CHAPTER Good visibility – pictorial presentation of data 5 Chapter objectives This chapter will help you to: ■ illustrate qualitative data using pictographs, bar charts and pie charts ■ portray quantitative data using histograms, cumulative fre- quency charts and stem and leaf displays ■ present bivariate quantitative data using scatter diagrams ■ display time series data using time series charts ■ use the technology: data presentation in EXCEL, MINITAB and SPSS ■ become acquainted with business uses of pictorial data presentation In the last chapter we looked at arranging and tabulating data, taking the first steps in transforming raw data into information, bringing meaning to the apparently meaningless. In this chapter we will continue this theme by considering various ways of portraying data in visual form. Used appropriately the diagrams and charts you will find here are very effective means of communicating the patterns and meaning con- tained in data, specifically the patterns and sequences in distributions. 136 Quantitative methods for business Chapter 5 There are techniques that are very common in business documents so being able to understand what they mean is an important skill. There are many different diagrams and charts that can be used to do this, so it is important to know when to use them. The techniques we use depend on the type of data we want to present, in the same way as the suitability of the methods of arranging data featured in the last chapter depended on the type of data. Essentially, the simpler the data, the simpler the presentational tools that can be used to represent them: simple nominal data restricted to a few categories can be shown effect- ively in the form of a simple bar chart whereas ratio data require the more rigorous scaling of something like a histogram. 5.1 Displaying qualitative data Section 4.4.1 of Chapter 4 covered the arrangement of qualitative data in the form of summary tables. As well as being a useful way of display- ing qualitative data, a summary table is an essential preliminary task to preparing a diagram to portray the data. A diagram is usually a much more effective way of communicating data because it is easier for the eye to digest than a table. This will be important when you have to include data in a report or presentation because you want your audience to focus their attention on what you are saying. They can do that more easily if they don’t have to work too hard to understand the form in which you have presented your data. Displaying qualitative data is fairly simple if there are few categories of the attribute or characteristic being investigated. With more cat- egories, the task can be simplified by merging categories. There are three types of diagram that you can use to show qualitative data: pictographs, pie charts and bar charts. We will deal with them in this section in order of increasing sophistication. 5.1.1 Pictographs A pictograph is little more than a simple extension of a summary table. The categories of the attribute are listed as they are in a summary table, and we use symbols to represent the number of things in each category. The symbols you use in a pictograph should have a simple and direct visual association with the data. A pictograph like Figure 5.1 can be an effective way of presenting a sim- ple set of qualitative data. The symbols are a simple way of representing the number in each category and have the extra advantage of empha- sizing the context of the data. Pictographs do have some drawbacks that may put you off using them. Unless you are artistically gifted and can create appropriate images by hand, you will probably have to rely on computer software to produce them for you. Creating a pictograph using a PC can be a labori- ous process. Spreadsheet and statistical packages cannot produce a pictograph for you directly from data, so symbols have to be grafted alongside text in a word processing package. If you do use pictographs you need to choose the symbols carefully. They should be easy to associate with the context of the data and not so elaborate that the symbols themselves become the focus of attention rather than the data they are supposed to represent. Chapter 5 Good visibility – pictorial presentation of data 137 Example 5.1 The table below lists four racehorse trainers and the number of horses they trained that won races at a horse race meeting. Show this set of data in the form of a pictograph. Trainer Number of winners Nadia Amazonka 5 Freddie Conn 3 Lavinia Loshart 1 Victor Sedlow 2 Trainer Number of winners Nadia Amazonka Freddie Conn Lavinia Loshart Victor Sedlow Each symbol represents 1 winner. Figure 5.1 Pictograph of the number of winners by each trainer You may occasionally see a pictograph in academic and business docu- ments; you are more likely to see them on television and in newspapers. The computer graphics software reporters and editors use is much more sophisticated than any that you are likely to have access to during your studies. 5.1.2 Pie charts The second method of displaying qualitative data that we will look at is the pie chart. Pie charts are used much more than pictographs in part because they can be produced using widely available computer software. A pie chart, like a pictograph, is designed to show how many things belong to each category of an attribute. It does this by representing the entire set of data as a circle or ‘pie’ and dividing the circle into segments or ‘slices’. Each segment represents a category, and the size of the seg- ment reflects the number of things in the category. Just about every spreadsheet or statistical package can produce a pie chart like Figure 5.2 either from the original data or from a summary table. You will find guidance on doing this using EXCEL, MINITAB and SPSS in the final section of this chapter. These packages provide vari- ous ways of enhancing pie charts: colour and shading patterns, 3D effects, and detached or ‘exploded’ slices to emphasize a particular segment. With practice you will be able to use these options in creating pie charts, but don’t overdo it. Remember that the pattern of the data is what you want to convey not your ability to use every possible gimmick in the package. Pie charts are so widely used and understood that it is very tempting to regard them as an almost universal means of displaying qualitative 138 Quantitative methods for business Chapter 5 Example 5.2 The Steeralny Appliance Repair Service has depots in Crewe, Doncaster, Exeter and Frome. The numbers of call-outs from each depot on one day are given in the following table: Depot Call-outs Crewe 36 (26.1%) Doncaster 57 (41.3%) Exeter 28 (20.3%) Frome 17 (12.3%) Total 138 (100.0%) data. In many cases they are appropriate and effective, but in some situ- ations they are not. Because the role of a pie chart is to show how different components make up a whole, you should not use one when you cannot or do not want to show the whole. This may be because there are some values missing from the data or perhaps there is an untidy ‘Other’ category for data that do not fit in the main categories. In leaving out any data, either for administrative or aesthetic reasons, you would not be pre- senting the whole, which is exactly what pie charts are designed to do. One reason that people find pie charts accessible is that the analogy of cutting up a pie is quite an obvious one. As long as the pie chart looks like a pie it works. However if you produce a pie chart that has too many categories it can look more like a bicycle wheel than a pie, and confuses rather than clarifies the data. If you have a lot of cat- egories to present, say more than ten, either merge some of the cat- egories in order to reduce the number of segments in the pie chart or consider an alternative way of presenting your data. 5.1.3 Bar charts Another method of portraying qualitative data is the bar chart. Like pie charts, bar charts are widely used, fairly simple to interpret, and Chapter 5 Good visibility – pictorial presentation of data 139 These data are presented in the form of a pie chart in Figure 5.2. Figure 5.2 Number of call-outs by depot Crewe (36, 26.1%) Exeter (28, 20.3%) Frome (17, 12.3%) Doncaster (57, 41.3%) can be produced using spreadsheet and statistical packages. However because there are several different varieties of bar charts, they are more flexible tools. We can use bar charts to portray not only simple categorizations but also two-way classifications. The basic function of a bar chart is the same as that of a pie chart, and for that matter a pictograph; to show the number or frequency of things in each of a succession of categories of an attribute. It repre- sents the frequencies as a series of bars. The height of each bar is in direct proportion to the frequency of the category; the taller the bar that represents a category, the more things there are in that category. The type of bar chart shown in Figure 5.3 is called a simple bar chart because it represents only one attribute. If we had two attributes to display we might use a more sophisticated type of bar chart, either a component bar chart or a stack bar chart. The type of bar chart shown in Figure 5.4 is called a component bar chart because each bar is divided into parts or components. The 140 Quantitative methods for business Chapter 5 Example 5.3 Produce a bar chart to display the data from Example 5.2. Crewe Doncaster Exeter Frome 0 10 20 30 40 50 60 Depot Number of call-outs Figure 5.3 A bar chart of call-outs by depot alternative name for it, a stacked bar chart, reflects the way in which the components of each bar are stacked on top of one another. A component bar chart is particularly useful if you want to emphasize the relative proportions of each category, in other words to show the balance within the categories of one attribute (in the case of Example 5.4 the depot) between the categories of another attribute (in Example 5.4 the type of call-out). Chapter 5 Good visibility – pictorial presentation of data 141 Example 5.4 The call-outs data in Example 5.2 have been scrutinized to establish how many call-outs from each depot concerned washing machines and how many concerned other appli- ances. The numbers of the two call-out types from each depot are: Display these data as a component bar chart. Washing machine Other appliance Depot call-outs call-outs Crewe 21 15 Doncaster 44 13 Exeter 13 15 Frome 10 7 Figure 5.4 A component bar chart of call-outs by depot and appliance type Washing machine Other appliance Crewe Doncaster Exeter Frome 0 10 20 30 40 50 60 Depot Number of call-outs If you want to focus on this balance exclusively and are not too concerned about the absolute frequencies in each category you could use a com- ponent bar chart in which each bar is subdivided in percentage terms. If you want to emphasize the absolute differences between the cat- egories of one attribute (in Example 5.4 the depots) within the cat- egories of another (in Example 5.4 the types of call-out) you may find a cluster bar chart more useful. The type of bar chart shown in Example 5.6 is called a cluster bar chart because it uses a group or cluster of bars to show the composition of each category of one characteristic by categories of a second charac- teristic. For instance in Figure 5.6 the bars for Crewe show how the call- outs from the Crewe depot are composed of call-outs for washing machines and call-outs for other appliances. At this point you may find it useful to try Review Questions 5.1 to 5.3 at the end of the chapter. 142 Quantitative methods for business Chapter 5 Example 5.5 Produce a component bar chart for the data in Example 5.4 in which the sections of the bars represent the percentages of call-outs by appliance type. Washing machine Other appliance FromeExeterDoncaster Crewe 100 90 80 70 60 50 40 30 20 10 0 Depot Percentage of call-outs Figure 5.5 A component bar chart of percentages of call-outs by depot and appliance type Chapter 5 Good visibility – pictorial presentation of data 143 Example 5.6 Produce a cluster bar chart to portray the data from Example 5.4. Washing machine Other appliance FromeExeterDoncaster Crewe 50 40 30 20 10 0 Depot Number of call-outs Figure 5.6 A cluster bar chart of call-outs by depot and appliance type Example 5.7 In Example 4.6 the numbers of free refills taken by 20 customers visiting the UREA department store cafe were tabulated as follows: Number of Number of refills customers 06 17 25 32 5.2 Displaying quantitative data Quantitative data are more sophisticated data than qualitative data and therefore the methods used to present quantitative data are generally more elaborate. The exception to this is where you want to represent the simplest type of quantitative data, discrete quantitative variables that have very few feasible values. You can treat the values in these data as you would categories in qualitative data, using them to construct a bar chart or pie chart. 5.2.1 Histograms In general quantitative data consist of a rather larger variety of values than the data portrayed in Figure 5.7. In section 4.4.2 of Chapter 4 we saw how grouped frequency distributions could be used to arrange quantitative data. Here we will look at what is probably the most widely used way of displaying data arranged in a grouped frequency distribution, the histogram. This is a special type of bar chart where each bar or block represents the frequency of a class of values rather than the frequency of a single value. Because they are composed in this way histograms are sometimes called block diagrams. You can see that in Figure 5.8 there are no gaps between the blocks in the histogram. The classes on which it is based start with ‘0–19’ then ‘20–39’ and so on. When plotting such classes you may be tempted to leave gaps to reflect the fact that there is a numerical gap between the end of the first class and the beginning of the next but this would be 144 Quantitative methods for business Chapter 5 Figure 5.7 shows these data in the form of a bar chart. Figure 5.7 Number of customers by number of refills 3210 8 7 6 5 4 3 2 1 0 Number of refills Number of customers [...]... other classes we could use ‘ 65 to 84’ The amended classes with their frequency densities are: Age range 0–14 15 24 25 44 45 64 65 84 Frequency 0 5 20 18 7 Frequency density 0/ 15 ϭ 0.00 5/ 10 ϭ 0 .50 20/20 ϭ 1.00 18/20 ϭ 0.90 7/20 ϭ 0. 35 Chapter 5 Good visibility – pictorial presentation of data 147 1. 25 Frequency density 1.00 0. 75 0 .50 0. 25 0.00 0 15 25 45 Ages 65 85 Figure 5. 9 Histogram of ages of customers... display in Example 5. 15 has the same role as the scale on the horizontal or ‘X’ axis of a histogram, in that it specifies the order of magnitude Example 5. 15 Musor Burgers operate fast food restaurants The seating capacities of the 27 restaurants they operate in East Anglia are: 53 59 52 38 50 56 59 48 52 62 74 55 51 52 47 51 41 52 28 73 41 45 68 61 47 39 48 Produce a stem and leaf display for these data... the former because it consists of blocks rather than data It is possible to Example 5. 16 Five of the Musor restaurants whose seating capacities are given in Example 5. 15 are in city centre locations The seating capacities for these five restaurants are shown in bold type below: 53 59 52 38 50 56 59 48 52 62 74 55 51 52 47 51 41 52 28 73 41 We can embolden these values in the stem and leaf display 45. .. given in Example 5. 15 East Anglia 9 8 7 7 5 1 9 9 6 5 3 2 2 2 2 1 1 8 2 4 Stem 8 8 1 0 1 3 2 3 4 5 6 7 8 9 Bristol 9 1 0 0 2 1 2 1 3 6 4 5 6 8 9 1 7 9 5 6 8 7 Leaf unit ϭ 1 By looking at the display in Example 5. 17 you can see that in general the restaurants in the Bristol area have larger seating capacities than those in East Anglia  156 Quantitative methods for business Chapter 5 On the left-hand... stem line will be for the stem digit 2, and the last one for the stem digit 7 The first stem line will have a leaf digit for the lowest value, the 8 from 28 The second stem line, for the stem digit 3, will have two leaf digits, the 8 from 38 and the 9 from 39, and so on  154 Quantitative methods for business Stem Chapter 5 Leaves 2 3 4 5 6 7 8 8 8 3 2 4 9 7 1 1 5 7 8 9 2 0 6 9 2 5 1 2 1 2 8 1 3 This... one stem and leaf display you simply list the leaf digits for one distribution to the left of the list of stem digits and the leaf digits for the other distribution to the right of the stem digits Example 5. 17 The seating capacities for the 22 Musor restaurants in the Bristol area are: 61 60 69 54 87 82 73 61 78 70 59 52 49 56 51 86 58 91 75 55 67 76 Produce a stem and leaf display to show these data... plotted against the X, or horizontal, axis Chapter 5 Good visibility – pictorial presentation of data 159 Example 5. 21 The maximum daytime temperatures (in degree Celsius) and the quantities of barbecue fuel (in kg) sold at a service station on 13 days were: Temperature (°C) Fuel sold (kg) 15 10 17 15 18 25 18 20 19 45 20 50 21 40 22 85 24 130 25 1 35 27 170 27 1 95 28 180 Decide which is the dependent (Y)... another variable  158 Quantitative methods for business Chapter 5 Example 5. 20 Produce a histogram to portray the data in Example 5. 19 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 stem line will be the class ‘200 and under 300’ and so on 7 6 Frequency 5 4 3 2 1 0 200 300 400 Price 50 0 600 Figure 5. 14 Histogram... further discussion of cumulative frequency graphs in the next chapter because they offer an easy way of finding the approximate values of medians, quartiles and other order statistics At this point you may find it useful to try Review Questions 5. 4 to 5. 9 at the end of the chapter  152 Quantitative methods for business Chapter 5 Example 5. 14 The size of cash payments made by 119 customers at a petrol... supplied to the Komnata office building over two years were: Quarter Year 1 2 1 2 3 4 £63 75 £6941 £2791 £2309 £2964 £3128 £8283 £ 853 7 162 Quantitative methods for business Chapter 5 Produce a time series plot to show these data Energy cost (£) 10,000 50 00 0 1 2 3 4 1 Quarter 2 3 4 Figure 5. 17 Quarterly energy costs 5. 5 Using the technology: presenting data in EXCEL, MINITAB and SPSS In this section you . 5. 15 are in city centre locations. The seating capacities for these five restaurants are shown in bold type below: 53 38 59 62 51 51 28 45 61 39 59 50 48 74 52 41 73 68 47 48 52 56 52 55 47 52 . Figure 5. 8 we can conclude Chapter 5 Good visibility – pictorial presentation of data 147 Figure 5. 9 Histogram of ages of customers opening bank accounts 856 5 452 5 150 1. 25 1.00 0. 75 0 .50 0. 25 0.00 Ages Frequency. try Review Questions 5. 1 to 5. 3 at the end of the chapter. 142 Quantitative methods for business Chapter 5 Example 5. 5 Produce a component bar chart for the data in Example 5. 4 in which the sections