Presentation of data


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1 2 Presentation of data Using various types of graph and chart to illustrate data visually In this chapter we are going to investigate some basic elements of data presentation. We shall look at ways in which collections of data can be presented in an appealing way to give us a visual indication or summary of what the overall data is telling us. Key topics Analysing data Plotting graphs Drawing charts Key terms line graph scatter graph correlation bar chart histogram pie chart Line graphs When you have a series of measurements taken over time, they are often represented as a line graph. This involves plotting all the points on a graph, and then connecting them together from one point to the next. You often see this sort of graph in the news for example, showing the interest rate over the past few months or years. Here are the UK inflation rates for an 18month period in 2009/10 (you can obtain these figures, along with numerous other data, from the Office for National Statistics). Jan 09 Feb 09 Mar 09 Apr 09 May 09 Jun 09 Jul 09 Aug 09 Sep Oct 09 Nov 09 Dec 09 Jan 10 Feb 10 Mar 10 Apr 10 May 10 Jun Presentation of data 11
2 To plot these on a graph, you need to create two axes, one going horizontally across (which will represent our months), and one going vertically up (which will represent the inflation rate). Note that you should label the axes clearly as to what corresponds to what. For each month, go up to the appropriate inflation rate and mark the point with a cross, or a solid point, or some other clear symbol. For example, to plot the first value, go to the label for Jan 09, and then go up until you reach 3.0, marking it in some way. Once you have filled in all the values, connect them together with a series of straight lines, as in Figure 2.1. Your graph may well look different, because you will probably choose different scales, titles, labels and so on, but this will give you an indication of what it should look like Inflation rate (%) Jan 09 Apr 09 Jul 09 Oct 09 Jan 10 Apr 10 Jul 10 Month Figure 2.1 Example of a line graph It s more obvious from this graph what the overall trend was, rather than just looking at a long list of numbers. You get the impression that the rate fell rapidly and then recovered, which is not as easy to tell from a simple, raw list of data and numbers. For any set of data that is taken over a period of time at regular intervals, a line graph is usually a good way to show the overall trend. Scattergraphs A scattergraph is what you get when you simply plot every point on the graph without making any attempt to connect them together. You 12 Introductory statistics
3 can use it for data when both the x (horizontal) and y (vertical) axes of the graph can take a range of values (not necessarily in order of time just a random collection of data). If the data is scattered widely, then there appears to be no correlation (relationship) between the two things. If they form something close to a line, then there is a good correlation. For example, the following data might have been obtained by recording people s height (in metres) and their weight (in kg). Height (m) Weight (kg) On a scattergraph this could be plotted as shown in Figure 2.2. Note the scale: why start at 1.4, not 0? There appears to be a strong correlation between height and weight: they seem to fall pretty well in a line. This is what you might expect: you would expect taller people to weigh more Weight (kg) Height (m) Figure 2.2 Example of a scattergraph showing a positive correlation If the data lies in an upward line like this (so that as one thing gets bigger, so does the other), you would say that there is a positive correlation between the two things. If the data slopes the other way (so that as one thing gets bigger, the other gets smaller) you would say that there is a negative correlation. The words strong and weak are used for correlations. Where the two things are, clearly, very closely linked, you would say it is a strong Presentation of data 13
4 correlation, whereas if there is some connection, but it is small, you would say it is a weak correlation. Things aren t always correlated. Here is data analysing the same people with the number of shirts they own: Height (m) No. of shirts Again draw a graph (Figure 2.3). This time there doesn t appear to be a connection: the points are scattered everywhere, and they don t lie in anything like a line. Again, this is probably what you would expect: why should a person s height relate to how many shirts they have? Hence there is no correlation here Shirts Height (m) Figure 2.3 Example of a scattergraph showing no correlation Also note that there would be no point in drawing a line between the points here in these sorts of graph. We use a line graph when we have a series of measurements taken over time, but for a general set of measurements with no time flow to them, we just use a scattergraph. Bar charts When the data you get can be classified into a small number of categories, you can often usefully express it as a bar chart. 14 Introductory statistics
5 For example, suppose a survey was done of people s eye colour, and the following results were obtained: Blue: 32 people Brown: 78 people Green: 6 people To plot this as a graph, label the horizontal axis with blue, brown and green, and then draw bars for each one to represent the appropriate number. You should get a graph that looks something like Figure Number Blue Brown Green Colour Figure 2.4 Example of a bar chart You can do this in other ways as well. For example, you might put the colours on the vertical axis and draw horizontal bars, or you might colourcode the bars, or you might draw them without gaps between the bars. It doesn t really matter; choose the method of presentation that suits what you want to present the best. The word histogram is often used instead of bar chart. Although it does have a precise mathematical meaning, most people use it interchangeably for bar chart, and you can assume that a histogram is simply a bar chart as we have drawn here. Presentation of data 15
6 Pie charts A pie chart is a way of representing proportions. For example, suppose 50 people were surveyed and asked their views on a product. The results were as follows: Very good: 23 Good: 11 Average: 8 Poor: 6 Very poor: 2 To draw these figures on a pie chart, we are going to divide a circle into segments corresponding to the options: the larger the segment, the more people chose the option that it represents. A circle is made up of 360 degrees (written as 360 ). You should know how to use a protractor to measure an angle; if you don t know, then ask someone to show you how to use it. Do get hold of a basic maths set, with a ruler, protractor, set square, etc. You can buy them cheaply from standard stationery/ discount stores. They can come in useful, even at times you don t expect; there are lots of times you just want a ruler to draw a straight line, for example. The proportion of people who opted for very good is A circle has 360 in it. The technique to follow is to convert this to the corresponding proportion of 360: this is the number of degrees that the very good segment should occupy. Do this: Work out the proportion as a decimal on your calculator. In this case we get 23/ Multiply this number by 360 on your calculator; you get So the very good segment should be Similarly, you will find that the good segment should be 79.2, the average segment should be 57.6, the poor segment should be 43.2, and the very poor segment should be Introductory statistics
7 Figure 2.5 Example of a pie chart showing the vertical radius only Draw a circle, and draw a vertical radius (a line from the centre to the edge) (Figure 2.5). Now, carefully, with a protractor draw the very good segment, so it should form an angle of You get something like Figure 2.6. very good Figure 2.6 Example of a pie chart showing the very good segment only Continue like this for each segment. Label each segment clearly. When you are presenting a pie chart as part of a formal document, we recommend you use a different colour for each segment. Sometimes in pie charts we would also include the numbers or, more commonly, the percentage of people making each choice, as in Figure 2.7 (you should check for yourself that the percentages are correct). Presentation of data 17
8 poor 12% very poor 4% average 16% very good 46% good 22% Figure 2.7 Example of a pie chart showing all segments and percentages Summary It is vital to present data in an easytounderstand way. When people see the results of a byelection, for example, most of them don t particularly want to see the actual number of votes cast for each candidate; they want them expressed in a visual format that makes the result jump out at them. Similarly, not everyone can see immediately what a series of inflation rate figures mean, but a picture shows the trend. People don t want to understand long lists of figures; they want a simple picture summarising them. In a sense, this is what statistics is all about. When presenting data, use the most appropriate form, but also try to catch the attention of the audience who are looking at it whether this be in a report, or in a presentation, or in whatever form you are presenting your results. Good use of colours can help attract people, and by drawing attention to the main features you want understood, you can use the statistics to highlight clearly what you want to say. Of course, keep things simple, and don t confuse people, but good choices of colours and presentation methods can very effectively sell your message. 18 Introductory statistics
9 Exercises 1 (a) Present the following data showing the number of eggs laid on a chicken farm each day as a line graph: Day Eggs (b) Present the following data showing the interest rate of a credit card over 12 months as a line graph: Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Rate The following data shows the average temperature in successive weeks, and the corresponding figures for sales of drinks and batteries in a store. Plot the data on two scattergraphs: (a) one for temperature and drinks, and (b) one for temperature and batteries. Does there appear to be a correlation in either case? Temperature Drinks Batteries (a) In a survey of an online shop, the percentages of people rating the quality of the shopping experience in various categories were: Excellent: 26% Good: 43% Average: 12% Poor: 13% Very poor: 6% Plot this information as a bar chart and as a pie chart. (b) In an election for a class representative, the 40 votes were cast as: Alex: 3 votes Bina: 19 votes Chloe: 12 votes Darren: 6 votes. Plot this information as a bar graph and as a pie chart. Presentation of data 19
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