because it plays a vital role fa several statistical techniques that you will meet square rooting or taking the square root of a numer is the process of working out what mimber squared would produce a particular number i is represented by the radical or Hex sign so the square root of 9 would be shown as V9 The result of V3 is 3 because the number 3 multiplied by itself gives vou 9 MP D Pf m E o nnn n eruta lente nutus IIIa IIIa 12 65 to 2 decimal places i i H Fractions proportions and perceninges e e e Fractions proportio
7. crude estimate You could get a more accurate approximation if you rounded each figure to the nearest ten pence 3 E 7 i H i 7 E i E i E H H i Approximate total cost 1 50 1 70 0 90 0 80 0 60 5 50 3O 2M sss Ies Ps ee EIS Fach of the five figures used here is rounded up by one penny so you can get the exact total by taking five pence away fram 5 50 which comes to 5 45 1 4 Technological support Although the subject of Statistics is about numbers the amount of time you will spend actually performing calculations during your study of the subject can be minimized by using readily available technology specifically a suitable calculator and appro priate computer software Hf you do not already have a calculator you reality need to get one it is an essential tool for the numerical aspects of your course and probably some of the not so numerical parts of it as well To be of use to you in statistical work the calentator you us have must have a square root function and it really is worth spending a little more money to get one with statistical functions E oometmes such calculators are described as having a statistical E mode or an SIY standard deviation mode Whatever Itis caned by the manuf
8. results but let the machine do the hard work for you So what is the right software There are two types of software that can heip you with statistical tasks statistical packages and spreadsheet packages Statistical packages such as MINITAB which has been used to produce the diagrams and results for this book Splus and SPSS offer a full range of statistical functions and can carry out just about alt of the techniques you are likely to meet during your studies The authors of packages of this type are usually qualified in Statistics Spreadsheet packages such as Excel are intended primarily for accounting work ard offer a more limited range of statistical functions but nonetheless can perform the majority of methods you will probably need to use Aithough these two types of package offer different ranges of functions and different styles of output they have become increasingly similar in some respects The data storage layouts in statistical packages have become more like spreadsheets num bers are usually stored in the rows and columns of a spread sheet in Excel and in the rows and columns of a worksheet in MINITAB The statistical output generated by spreadsheet packages icoks more like that produced using a statistical 77 package Z hoot le n ol ITOP fai we te ae Hosptali Stats to Gc That are ine relevant commands to use in a spreadsheet package and or a statistical package to store t
9. room charge of 60 25 for an evemng meal 8 for Minibar items and a 10 discount for using a promotional voucher What is the total amount that should be on the bill The answer can be shown sg Total amount 60 25 8 10 83 Hn CUOO EAA AAA UWIAA ee eee ee A ee on o mn aaa ss aaah fs NIIS tede ee AN NINE You can s e that round brackets have been used both to highlight the fact that there is a negative number in the sequence and to indicate that i must be dealt with first This means deciding how fo tackle the apparently contradictory sequence of symbols In fact the minus sign overrides the plus sign so adding a number is therefore the seme as subtracting a o number The arithmetical expression used to find the total 2 amount in Example 1 4 has exactly the same result as the following expression which combines addition and subtraction Total amount 604 25 8 30 83 A But what do you do if you nave to subtract a negative number In fact subtracting a negative number produces the same result as i adding a positive number B 11 enn ae ELLA S ciats to Go The sharp eyed Front Office Manager in the hotel mentioned in Example 1 4 spots that the voucher is out of date What effect will this have on the total amount of the bill They would have to take away the reduction from the previous total so now Hob erate Q8 2 Mt Total amount
10. total number of persons residing in a defined area at a given time In Olatistics a population is the complete set of things we want to investigate These may be human such as ali the people who have visited a theme park or inanimate such as the flights made by an aircraft Sample A subset of the population that is a smaller number of items picked from the population A random sample is a sample whose components have been chosen in a random way that is on the basis that any single item in the population has no more or less chance than any other to be included in the sample Lae eA Z 1 3 2 The basic numerical skilis you need Addition and subtraction e nm Addition represented by the plus sign is the process of putting two or more numbers together to make a sum or total As M long as the numbers being added together are positive Le more kl than zero the resulting total grows as more numbers are LE added Mel Staning out A member of staff at a drive through conducts four operations in the course of serving a customer If these tasks take 10 12 7 and 8 seconds what is the total time that will elapse between the time a customer arrives at the order point and the time they can depart from the service point tre ARMIS PR You can get the answer by adding together the times taken for the four operations AAA AAMAS VP ee Total ume 10 1Z 7 48 37 seconds z Besse cent tene Me d REI
11. H the variable X is defined as ihe money taken per ransaction n a Calculate X the Total amount taxon through the tK a b Caiculate 2X and explain what ihe answer means i You have to fly from London to Tashkent The piane is dus to depart at 21 30 and the airline insists that you check in two hours before take off You estimate thai it will take an hour and a half to drive to the airport and a further 20 minutes to make your way from the car park to the check in desk a What ime should you start your journey to the airport b The fign is scheduled io take 6 hours 45 minutes Going through passport controi and collecting your bageage should take an hour H local time is five hours anead of UK time by what time should the person who is meeting vou aim to be at ihe airport in Tashkent A tour operator is oraenizing a coach trip around Bavaria She has two vehicles avaiable in Munich that could be usa in most respects ine velicies are identical so she will use the one thet has tne potier fuel economy According io the records the fret vehicle which has bean used extensively in the UK does 15 miles per gallon The second one used entirely within Germany has a recorded uei efficioncy figure of 20 litres of fuel per 100 kilometres travelled Which coach should she use There are 4 546 ires in a gallon and 1 609 kilometres in a mile to 3 decimal places A pub manager wants to create a square paved area immediately outsi
12. R AEREA EAEAN EAEE ettet DANENA EEEE Because Statistics often involves combining observations the arithmetical process of addition is a process you wil come across in the context of several techniques deali with later in the book Although you are probably already familiar with addition you may not have encountered the symbol called sigma which 1s used in Statistics to represent it Sigma is the capital letter 5 from the Greek alphabet written as R is the letter s because s is the first letter of the word sum 1t is a Greek letter because at the time that much of the theory that makes up the subject of Statistics as we know if today was develoned the so called classical languages of the ancient world were taught in the schools and universities The Greek language with its particular alphabeti therefore provided the pioneers of Statistics and other fledgling disciplines with a ready source of distinctive Symbols The symbol 2 sigma stands for the sum of when it is used in Statistical expressions for example means the sum of a set of observed values of the variabie X angi Sometimes it is necessary to specify precisely which observed values of X are to be added together To show this the letter is used to count the observations for example S Se means the sum of the first to the fourth EE ixi Observations of the variable X en The expression x V below
13. a mile to 2 decimal places so to reply to her question you need to find how many times 0 62 will go inte 7 that is you must divide 7 by 9 62 Kilometres to the airport 7 0 62 11 29 to 2 decimal places E eS ia a mere M d AM ARARARARAN AAAA ees ies KI PNIS a a a a Squaring and square rooting s Squaring or taking the square of a number is the process of muliplying a number by itself The process is represented by the number with a superscript showing the number two for example the square of three or three squared would be written 3 which tells us to multipiy three by three If the number you want to square is more than one the result will be larger than the number itself for instance the square of three is nine However if the number you want to square is less than one the result will be smaller than the number itself for example tne square of a half is a quarter Mi The fioor covering of the dance space in a live music venue has to be replaced If the 5 dance floor is 4 2 metres long py 4 2 metres wide how much new Noor covering willbe needed e To find an area multiply the length by the width In this case because the area is a square a Score PM d A tas r m E icit B i D ME ad that is the tength and width are the same we need only take the square of 4 2 2 ue Floor area 4 2 17 64 square metres E T un m m eye n mais io Ge pe eee mart artt mat
14. acturer if you have a calculator that can perform a statistical operations it will assist you immensely 3 When you have your calculator the first thing that you shouid i do is to make sure vou don t lose the instructions Your calculator Es is a sophisticated scientie instrument that can do nach more for is you than you might imagine but you can oniy Gre out how ii ie vou have the instructions As a safeguard itis a good Idea to keep x a photocopy of them in a safe place Starting ut Ue ee eee oe eee en eee You will most likely have access to a computer perhaps ai home but almost certainly at your place of study Because today computers are used so widely to send messages and to access internet facilities it is easy to forget that computers were originally developed as machines to process data The computers we have today still possess that capability With the right software the machine vou use should become an invatusbie aid to you in carrying out statistical work It will do most of the laborious calculations for vou leaving you free to concentrate on learning how to understand and interpret the results This reflects how you are likely to be involved in using statistics later in your career it is your perception and inter pretation of results that will be important rather than whether you can compete with a computer to do the calculations Of course if is important to be able to understand how the computer has arrived at the
15. blv 2 look at the notes end pound coins in your purse or pocket and make an approximation Oniy if you are particularly concerned about how much there is or have time on your hands are vou likely to count every penny Rounding and approximation are therefore not entirely new concepts io you if you can apply them systematically m your numerical work you will develop a skill which will give yoza better feel ior numbers enable you to spot mistakes and think numerically on your feet 5 Stats to Ga a EE R AAAA A o A A A POP9 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 order your eves take in the prices of the items you want one burger 1 49 another burger 1 69 one portion of fries 89p one cold drink 79p one hot drink 59p You want to work out roughly how much it will be so you can decide whether to count up vour change or get out a note If you want a really quick answer round up each item to the nearest pound Approximate total cost 2 2 1 1 1 7 Because we have rounded every figure up this result will be an overestimate so we can be certain that the total cost will be no more than this but itis a rather
16. cing the loss of an income may weil halve its consumption of clothing but is likely to abandon the idea of going on holiday completely How do organizations cope with this degree of change The answer in some cases is that they don t Many of the companies that dominated the sector a generation ago no longer exist They became history because they failed to respond to the changing market Others survived and some small operations thrived becoming markei ieaders within the lifetimes of their founders Although tuck and the good fortune of happening to be in the right market place with the right product may have played a part to succeed in a changing environment an organization needs to recognize ihe changes and anticipate the consequences for iis operations How can it do that By constantly studying its markets and monitoring its operations This means counting and measuring key factors in other words gathering numerical facta or statistics in every orgenization there is a flew of numbers which are either deliberately coilected or arise from the regular interactions with customers suppliers and other significant organizations These figures in themselves cannot tell the organization what is going on in the market or how it is performing One of the responsibilities of management is to ensure that such figures are used which means they have to be processed and analysed The patterns that emerge from this analysis provide information that
17. de the main bar of the pub A builder offers him 175 one metre square paving slabs thai were aft over fram another jab at a very competitive price What are the dimensions of the largest paved area tha could be laid using these slabs assuming that tne pun manager does not want any slabs cut
18. he costs of the items listed in Exampie 1 15 and to produce the total cost of the order Using Excel inter the first value in Cel Al then press Enter e nier the next value in Cell A2 press Enter and repeat untii all the values are stored in Cells Al to AS and the cursor is resting in Cell A6 e Cick on the Autosum button Gabelled 3 that is located amongst the toolbars at the top of the screen The message SUNMCAT ASY wil appear in Cel AS oT ax vw Press the Enter key The figure that now appears in Cel A6 should be 5 45 the total cost of the items Using MINTTAB e fnier the first value in Row 1 of Column 1 C1 of the worksheet that occupies the lower halt of the screen and then press Enter Enter the next value in Row 2 of Cl press Enter and repesi until all the values are stoned in Rows to Sof C1 o Click on the Cale Calesistions menu at the ton of the screen e Click on Column Statistics in the Cale puii down menu In the Command Window that appears select Sum click on the box beside input variable type C1 in the box and click the OK button A message telling you that the sum of C1 is 5 45 appears in the session window that occupies the upper half of the screen n MoO Nnnna nananana Ter ers Tree if you have a choice learn how to use the statistical package at your disposal If you Rave Gime learn to use both the statishca
19. iable E e Value A specific amount that it is possible for a variable to be Por example the number of rooms soid in a 100 bedroom hotel Stats to Go mae malae ee ee ri ee ee ee could be 53 or 68 or 93 These are all possible values of the variable number of rooms sold e Observation or observed value A value of a variable thai has actually occurred i e been counted or measured For example if hotel staff sell 75 rooms for a particular night that is an observation or observed value of the variable number ot rooms sold An observation is represented by the lower case of the letter used to represent the variable for instance x represents a single observed value of the variable X A smali numerical suffix is added to distinguish particular observations in a set x would represent the first observed value x the second and so on e Random This adjective refers to something that occurs in an unplanned way A random variable is a variable whose observed values arise by chance The sales of bottled beer in a pub are a variable which is random whereas the number of days in a month is a variable which is not random ie its observed values are pre determined e Distribution The pattern exhibited by the observed values of variable when they are arranged in order of magnitude A Hieoretical distribution is one that has been deduced rather than compiled from observed values Population Generally this means ihe
20. l package and the statistical functors of the spreadsheet package g After ali in the course of your career the software you use will Z5 evolve and you will need to adapt to it so why not get used to learning how to use a variety of software while you are studying if you have to choose between a spreadsheet and a statistical E H package it may help to consider some of ihe pros and cons of each a The advantages of a spreadsheet are be They are fairiy straightforward to use E Basic calculations and diagrams can be produced quickly and amp easily 7 e They are useful for more than statistical work e g for F accounting ot manpower planning Starting aut ee a a mm sec e e e e e e e e a e e e eben Ea PA A APAE LET CPI LP ALTI DLL De EA PAPAA PEPE PEPPERS 2 A Re A The disadvantages of a spreadsheet are They can perform only a limited range of statistical tasks e The control vou have over the composition of some output particularly diagrams is limited and tricky io manage The advantages of a dedicated statistical package are They can carry out a comprehensive range af statistical operations The methods they use and the output they produce are statistically imeticulous The disadvantages of a dedicated statistical package are e They can be more difficult to kearn fo use e Transferring output into other software may be elaborate Because computer software is continually being u
21. ll provide support for the numerical work you wil undertake throughout your course The first five chapters of the book inchiding this one deal with topics that you are jikely to meet during the first stage of your course They deal largely with descriptive techniques that is methods that will enable you to arrange or analyse data in a way that helps describe the situation being studied Chapters 9 cover topics that vou may meet at a later stage of your course They deal with inferential techniques that is methods that enable you to make inferences or draw conclusions about an issue in general based on the study of a comparatively modest amount of data ihe tual chapter is designed to help you tackle numerical aspects of the final vear project or dissertation you will pronably be asked to write ine book will introduce you to a variety of anaiytical techniques that together constitute a toolkit of methods that can be used to investigate situations and help solve problems Like any other tool kit the key to using it properiv is to know not only what each tool does but to know how and when to use it The book wil help you develop this ability by illustrating the application of the methods described using contexts taken from the hospitality and tourism sectors Each technique will be explained and demonstrated Any calculations will be explained in words before svmbois are used to represent ihe process Being able to apply a tech
22. nd why the ability to deal with numbers 2S important e io seo how this book can help you develop that ability amp To prapare effectively to study Statistics In this enapter you will find o A discussion of the importance of numbors to hoso ality and tourism businesses e A description of the aporeach and sivie used in ihis book e An introduction to key words e Guidance on basie numerical skills you will need 10 Use e Advice on technologies support REA ini ETT ELE dc A A A AAA A ATT Pa 1 Pa APET c al Stats to Go A AALALA eT TS LR WHTUNT RT ROLE FTU A AS UE RR ULLA dt L AA L FUR LII eee x 1 1 Numbers in the hospitality and tourism industries This book is atout analysing numbers But why should analysing numbers matter to someone studying hospitality or tourism How relevant can it be tor someone planning to build a career in hospitality or tourism To understand this and to spereciate why the study of umbers is buit inio your course consider how the hospitality and tourism sector has changed in the course of a generation The set of orgarizations that operate in the sector and the products they ofter have changed dramaticauy if you lock at films or read novels that reflect the Hves people ted twenty or toirty veers ago you will notice the changes Almost all licensed premises were male oriented places that provided a fairly narrow range of beverages and no hot food At work people a
23. nique to produce ine correct result from a calcuistion is important especially if viu find learning by doing useful but it is by no means the end of the story B is even more important io be able to interpret the results that the technique has enabled you to produce and te communicate the meaning of those resulis In your future career you may oe asked to apply techniques of analysis but you are much more Hkely to need to be able to explain results perhaps to jucdge whether appropriate techniques have been used to produce them The book therefore provides you with not only a description of each Starting sut 0 ee EF A a a A T o E a WR ATL LM FT T GL L LLL re technique and an illustration of its use but also a discussion of the types of results you could get and what each of them would mean At the end of Chapters 1 9 there are a set of review questions that you can use to confirm your understanding of the methods and ideas featured in each chapter You can find answers to these questions at the back of the book 1 3 Taking the first steps There ate two key preliminary tasks that are worth investing a Hie Gime and etfort on getting to grips with from the very beginning The first is to understand a few key words which may be completely new to you or whose meanings in the context of this subject are unfamiliar to you The second is to review a set of basic arithmetical operations which are involved in the use of some of
24. ns and percentages sound very diferent but they are only different ways of doing the same thing expressing a part of something in relation to the whole IE for example water constitutes 100 g of 500 g of hanm this could be explained as either water constitutes one fifth of the weight of ius product Or water constitutes 0 2 of the weight of Eis product Or water constitutes 20 per cent of the weight of this product One fifth is the fraction 0 2 is the proportion and Z0 per cent is the percentage They are different ways of saying the same thing because there are fve fifths in one five lots of 0 2 in one and five lots of 20 per cent in 100 per cent You shouid bear in mind that each of them is a number less than one Iinciuding fhe percentage which doesn t Joox as if if is less than one Starting aut a ee ee GHLRNL LOGLENNL GL L OGNLLGCENS LE TONS GUN TOLL mea an It is easier to use percentages if you understand that the literal meaning of per cent is per hundred The word cent originally meant one hundred a Roman centurion was an officer in the Roman army in charge of one hundred men This will especialy help when you have to perform arithmetical operations using percentages The proprietor of a souvenir shop located in the oid part of a famous Earopean city mekes a deal with a tour guide In return for the tour guide escorting parties of tourists to the shop the proprietor will give the tour guide 40 per ce
25. nt of the profit the shop makes from the money the tourists spend Tf the profit margin on the souvenirs is 60 per cent anc the fist group of tourists spends 735 how much money will the tour guide get The shop receives a profit of 66 per cent of 735 and the tour guide should receive 40 per cent of the 60 per cent of 735 so Guide s share 40 100 x 60 100 x 735 176 40 p P ERE ELTE j Notice that in Example 1 14 the percentages appear in tne expression as amounts per hundred Rounding and approximation e a You may find it easy to manipulate figures in your head or you may find such a skill impossible and marvel at those who possess it The truth is the anyone can learn how to carry out mental arithmetic the tricks are to round the numbers involved so that they are easier to deal with and to use approximation to get balipark result which can be refined with a litle more effort People who find it easy to work out numerical problems in their head often use rounding and approximation intuitivery that is without ihiking about it In fact you may already round certain numbers as a matter of course If someone asks how old you are you wouid say 18 or 21 as appropriate you wouldn t sav 18 years 3 months and 10 days or 21 63 years Automati cally you round down to the nearest completed year of your age if you want to check how much money you have you proba
26. nutes The answer is Z so the total journey time is 2 hours 120 of the total number of minutes and 24 minutes the number of minutes left over when 120 is subtracted from 144 Starting cut 0 ee L FT i LL EE E LE E ETLE o E a L L OL L L E L S LLL L LE aaa a p g e a MM memes mood dee ee ae ATTE os A A if the traveler described in Example 1 6 begins her journey at 11 am in the morning what time wii she arrive at her destination and how would this time be expressed using the 24 hour chock i i 1 i E MM SABAM ees Bal To get the answer work in hours first then minutes Arrivai time 11 2 hours 1pm Jo manum AME ET IA AMNIS ARABI S ANIM S PS tort totu c 2 24 minutes 1 24pm To express this using the 24 hour clock add 12 to the number of hours because the arrival time is atier midday Arrival ime 124412 13 4 AMMIAN eee s Mt UNAM isses inima 07 we But what if the traveller started her journey later than expected at 11 45 what time would she arrive This is a Uitte more complicated because the departure time and total journey time are measured in both hours and minutes To find the answer we cen start by adding the hours ii 2 13 then add the minutes together 45 24 69 Since this amount of minutes is longer than an hour we have to express it in hour and minutes and add the result to the sum of the hours 69 minutes 1 hour and 9 minutes e 13 14 hours
27. o Haly the USA and jepan is usually only a short distance away The popularity of food from exotic places of course reflects the transformation in the holiday market A long haul holiday is hkeiy to be one of several hotidays taken during a yearn A shopping weekend in New York is no longer purely a bizarre i ndulgence Gf the super rich Business travel has become a major market with specialist operators Retired peopie are often the most avid travellers transforming the off season business for many resorts As far as Seating out E rA AA AT FFTTI FFTLLFI IBLILTI IL UTT ee Pe UD Dee Eee a PPa a a IE De A Pe a eee ee ni a re an M 5 M M 4 4 Ea LB A e RENE LLELEN Los o lL m esce TET FAS children are concerned the emergence of the theme park and the all weather activity centre means that holiday decisions for any families are more overtly child driven These are fundamental and far reaching changes Experts may disagree about the factors that have caused them but as a result of them the business environment faced by hospitality and tourism organizations has altered profoundiy and wil almost certainly continue to do so A further source of uncertainty for the hospitality and tourism sector is the fact that ifs products are typically considered luxury goods aud services that are purchased trom discretionary income Demand for them is therefore highly sensitive to consumer confidence and taste A familv fa
28. ocess of subtracting or taking away one or more numbers from another As long as the numbers being subtracted are positive i e more than zero Ehe result reduces as more numbers are subtracted E The gross weekly pay of a tour guide is 200 If her stoppages are 28 tax 9 National Insurance and 52 accommodation charge what is her weekly take home pay care You can get the answer by subtracting the stoppages from the gross wage selene sv wea nana eee S SMS SE eee AVES AXES d Take home pay 200 28 9 52 11 i epenn en MAS Starting cut TLEAN La a T conn An alternative approach to this operation is to add the stoppages first and then subtract the total stoppages from the gross pay This wouid be represented in the following way Take nome pay 200 628 9 52 11 The round brackets dictate that the operation shown within them must be carried out first They are used to indicate priority You may well find addition and subtraction fairly easy but there are cases where they axe not so straightforward first when negative numbers are involved and second when the operation involves numbers measured in awkward undis e g minutes and hours Addition and subtraction may give you some difficulty if negative numbers are invoived If a negative number is added to a total i reduces the total A custorner s hotel bil consists of the following items a
29. pgraded and improved the disadvantages are being reduced and the adver tages extended so check the latest avaliable versions before making your decision Whatever package you use for your statistical work don t expect to know how to use all its functions straight away It is worth investing some time in learning how to get the best out of the software you use Any package should have a help facility use it to search for advice It is really an on line user manual available at your fingertips You will find that what you regard as awesome when you begin will very soon become familiar match the words listed on the left a statistics i something that occurs by chance D Statistics i a subset of a popuiation c random ill a compiete set of things to study d sample iv a value of a variable that has occurred e population v a set of numerical data observation vi the study of statistics 1 2 Match each of the symbols on the feft to ine definitions listed on the right a X the number of observed values b X di the third in a set of observed values of the yariablo X c x d a variable Sists to Ga r a 2 ee A Ed ee m rs ee eee 1 3 i24 1 6 di n iv a single observed value of the variable X fe X vi the sum of A till roi from a cash register in a caf bar shows the toilowing transactions Beverages 4 85 Food 2 65 Foad 8 54 Food 7 20 Beverages Yan ast
30. s enables managers to understand the situation they face and base EP their decisions on that understanding The ability to analyse figures and interpret the results is gt therefore considered a key management skill Look at recruit E ment advertisements for management posts and you will see that _ employers attach great importance to numerical skills and oroblem solving if you want o build a successful management career these are skills that you have to acquire sooner or later Your course will 2 provide you with the opportunity of developing them Make the most of that opportunity and vou wit have a cutting edge skill that will pay dividends for you in the future Stais ta Go ape ae ea A LAAPA LA I LPM S r S E L a ALLP MU A LTE d L PU eee weet ow imis book is organized This book will help you deal with tee numerical parts of your course How you uae it depends on how you approach the study of numbers you are about to start H can be a crutch to help you limp through what may seem Uke an unwelcome revisit to the sums of schooldays or it can be a springboard that will help you accumulate 2 key investment for your future the skill of numeracy This book may influence your attitude to studying numbers but it cannot decide tf The attitude you take is something for you fo develop hut whether this book is to be a crutch or a springboard for vou it is intended to be a guide which wi
31. sis Appendix Solutions fo selected review questions Index 141 142 147 153 136 158 16i i65 i74 187 190 i93 197 195 211 224 226 227 236 250 254 256 ASH 468 273 2 7 Preface This book is intended to equip students and others interested in ine hospitality and tourism industries with an understanding of Statistics As the sub title implies this is a guide to using Statistics rather than a specialist Statistics texthook The book provides an accessible insight into the use of a variety of statistical techniques These techniques are discussed and dem onstrated using worked examples set in hospitality and tourism contexts The book aims to encourage readers to use computer software to carry out statistical work it provides guidance on the use of MINITAB and the statistical aspects of Excel As a consequence the use of statistical tabies has been kept to a minimum solutions to review questions are included These are intended to help students monitor their own progress and make the book an effective basis for independent learning MIUNITAS is a registered trademark of Minitab Inc 2081 Enterprise Drive State College PA 16801 OSA hiipi wr mimidteb conm Acknowledgements The author would like to thank Allison for her creative ideas and critical evaluation Max and Tom for their forbearance and his coBieague Tan Lincoln for her assistance This chapter will help you a To understa
32. te food chosen from a limited range of traditional fare in a workplace canteen Fish and chips was the stapie fast food and dining out was an infrequent pleasure for mast people For those who did dine out the limits of exotic eating amounted to Chinese or Indian restaurants Holidays were taken once a year largely within the UK Often families wouid return to the same resort sometimes the very same place to stay year after year The fun lovers could go to holiday camps the very adventurous impressed their neighbours by going io Spain Apart from the journeys of travelling salesmen business travel hardly existed People who made it to retire ment age lived on modest pensions and txavelied little except to see relatives Por children there were beaches parks and funfairs iow strange aii that seems how very different things are today We have a wide variety of licensed premises where managers and owners try to create an ambience and offer feod and beverages to appeal to target market sepmenis ine workpiace canteen with its own kitchens hes all but dis appeared instead contractors deliver a wide range of sand wiches and cook chill food to work based outlets The phrase fast food unknown a generation ago has become very big business compared to which the traditional fish and chip shop seems like a cottage industry The centre of even a modest aized town provides a cosmopolitan selection of restaurants The cuisine of Thailand Mexic
33. the methods demonsirated further on in the book Being clear about these basics from the start will mean you avoid unnecessary confusion later on You wil find that the terms explained below are used many times an this book They are the first words in a technical vocabulary that will become familiar io vou as you proceed As you wii find with other subiects you study or interests that vou have outside college there are specialist words and phrases to comprehend but once you have grasped their meaning you wili get used to using them as a matter of course 1 23 1 The key words you need to know 6 Date A plural noun the singular form is datum which means a set of known or given things facts Note that data can be numerical e g age of people or nor rramerical e g gender of people e statistics Without a capital letter Le in its lower case form this means a set of numerical data or figures that have been collected systematically E Statistics With a capital ietter this is a proper noun that means the study of statistics the set of methods and theories that can be used to arrange analyse and interpret numerical data A variable A quantity that varies the opposite of a constant For example the number of rooms sold in a hotel is a variable whereas the number of hours in a day is a constent In the x expressions that we will use to summarize methods a capital letter usually X or Y will be used to represent a var
34. the sigma iels us to start the addition with the first observed value of x and the F above the sigma sign z tells us to finish the addition with the fourth observed value i E nS even Stats 10 Go In the situation described in Example 1 1 we could show that the total time taken to serve a customer in the drive through facility which we could represent by T is the sum of the time taken to perform four tasks bv using the expression HMM n SASSARI SARAE NAR ee NARRA VV VV VV VV UV a a a a k a P ot DE tftp tig tty 104324748 37 ee eue Set ettet ettet vat sse tlie oes er s nde n uals tuus Si lee n nur ee e a a a Aa aa a a ne aaa e a I a e tf ae see a ee f e eene annee As feu ne a Ia e ann e ee A Tene te Mv Hf it is necessary to indicate that all of a set of observations should be added together and the exact number of observations is not known we use the letter to represent the last observation in the set sa Xx means the sum of the first to the last 1 Observations of the variable K i As you proceed with vour study of the subject you will find that the letter n is used throughout Statistics to represent the number of observations in a set At first these types of symbol may appear strange to vou but it is worth learning to recognize and use them they can become very useful shorthand forms which will save you space and time in future work Subtraction represented by then minus sign is the pr

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