Once the data has been collected, it must be organised in a manner that allows for the information to be extracted most efficiently. One method of organisation is to display the data in the form of graphs. Functions and graphs have been studied in Functions and Graphs, and similar techniques will be used here. However, instead of drawing graphs from equations as was done in Functions and graphs, bar graphs, histograms and pie charts will be drawn directly from the data.
Bar and Compound Bar Graphs
A bar chart is used to present data where each observation falls into a specific category and where the categories, this is often for qualitative data. The frequencies (or percentages) are listed along the
A compound bar chart (also called component bar chart) is a variant: here the bars are cut into various components depending on what is being shown. If percentages are used for various components of a compound bar, then the total bar height must be 100%. The compound bar chart is a little more complex but if this method is used sensibly, a lot of information can be quickly shown in an attractive fashion.
Examples of a bar and a compound bar graph, for Data Set 1 , are shown in Figure 1. According to the frequency table for Data Set 1, the coin landed heads-up 44 times and tails-up 56 times.
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Histograms and Frequency Polygons
It is often useful to look at the frequency with which certain values fall in pre-set groups or classes of specified sizes. The choice of the groups should be such that they help highlight features in the data. If these grouped values are plotted in a manner similar to a bar graph, then the resulting graph is known as a histogram. Examples of histograms are shown in Figure 2 for Data Set 2, with group sizes of 1 and 2.
| Groups | ||||||
| Frequency | 30 | 32 | 35 | 34 | 37 | 32 |
| Groups | |||
| Frequency | 62 | 69 | 69 |
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The same data used to plot a histogram are used to plot a frequency polygon, except the pair of data values are plotted as a point and the points are joined with straight lines. The frequency polygons for the histograms in Figure 2 are shown in Figure 3.
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Unlike histograms, many frequency polygons can be plotted together to compare several frequency distributions, provided that the data has been grouped in the same way and provide a clear way to compare multiple datasets.
Pie Charts
A pie chart is a graph that is used to show what categories make up a specific section of the data, and what the contribution each category makes to the entire set of data. A pie chart is based on a circle, and each category is represented as a wedge of the circle or alternatively as a slice of the pie. The area of each wedge is proportional to the ratio of that specific category to the total number of data values in the data set. The wedges are usually shown in different colours to make the distinction between the different categories easier.
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Method: Drawing a pie-chart
- Draw a circle that represents the entire data set.
- Calculate what proportion of 360(1)
- Draw a wedge corresponding to the angular contribution.
- Check that the total degrees for the different wedges adds up to close to
Exercise 1: Pie Chart
Draw a pie chart for Data Set 2, showing the relative proportions of each data value to the total.
Solution
- Step 1. Determine the frequency table for Data Set 2. :
Table 3 Total Data Value 1 2 3 4 5 6 – Frequency 30 32 35 34 37 32 200 - Step 2. Calculate the angular size of the wedge for each data value :
Table 4 Data Value Angular Size of Wedge 1 2 3 4 5 6 - Step 3. Draw the pie, with the size of each wedge as calculated above. :
Figure 5 
Note that the total angular size of the wedges may not add up to exactly 360
Line and Broken Line Graphs
All graphs that have been studied until this point (bar, compound bar, histogram, frequency polygon and pie) are drawn from grouped data. The graphs that will be studied in this section are drawn from the ungrouped or raw data.
Line and broken line graphs are plots of a dependent variable as a function of an independent variable, e.g. the average global temperature as a function of time, or the average rainfall in a country as a function of season.
Usually a line graph is plotted after a table has been provided showing the relationship between the two variables in the form of pairs. Just as in (x,y) graphs, each of the pairs results in a specific point on the graph, and being a line graph these points are connected to one another by a line.
Many other line graphs exist; they all connect the points by lines, not necessarily straight lines. Sometimes polynomials, for example, are used to describe approximately the basic relationship between the given pairs of variables, and between these points.
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Exercise 2: Line Graphs
Clawde the cat is overweight and her owners have decided to put her on a restricted eating plan. Her mass is measured once a month and is tabulated below. Draw a line graph of the data to determine whether the restricted eating plan is working.
| Month | Mass (kg) |
| March | 4,53 |
| April | 4,56 |
| May | 4,51 |
| June | 4,41 |
| July | 4,41 |
| August | 4,36 |
| September | 4,43 |
| October | 4,37 |
Solution
- Step 1. Determine what is required :
We are required to plot a line graph to determine whether the restricted eating plan is helping Clawde the cat lose weight. We are given all the information that we need to plot the graph.
- Step 2. Plot the graph :
Figure 7 
- Step 3. Analyse Graph :
There is a slight decrease of mass from March to October, so the restricted eating plan is working, but very slowly.
Exercises - Graphical Representation of Data
- Represent the following information on a pie chart.
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Table 6 Walk 15 Cycle 24 Train 18 Bus 8 Car 35 Total 100 - Represent the following information using a broken line graph.
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Table 7 Time 07h00 08h00 09h00 10h00 11h00 12h00 Temp ( 16 16,5 17 19 20 24 - Represent the following information on a histogram. Using a coloured pen, draw a frequency polygon on this histogram.
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Table 8 Time in seconds Frequency 16 - 25 5 26 - 35 10 36 - 45 26 46 - 55 30 56 - 65 15 66 - 75 12 76 - 85 10 - The maths marks of a class of 30 learners are given below, represent this information using a suitable graph.
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Table 9 82 75 66 54 79 78 29 55 68 91 43 48 90 61 45 60 82 63 72 53 51 32 62 42 49 62 81 49 61 60 - Use a compound bar graph to illustrate the following information
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Table 10 Year 2003 2004 2005 2006 2007 Girls 18 15 13 12 15 Boys 15 11 18 16 10
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