Click on the headings below to browse through the Graphs chapter:

Graph types and their uses
Scattergrams
Line graphs
Area graphs
Bar graphs
Histograms
Population pyramids
Pictographs
Pie graphs
Double-axis graphs
Essential graph features
Scale
Symbols
Labelling
Units of measurement
Gridlines
Presenting multiple variables
Statistical analyses
Error bars
Using multiple graphs for data comparison

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### Graph types and their uses

##### Scattergrams
Scattergrams are plots of data points that are used to show the correlation between variables (see Figure 1 for an example). Statistical analyses are commonly used to draw a line of best fit through the points to indicate the direction and strength of the correlation. Scattergrams are commonly used to display the results of a scientific experiment.

Figure 1. Breaking distances for vehicles travelling at 80km/h (Author date[1])

##### Line graphs
Line graphs represent the change in variable Y (vertical axis) as a function of the continuous variable X (horizontal axis). Line graphs are often used to show how a variable has changed over time. More than one data class can be represented on the Y axis (example given in Figure 2).

Figure 2. Population growth within continents over the next 40 years (PRB 2009)
##### Area graphs
Area graphs are similar to line graphs in that they show the distribution of continuous (non-discrete) data. However, the area beneath each line is shaded (using different colours) to emphasise the difference between data classes (Figure 3). Area graphs can be useful to show how cumulative totals change over time.

Figure 3. Changes in heavy metal contamination in Brisbane’s drinking water since the addition of the DSGT treatment plants (Author date)

##### Bar graphs
Bar graphs present the relationship(s) between two or more non-continuous variables, whereby the strength of the relationship is proportional to the length of the bars (Figure 4). The bars can either be placed vertically or horizontally, and can show negative values. Bar graphs are useful for comparing multiple variables.

Figure 4. 2008 Populations in Australian States and State Capitals (NSW Government 2008)
##### Histograms
Histograms are a special type of bar graph used to present the frequency distribution of univariate data sets (Figure 5). They plot either continuous data or groups of numerical data. Histograms visually reveal the distribution the centre, spread, skewness, and the presence of outliers and multiple nodes in the data.

Figure 5. Grades achieved by GEOM1000 students, semester 1 2009, St. Lucia, UQ (Author date)

##### Population pyramids
Population pyramids are used to show the distribution of a certain population (e.g. regional, national) in terms of age and sex (Figure 6). There are a few conventions to follow when creating population pyramids:
• Males are shown on the left and females on the right, and are labelled as such
• Age groups are given in 5 year intervals
• Populations can either be presented as absolute values or percentages. If you are using percentages, they must reflect the total population (not the population within each sex).
• The same scale must be used to represent male and female populations
• Gridlines should be used for the X-axis so that the reader can estimate population values

Figure 6. ERP and Composite Estimate of Indigenous Australians in the Peninsula ATSIC region, 1996 (Taylor and Bell 2002)

##### Pictographs
Pictographs use symbols and images to represent the value of data (Figure 7). Although pictographs are able to convey the relative size of data sets, they are limited in that they make it difficult to determine the absolute value of data. For this reason, it is recommended that you do not use pictographs if you anticipate that the reader would be interested in absolute data values.

Figure 7. Membership numbers for after-school clubs (Harcourt School Publishers n.d.)
##### Pie graphs
Pie graphs are used to visualise the way in which an entity is divided up into smaller parts (Figure 8). While pie graphs may be useful in certain circumstances, it is generally recommended that they be avoided if you are presenting a large number of variables. If you do choose to use a pie graph, you should abide by the following conventions:
• Structure pie graphs so that the largest segment begins at 12 o’clock, with the remaining segments running clockwise in decreasing order.
• Label each segment of the pie with either the total value or percentage. If you label with percentages, be sure to provide the total value somewhere in the graph so that the reader can convert the percentages (should they wish to).
• Use different shading or patters for each pie segment, as this will create contrast and improve readability.

Figure 8. Sales at The Fruit Market, Brisbane 2009 (total sales = \$450 000) (Author date)

##### Double-axis graphs
Double-axis graphs are used to present three or more variables on a single graph. They achieve this by having two or more Y axes. Double-axis graphs are useful for comparing interrelated variables. For example, Figure 9 simultaneously presents the historic temperature and atmospheric CO2 records of Earth over the past 800,000 years .

Figure 9. Earth’s climate history as reconstructed from Antarctic Ice Cores (McInnes 2009)

### Essential graph features

In order to effectively present and communicate data, graphs must have a:
• Title- Graphs have succinct yet comprehensive titles that inform the reader about their content. Graph titles are placed beneath the graphic as a caption (so if your computer program automatically places a title at the top of a graph, you must drag it to the bottom). The title should not simply repeat the axes labels, or contain the words “Graph of” or “Plot of”.
• Axis labels- Both the x (horizontal) and y (vertical) axes must have a label to indicate which variable they represent, and if necessary the unit of measurement into which the variables are divided. Origins should always be labelled on graphs (unless a logarithmic scale has been used, as the log of zero is not defined).
• Tick marks-Tick marks are used to indicate the scale of the graph. Major tick marks are labelled with a number, symbol or word, depending on the type of data being presented.Minor tick marks are placed within the major tick marks and are not labelled. They are designed to help the reader estimate detailed values off a graph (should they wish to).
• Source- Reference the source of your graph in the style consistent with the textual component your report. The reference should either be placed in the title or beneath the title in a source line.
• Legend (if presenting multiple variables)- Legends are used to indicate the meaning of the shading and/or symbology used in a graph. They should be enclosed by a border, given a title and placed to the right of the graph, below the graph, or if small enough they can sit within the plot area.

When you are creating a digital graph, your computer program will automatically set it to a default size, scale and appearance. However, the default settings are rarely (if ever) the most suitable way in which to present your graph as it will not have taken into account the content and context of your data. Customise your graph by adjusting the shading, scale, symbology and labelling to suit the type of data being presented and the style of your paper:
• Graphs should be shaded using subtle colours and hatching.
• The type of shading used in a given graph should be chosen to suit the data it contains, and the style of your paper.
• Bear in mind that the rule of thumb is to present graphics using the least amount of ink necessary.
##### Scale
• Graph scales should be chosen to suit the range of data values so that the data fills up as much space of the graph as possible.
• When the range of data in your graph is very large, it is best to use a logarithmic scale in the relevant axis (or axes).
• If you are beginning an axis with numerical markings on a point other than zero, you should indicate this clearly in the graph label.
##### Symbols
• Symbols should be used to represent different variables in graphs.
• Symbols need to be large enough to be legible, and able to be easily distinguished from one another.
• Bear in mind that certain symbols have inherent meaning, as do certain colours.
##### Labelling
• Labels should all be placed in the same orientation so that the reader does not have to turn the page.
• Make sure your labels are sufficiently large so that they are legible.
• Use visual hierarchy to indicate levels of significance (e.g. use bold, italics, and larger font size to make the most important labels stand out).

##### Units of measurement
• To save time and space, the units of measurement used on your graph axes are indicated in the axes labels and enclosed in brackets.
##### Gridlines
• Gridlines are lines that extend from your tick marks across the length of your graph.
• It may be useful to include gridlines when you have a large or wide-ranging graph, and you anticipate that readers may have trouble reading values off the graph.
• Gridlines run behind the plotted data so that they do not obscure the graph, and are weighted finely.
##### Presenting multiple variables
• When presenting multiple variables, you need to use shading and symbols to represent different data classes.
• Use a legend to indicate the meaning of the shading and/or symbology used in the graph.
• It is recommended that no more than 4 data classes be presented in a single graph, as any more than this becomes confusing.
##### Statistical analysis
• If you have used statistical analysis in your graph, you should present all relevant equations and values either in the plot-area of the graph (providing there is sufficient space) or beneath the graph as notes.
• If you have used computer software to perform your statistical analysis, you will need to reference this.
##### Error bars
• If you are presenting means (averages) of a variable in your graph, you should always include error bars to indicate the associated uncertainty of each mean.
• Note that the value of error bars is rarely the same for each mean. If your computer program automatically generates error bars of equal value it is likely they are incorrect.
##### Using multiple graphs for data comparison
Graphs are excellent tools for comparing related data sets. However, there are a few things you need to consider when presenting multiple graphs for comparison:
• each graph must be presented at the same size and scale so that the reader can make direct visual comparisons;
• the graphs needs to appear on the same page if they are to be easily compared; and
• human eyes find it much easier to compare lengths than areas, thus it is recommended that you do not use do not use series of pie graphs, area graphs or stacked bar graphs to compare data sets.