4 Workig with umbers this chapter covers... This chapter is a practical guide showig you how to carry out the types of basic calculatio that you are likely to ecouter whe workig i accoutig ad fiace. The importat lesso here is that you should use your commo sese as well as your calculator whe workig out a solutio. These techiques iclude: carryig out calculatios ad usig estimatio to check what you have doe covertig umbers i words ito figures usig additio, subtractio, multiplicatio ad divisio usig fractios to express the part of a whole dealig with percetages to calculate a variety of figures, for example: - workig out ad checkig discouts o ivoices - calculatig ad checkig Value Added Tax o ivoices - workig out the levels of differece betwee actual ad budgeted figures dealig with averages, for example calculatig the average value of ivetory held by a busiess usig tables to preset umbers uderstadig (but ot creatig) the differet types of graphs ad charts which ca be used i reports to illustrate umbers ad treds
w o r k i g w i t h u m b e r s 5 1 b a s i c c a l c u l at i o s p r o c e s s i g o f u m e r i c a l d a t a Workig i fiace ad accoutig ofte ivolves processig large volumes of figures. This may be carried out usig electroic aids: a computer accoutig program for calculatig ivoice totals a spreadsheet for processig a budget a calculator maybe with a tally roll for addig up log lists of figures, eg the total of customer cheques to be paid ito the bak a c c u r a t e c h e c k i g o f d a t a e s t i m a t i o I all these cases accuracy of iput of the figures is very importat ad should be routiely checked as part of the office procedures. I the case of the additio of colums of figures, oe way of checkig accuracy is to carry out the procedure twice, ad get somebody else to call out the figures if there is a discrepacy. Estimatio is also very importat whe you carry out or check a calculatio. Does the total seem about right? Commo sese is critical. For example, does the admi office really eed to order 2,500 pes, or should it be 25? The situatio below is based o a real icidet ad shows the serious dager of ot usig commo sese or checkig figures properly. olie Electroics store apologises for 49p tv error Thousads of iteret shoppers who bought a TV ormally priced at 499 but quoted at a olie price of 49p have bee told the deal was too good to be true. The iteret store is refusig to hoour the website deals ad has apologised, sayig the mistake i pricig was dow to a "geuie iteral error". About 10,000 customers had bought the 32" TV over a Bak Holiday. But the compay has ow cacelled all the orders ad is givig refuds. A compay spokesperso commeted that this problem was dow to a ufortuate mistake "while keyig i data".
5 2 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l c o v e r t i g w o r d s i t o u m b e r s Aother basic umeracy skill is the ability to covert umbers writte i word form ito actual umbers, for example: 10.5 millio = 10,500,000 This is straightforward, but it is importat to appreciate that some of the larger umbers are less well kow. Oe billio, for example is a thousad millio. The UK Natioal debt (ie what the UK govermet has borrowed) at the time of writig was a immese 1,400 billio: 1,400 billio = 1,400,000,000,000 It is rather ulikely that you will be dealig with figures of this size, but it is a basic umeracy skill to kow the meaig of this termiology. a d d i t i o Addig a series of figures is very straightforward i priciple, but care eeds to be take: whe dealig with figures with a decimal poit sometimes the umber of decimal places varies, for example: 45.6 + 67.98 + 95 = 208.58 whe dealig with figures which vary i size, for example: 23,567 + 74,349,117 + 76 = 74,372,760 As metioed before, it is good practice to carry out all calculatios twice to check for accuracy ad the, if possible, get them checked. s u b t r a c t i o a d a d d i t i o The process of subtractio is similar to that of additio except that you are deductig figures rather tha addig them. Fortuately the calculator with its + ad fuctio keys will deal automatically with more complex calculatios which ivolve subtractio, or sometimes a mix of additio ad subtractio. For example combiig two egative figures, eg 2 mius 2 equals 4 combiig a egative figure ad a positive figure, eg 20 plus + 40 equals 20 Agai, it is good practice to carry out all calculatios twice ad get them checked.
w o r k i g w i t h u m b e r s 5 3 u s i g m u l t i p l i c a t i o a d d i v i s i o Multiplicatio is commoly used whe drawig up ivoices ad credit otes maually, ad also whe checkig them. For example, if you receive a order for 10 red box files which cost 4.00 each, you will produce a ivoice which will show: product quatity x uit price, ie 10 x 4.00 = 40.00 This will appear as show i this ivoice extract: product descriptio quatity price uit total discout et code % BF-R Box file (red) 10 4.00 each 40.00 This is straightforward eough; you just eed to make the calculatio ad check it ad apply the estimatio test. Does 40 seem a reasoable aswer? The last two colums of the above ivoice, which iclude a percetage discout colum, are left blak for ow. We will explai how to calculate discouts later i this chapter. The use of percetage calculatios i busiess is very commo ad is explaied i the ext sectio. Divisio ca be see as the opposite of multiplicatio. Divisio works out how may times oe umber is cotaied i aother umber. For example if a busiess receives 12 bottles of wie as a preset ad they have to be shared equally by 6 employees, the aswer is that they will receive 2 bottles each. The calculatio here is very simple: 12 6 = 2 bottles each Divisio is commoly used i accoutig whe workig out the cost of a product: the cost is divided by the umber of uits to produce a uit cost. Divisio also forms the basis of fractio ad percetage calculatios, as will be explaied o the ext few pages. f r a c t i o s A fractio is used to express a part of a whole (uit). a example of a fractio is 3 /4 the umber above the lie (the umerator) is the umber of parts ivolved here it is 3 parts the umber below the lie (the deomiator) is the umber of equal parts ito which the uit is divided here it is 4 parts
5 4 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l c a l c u l a t i o s u s i g f r a c t i o s If you eed to work out a part of a whole usig a fractio you: multiply the whole amout by the umber o the top of the fractio divide the result of this by the umber o the bottom of the fractio For example, if you eed to work out 3 /4 of 12.00 the calculatio is: 3 (ie the umber o the top of the fractio) x 12.00 = 36.00 36.00 4 (ie the umber o the bottom of the fractio) = 9.00 So 3 /4 of 12.00 is 9.00. As a fractio is a part of a whole it ca be used to calculate a sum of moey which is icluded i a total amout. For example, you may wat to kow how much VAT charged at 20% is icluded i a 24 purchase so that you ca eter the VAT i the accouts. The fractio used here is 1 /6. This is kow as the VAT fractio. The calculatio is: 1 x 24 = 24 = 4 VAT 6 6 This meas that the purchase price before VAT was 20 ad the VAT was 4. r a t i o s a d f r a c t i o s A ratio shows the comparative umber of differet items i a group. For example, if you have a class of 22 studets which has 9 males ad 13 females, the ratio of male to female is 9 to 13; this is writte as: 9 : 13 If oe of the females dropped out of the class the ratio would become: 9 : 12 Note that you could divide these umbers by the same umber, ie 3, to produce the ratio: 3 : 4 It is ormal practice to reduce a ratio to the lowest possible whole umbers, by dividig both umbers by the same whole umber. Note also that you ca covert a ratio ito a fractio. Takig the example of the class where the ratio of males to females is 9 : 13, you ca state that: there are 9 males i a group of 22, so the fractio of males i the group is 9 /22 there are 13 females i a group of 22, so the fractio of females i the group is 13 /22
w o r k i g w i t h u m b e r s 5 5 d E a l i g w i t h p E r c E ta g E s d e f i i t i o a p e r c e t a g e i s a p a r t o f a w h o l e The phrase per cet meas out of every hudred. So 50% meas 50 out of every hudred. A percetage tells you what proportio oe umber is i relatio to aother. I other words, a percetage is a part of a whole, where the whole is 100. It is the top umber of a fractio whe the bottom umber is 100: 50% = the fractio 50 = 1 ie, a half 100 2 If you go to a party where there are twety people, your parter might use a fractio ad say I do t kow half the people here. The way to work out the percetage of people your parter kows is to divide the umber kow (the part ) by the total (the whole ) ad the multiply the result of this by 100. The formula is therefore: the part x 100 = percetage of the part the whole Suppose your parter kew 12 of the 20 people at the party. The percetage of people kow would be: 12 people x 100 = 60% are kow 20 people w o r k i g o u t a p e r c e t a g e o f a g i v e u m b e r This is a very commo use of percetages i orgaisatios. Here you start with the percetage rate ad use it as a umber of hudreths to work out the figure you eed as a fractio of a give amout. Examples iclude: discouts a amout to subtract from a moey amout tax a amout, VAT for example, to add to sales This is doe by usig the formula: give percetage x amout = percetage amout 100 Suppose you wat to calculate 8% of 250. Usig the formula, the calculatio is: 8 (percetage) x 250 (amout) = 20 100
5 6 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l A easy way of doig this is to shift the decimal place of the percetage figure two places to the left ad the put this figure i a calculator ad multiply it by the moey amout. So i this case 8% becomes 0.08 ad the calculatio is simply: 0.08 x 250 = 20 c a l c u l a t i g d i s c o u t a m o u t s We will ow use the formula explaied o the previous page to calculate a discout amout. The ivoice extract show below shows the discout percetage give o the sales trasactio. This is most likely to be trade discout ie the discout give to customers who expect a discout as part of the tradig relatioship. Calculatig discouts ivolves workig out a percetage of the total of the products sold ad the deductig this from the total. The formula eeded to calculate the percetage discout which will be deducted is therefore: sales total ( ) x discout percetage = discout ( ) 100 Cotiuig the example o page 55 the sales total is 40 ad the trade discout is 20%. Applyig the formula, the calculatio is: sales total ( 40) x discout percetage (20) = discout of 8 100 Note that the discout amout of 8 is ot actually show o the ivoice; all you see is the amout before the discout is deducted ( 40) ad the et amout after the discout is deducted ( 32). This may seem cofusig, but it is commo practice. product descriptio quatity price uit total discout et code % BF-R Box file (red) 10 4.00 each 40.00 20 32.00 r o u d i g o f u m b e r s t o d e c i m a l p l a c e s Sometimes the discout amout will ot come out as a precise ad pece figure, ie to two decimal places. The umber of decimal places meas the quatity of umbers to the right of the decimal poit. I moey amouts this will obviously always be 2. The calculatio may produce somethig awkward like 91.9324 or 45.5786. I this case the four figures to the right of the decimal poit will have to be rouded up or dow to produce the correct umber of decimal places to
w o r k i g w i t h u m b e r s 5 7 correspod with the two digits showig pece - ie 2 decimal places. I this case: 91.9324 becomes 91.93 (rouded dow to the earest pey) 45.5786 becomes 45.58 (rouded up to the earest pey) The roudig rule is therefore: start with the right-had digit of the umber if it is 5 or higher delete it ad add 1 to the digit o its left if it is less tha 5 delete it ad leave the digit o the left as it is carry o util you have the right umber of decimal places (this is ormally 2 decimal places i the case of moey amouts i accoutig) r o u d i g t o t h e e a r e s t w h o l e u m b e r Whe you are told to roud a umber to the earest whole umber look at the umber to the right of the decimal poit, if it is 5 or greater tha 5 the umber to the left of the decimal poit icreases by oe, if it is less tha five it stays the same. 27.938 rouds to 28 because the 9 tells you to go up 28.345 rouds to 28 because the 3 tells you to stay the same a d d i g V a t ( s a l e s t a x ) t o a i v o i c e The ivoice used i the example o the last few pages is also likely to iclude Value Added Tax (VAT), which is a sales tax. This is worked out as percetage of the et total after ay trade discout has bee calculated. Like most taxes, VAT is quoted as a percetage rate, ad like most taxes VAT varies from time to time. I this book VAT is quoted at a rate of 20%. The ivoice with the VAT calculatio will appear as follows: product descriptio quatity price uit total discout et code % BF-R Box file (red) 10 4.00 each 40.00 20 32.00 Total 32.00 VAT @ 20% 6.40 TOTAL 38.40 VAT is calculated as a percetage of the cost of the goods. If ivoiced goods, as here, cost 32, the VAT (at the stadard rate of 20%) is calculated as:
5 8 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l 32 x 20 = 6.40 100 Importat ote: if the amout of VAT calculated comes out at more tha 2 decimal places, you ormally delete all digits to the right of the 2 decimal places. This is differet from the roudig rule set out at the top of the page. c a l c u l a t i g V a t w h e i t i s i c l u d e d i t h e t o t a l Sometimes you may have to deal with a low value ivoice or receipt which quotes a figure which icludes VAT at a certai rate, but does ot actually tell you what the VAT amout or the cost price is. You may have to calculate this VAT amout ad the cost before VAT to eter i the books; for example i the petty cash book. Let us take a example of a receipt or ivoice for 24.00 for some statioery. This icludes the cost of the statioery (100%) ad also the VAT (20%) added to this cost. The total amout therefore equates to 120% of the cost. The formula to use i this case is: VAT percetage x total amout( ) = VAT cotet( ) 100% + VAT percetage Applyig this formula to the total figure of 24.00, the calculatio is: 20% x 24.00 = a VAT cotet of 4.00 120% Therefore the 24.00 total amout is made up of a cost price of 20.00 ad VAT of 4.00 ( 20.00 is 24.00 mius 4.00). If the VAT rate is 20%, aother way of workig out the VAT icluded i a total amout is to multiply the whole amout by the VAT fractio of 1 /6, or more simply, divide the whole amout by 6 (see also page 54). The calculatio is therefore 24.00 6 = 4.00. Note that if the VAT rate chages, so will the VAT fractio. p E r c E ta g E s f o r m a a g E m E t a c c o u t i g The applicatio of percetages to your studies so far has cocetrated o basic accoutig ad bookkeepig, usig a ivoice as a example. Percetages are also very useful for reportig data, comparig the sales ad profit results for differet periods, for example, or commetig o the extet to which actual sales or profit results compare with the forecast made i a
w o r k i g w i t h u m b e r s 5 9 budget. These relate to maagemet accoutig (accoutig iformatio for decisio makig by maagers). p e r c e t a g e s f o r c o m p a r i s o There are may applicatios of percetages i maagemet accoutig. For example a shop ower might say that: 60% of our total sales for the year were made i the two moths before Christmas. This is much clearer tha sayig: 240,000 of our aual sales of 400,000 were made i the two moths before Christmas. To work out this percetage you eed to use the formula: the part of the whole x 100 = the percetage the whole I the example above, the calculatio is 240,000 x 100 = 60% 400,000 This is useful, for example, whe the busiess wats to compare pre- Christmas sales with other years: 60% of our sales this year were made i the two moths before Christmas; this compares with a figure of 55% for last year. This gives you a much clearer picture tha if you said: 240,000 of our aual sales of 400,000 were made i the two moths before Christmas; this compares with 192,500 out of a total of 350,000 made last year. This will oly give you a headache. p e r c e t a g e s a d b e c h m a r k s If you are studyig basic costig you will kow that a bechmark is a forecast figure which is set as a target by a orgaisatio for sales or costs for a future period, for example the ext year. Whe the ed of that period is reached the orgaisatio will compare the actual results, ad the bechmark forecast The differece betwee the two figures will the be calculated. This differece ca be stated by meas of a amout or a percetage of the
6 0 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l bechmark (forecast) figure. If the amout or percetage is greater tha what would be expected, it will eed to be reported to maagemet so that actio ca be take if ecessary. The example show below shows a compariso of two years sales figures for a busiess which sells moder art pictures. Study the table ad read the otes ad coclusio that follow. art world limited aual sales forecast actual differece percetage (bechmark) differece Year 1 400,000 420,000 + 20,000 5% Year 2 420,000 407,400 12,600 3% Workigs: the first colum of figures shows the forecast target sales figures the secod colum of figures shows the actual results for the year the third colum shows the differece betwee the forecast ad actual figures (a + meas more tha forecast, a meas less tha forecast) the last colum shows the differece show as a percetage of the forecast figure (ot the actual figure); the workigs are as follows: Year 1 Differece ( 20,000) x 100 = 5% Forecast/bechmark ( 400,000) Year 2 Differece ( 12,600) x 100 = 3% Forecast/bechmark ( 420,000) Coclusio 1 Sales for Year 1 are higher tha the bechmark by 20,000. The percetage differece for Year 1 is 5%, which meas that sales are 5% higher tha forecast. 2 Sales for Year 2 are lower tha the bechmark by 12,600. The percetage differece for Year 2 is 3%, which meas that sales are 3% lower tha forecast. 3 Maagemet will take actio if they thik it is ecessary.
w o r k i g w i t h u m b e r s 6 1 u s i g av E r a g E s A techique which is useful whe reportig o a series of performace figures, such as sales figures, is the use of averages. There are three commoly-used types of average: the mea, the media ad the mode. w h i c h a v e r a g e? Suppose the fiace maager of a kitche istallatio busiess wated to kow for budgetig purposes the average job completio time i days, from iitial equiry through to fial istallatio. He has just received the figures for the jobs completed last moth. The figures are (i days): 20, 25, 35, 35, 35, 36, 37, 55, 60, 65, 65 What is the average job completio time? We will look i tur at the mea, media ad mode averages. t h e m e a The arithmetic mea is probably the most commoly-used ad statisticallyreliable form of average. It is also kow as a weighted average. The arithmetic mea is the sum of all the figures divided by the umber of figures. The sum of 20, 25, 35, 35, 35, 36, 37, 55, 60, 65, 65 = 468 The arithmetic mea = 468 = 42.5 days 11 This tells the maager that, o average, a job takes approximately 43 days to complete. This will help him i the plaig ad budgetig process. Note: the result is ot a whole umber of days roudig up to 43 is ecessary the result takes ito accout all values if there had bee a exceptioal job takig 165 days istead of 65, the result will have bee a mea average of 568 11 = 51.6 days, a possibly distorted result t h e m e d i a The media is the value of the middle figure i a series of figures. Note that if there is o middle figure, as with a eve umber of values, the media is the arithmetic mea of the two figures earest to the middle. Here the media is 20, 25, 35, 35, 35, 36, 37, 55, 60, 65, 65 = 36 days.
6 2 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l This will ot be as helpful to the maager as the mea i this cotext; it is useful because it is ot distorted by extreme values (eg 185 days) the mea, however, is more reliable because a equal weightig is give to each value. t h e m o d e The mode is the value that occurs most ofte i a series. I this case the most commo period is 35 days (3 jobs), followed closely by 65 days (2 jobs). Note that these two time periods are very widely dispersed. This would suggest that this type of average is ot as helpful i the plaig process. The mode is more useful i areas such as market research i aswerig questios such as How much do people o average sped o a fast food meal? or What is the most commoly-occurrig size of T shirt? u s i g t h e m e a i i v e t o r y v a l u a t i o If you are studyig costig you will kow that it is importat for a busiess orgaisatio to be able to calculate its ivetory value, ie the valuatio of all the materials ad items it holds. Oe method of ivetory valuatio is AVCO (short for AVerage COst). It is very useful for ivetory that is added to from time to time ad mixed up with existig ivetory. Take, for example, a busiess importig ad sellig Chiese teis rackets. It buys i its teis rackets every moth ad stores them i the warehouse. Because the cost price of the rackets varies each moth (due to currecy fluctuatios) ad because the rackets are mixed up with rackets already held i ivetory it becomes virtually impossible to value the rackets uless a average cost is take, usig the mea (weighted average) method. The formula for this is: total cost of ivetory held = average cost of a item of ivetory umber of ivetory items held If the total cost of the rackets held is 110,000 (differet prices paid for cosigmets o differet ivoices over six moths) ad the umber of rackets held is 5,500, the average cost price ca be worked out as follows: 110,000 (cost of items) = 20 (average cost of item of ivetory) 5,500 (umber of items) I other words at the time that this calculatio was made each racket i the warehouse had cost the busiess, o average, 20. The busiess ca the use this figure to work out its sellig price ad make sure that it makes a profit.
w o r k i g w i t h u m b e r s 6 3 u s i g ta b l E s Tables of figures are ofte used i accoutig ad fiace for settig out data which is useful to maagemet. Sometimes they ca be icorporated ito a report (see ext chapter) to: provide iformatio illustrate a proposal Figures i a table which covers a exteded period of time (eg this year ad last year ) ca usefully provide a compariso for sales, costs ad profit. The techical term for this type of compariso of umbers over time is time series aalysis. Staff workig i accoutig ad fiace will eed to kow how to set out a table so that it is clear ad accurate. The most commo way of doig this is to use a computer spreadsheet or word processig program. A spreadsheet will also eable graphs ad charts to be extracted; these ca the be icluded i a report to illustrate data ad treds. c o s t r u c t i g a t a b l e If you are processig a set of figures at work you may have to costruct a table; alteratively the table may be i pro-forma form (ready made) or it may be output from a computer iformatio system, be completed as a computer spreadsheet or as a fuctio i Microsoft Word. The example show below shows the sales ad profit results for a limited compay over a period of four years. Study the table ad read the otes that follow. amico ltd: sales ad profit statemet report Year 1 Year 2 Year 3 Year 4 000s 000s 000s 000s Sales 500 970 1,430 1,912 Net profit 65 95 132 147 the title clearly sets out what the data is each time period is show i a vertical colum each time period is clearly headed up (it could be a year, a moth or a week)
6 4 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l the uits for the data are stated below the time period here 000s are chose to prevet the table beig cluttered up with uecessary zeros the types of data are set out i two rows ad labelled i the left-had colum ie Sales ad Net Profit (which meas profit after all expeses have bee deducted) lies are added to clarify the table it is ot ecessary i this case to draw a lie uder each row of data as the colums ca easily be read across; if, however, there was a large umber of colums, lies would be helpful p r e s e t i g a d i t e r p r e t i g t h e d a t a The figures set out i the table o the previous page ca be iterpreted just by readig them, but a much better picture ca be obtaied by presetig the data i the form of a graph or chart which will provide a very visual cocept of each tred ad help the uderstadig of the report. This process is usually carried out by usig a computer spreadsheet or chartig package. The graphs ad charts which follow o the ext few pages were produced by a simple spreadsheet program. l i E g r a p h The simplest form of visual represetatio of a time series is the lie graph. A lie graph, which ca be i a straight lie or a curve, shows the relatioship betwee two sets of data variables. Oe variable will always deped o the other. They are kow as: the idepedet variable the measuremet that is at a fixed iterval the depedet variable the figure that will deped o the idepedet variable A commo idepedet variable is time, ad a commo depedet variable is moey. s t r u c t u r e o f a l i e g r a p h y axis = depedet variable, eg moey ( 000s) x axis = idepedet variable, eg time (years)
w o r k i g w i t h u m b e r s 6 5 i m p o r t a t o t e : g r a p h s a d c h a r t s i y o u r s t u d i e s The AAT has stated that studets are ot required to costruct charts or diagrams i assessmets. They may however ecouter them as additios to reports ad other commuicatios. It is importat therefore that you kow how to read ad iterpret charts such as lie graphs, bar charts ad pie charts. The Case Study ad text that follows explai how each type of chart ca be useful i presetig particular types of accoutig iformatio. Case Study A M I C O LT D : L I N e g R A p H F O R S A L e S F I g u R e S s i t u a t i o You have prited out the sales figures for Amico Limited for the last four years from a spreadsheet ad also used the chart fuctio to produce a lie graph to show the tred i sales. You the eed to explai to a ew member of staff what is show o the lie graph. s o l u t i o The lie graph is show below. You have added the boxes ad text to set out what you have explaied to the ew member of staff so that they will be able to read ad iterpret the graph. amico limited: aual sales a title showig the source of the graph ad what it shows the y axis suitably labelled for Sales Reveue ( 000) a key explaiig what the lie represets the x axis suitably labelled for time period (years) the y axis does ot have to start at zero, but at a poit where the data starts
6 6 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l b a r c h a r t s A bar chart is a chart which sets out a series of bars, the height of which idicates the extet of the depedet variable. It is ormal to set out a bar chart alog the horizotal x axis but the practice ca be varied so that they stretch left to right from the y axis. Bar charts ca be simple, compoud or compoet, depedig o what data comparisos eed to be made. Most spreadsheet programs will produce various types of bar chart from give data. s i m p l e b a r c h a r t The simple bar chart is the most commo type. It works o the same basis as a lie graph ad illustrates a tred. Set out below is a simple bar chart which uses the sales figures for Amico Limited from the table i the Case Study o the previous page. Compare it with the lie graph i the Case Study. amico limited: aual sales Note that: the labellig covetios are the same as for a lie graph here the bars are shaded i grey the y axis goes dow to zero the whole legth of the bar is eeded (this is differet from the lie graph scalig)
w o r k i g w i t h u m b e r s 6 7 c o m p o u d b a r c h a r t Just as it is possible to have a lie graph with more tha oe lie, it is also possible to be give a bar chart with more tha oe set of data for each depedet variable eg sales for differet types of product. This is kow as a compoud bar chart. The example below shows the sales figures for product types X, Y ad Z for Amico Limited. amico limited: aual sales by product product X product Y product Z c o m p o e t b a r c h a r t A compoet bar chart is a bar chart which divides each bar ito segmets, showig how the total for each bar is made up. For example, if the aual sales totals for Amico Limited were made up of totals for three sales divisios A, B ad C, each bar could be show as havig three segmets. amico limited: sales by divisio
6 8 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l p e r c e t a g e c o m p o e t b a r c h a r t Aother way of presetig the sales data is to express the divisioal sales figures as percetages of the aual sales total i a percetage compoet bar chart. Each bar is the the same height, ie 100%, ad the subdivisios show the treds of divisioal sales over the four years. I the example below you ca see that the performace of Divisio A as a percetage of total sales fluctuates substatially each year, a tred that is ot show o the ordiary compoet chart (previous page) which idicates a steady icrease. This is the type of tred that the maagemet might eed to ivestigate. amico limited: percetage sales by divisio 100% 80% Sales A Sales B Sales C percetage % 60% 40% 20% 0% Year 1 Year 2 Year 3 Year 4 p i E c h a r t s A pie chart is a circle divided ito sectors to represet the parts of a whole i their correct proportios. It is called a pie chart because, like a meat or fruit pie, it is cut ito slices. Most spreadsheet programs will produce pie charts of varyig types from give spreadsheet data. Lie graphs ad bar charts are suitable for the presetatio of time series data data which varies from time period to time period. Pie charts, o the other had, are useful i showig the breakdow of a whole ito its costituet parts at a particular momet i time. If you take Amico Limited s sales figures for Year 1 you will equate the total sales of 500,000 with the whole pie circle. This will be divided ito segmets, each of which will proportioally represet a divisioal sales figure.
w o r k i g w i t h u m b e r s 6 9 The divisioal sales figures are as follows: Divisio A 300,000 Divisio B 110,000 Divisio C 90,000 Total sales 500,000 The pie chart for Year 1 looks like this: amico limited: sales by divisio Note that the segmets are labelled with the percetage sales. Remember that a percetage is worked out as: the part x 100 = percetage... i this case, 300,000 x 100 = 60% the whole 500,000 You may fid that you have a report which presets comparative pie charts. For example, the sales figures for two years could be compared as follows: amico limited: sales by divisio
7 0 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l Chapter Summary calculatios additio, subtractio, multiplicatio ad divisio carried out i the workplace should always be checked for accuracy, firstly by usig commo sese estimatio ad the ideally by aother employee carryig out the same calculatio. percetages are based o the cocept of fractios ad are commoly used i accoutig ad fiace, for example i the calculatio of discouts, Value Added Tax, compariso of performace data, ad i budgetig for measurig the differece betwee actual ad bechmark (forecast) figures. averages are used i accoutig ad fiace, for example i calculatig ivetory values i the AVCO (average cost) process. The presetatio of umerical data i table format is a importat skill for workig i accoutig ad fiace. Tables are ofte icorporated i reports for maagemet, sometimes supported by graphs ad charts which illustrate results ad treds very effectively. Key Terms estimatio percetage discout decimal place roudig bechmark mea average time series lie graph bar chart pie chart usig a commo sese approach to calculatio by seeig if the aswer produced seems reasoable per cet meas out of every hudred, so a percetage is the top umber of a fractio where the bottom umber is 100 a percetage of a amout deducted from that amout the umber of digits (umbers) to the right of the decimal poit; ad p are quoted to two decimal places, eg 4.99 i the case of ad p, reducig the umber of digits to two decimal places by roudig up or dow to the earest p i costig this is a forecast figure for future performace (eg sales) agaist which the actual figure is the compared the sum of a series of figures divided by the umber of figures this is also kow as a weighted average a series of data collected regularly over a period of time, eg aual sales figures a visual represetatio of a time series set out i a lie a chart which sets out a series of bars, the height of which idicates the extet of the value that varies a circle divided ito sectors to represet i the correct proportio the parts of a whole like a pie divided ito slices
w o r k i g w i t h u m b e r s 7 1 Activities 4.1 You work i the sales ivoice sectio of Wyver Statioery, a wholesaler. You have a small batch of ivoices to process for three differet customers. You are required to complete ad total the ivoice extracts, icludig trade discout ad VAT as required (ad rouded dow). (a) 20 box files (black), product code 109BK@ 4.00 each with 30% trade discout (b) 90 biros (red), product code 235RD @ 5.60 per box of 10, with 20% trade discout (c) 8 year plaers (blue), product code 563BL @ 12.95 each, with 10% trade discout (a) product descriptio quatity price uit total discout et code % (b) Total VAT @ 20% TOTAL product descriptio quatity price uit total discout et code % (c) Total VAT @ 20% TOTAL product descriptio quatity price uit total discout et code % Total VAT @ 20% TOTAL
7 2 w o r k i g i a c c o u t i g a d f i a c e t u t o r i a l 4.2 You are workig out some prices for a customer ad ote that some discout calculatios produce results ivolvig more tha 2 decimal places. You are to use the roudig rules to esure that all of the followig results are reduced to 2 decimal places: (a) 15% discout o a amout of 45.50 (b) 20% discout o a amout of 44.99 (c) 30% discout o a amout of 21.75 (d) 15% discout o a amout of 390.95 (e) 30% discout o a amout of 964.55 (f) 2.5% discout o a amout of 35.95 4.3 The followig amouts iclude VAT charged at 20%. You are to work out i each case the VAT amout ad the amout before VAT was added o. (a) 49.20 (b) 292.80 (c) 2.28 (d) 436.80 (e) 105.60 4.4 You work for Hypos eterprises. You have bee asked to complete the followig tables showig their aual sales ad profit figures for the last two years. You have bee asked to calculate ad commet o i each case: (a) the differece betwee the forecast ad actual figures, otig if it is + or (b) the differece as a percetage of the forecast (bechmark) figure hypos EtErprisEs aual sales forecast actual differece percetage (bechmark) differece Year 1 600,000 642,000 Year 2 640,000 608,000 hypos EtErprisEs aual profits forecast actual differece percetage (bechmark) differece Year 1 64,000 67,200 Year 2 65,000 63,050
w o r k i g w i t h u m b e r s 7 3 4.5 Show below are two pie charts based o the sales figures of Newbury Limited for Years 1 ad 4. State why you thik these pie charts are ot so useful i showig the year-to-year sales treds. 4.6 Calculate the average (mea, media ad mode) hourly rate of employees pay from the followig figures: Ady 7.50 Bella 7.75 Carlo 7.80 Dirk 7.85 estelle 7.90 Freddy 9.00 gia 11.00 Hal 11.00 Ia 14.20 Which average figure are you likely to use if you are compilig a report o wage costs, ad why?