|How will you present your findings? Will you use tables, graphs or both? What sort of table or graph is most appropriate?|
One of the most powerful ways to communicate data is by using graphs. Data presented in a graph can be quick and easy to understand.
A graph should:
Ambiguity can be reduced by
- be simple and not too cluttered
- show data without changing the data’s meaning
- show any trend or differences in the data
- be accurate in a visual sense – for example, if one value is 15 and another 30, then 30 should be twice the size of 15
It is important that you give each graph a heading. Axes must be labelled and any scale must have equal intervals. A key should be included where it is needed to interpret the data.
- avoiding 3D representations
- avoiding broken or uneven scales
Different graphs are useful for different types of information and it is important that the right graph for the type of data is selected. See What graph or display to use when for more information.
Consider the type of data you have collected when choosing a display or graph.
|Type of data||Appropriate display or graph|
|Categorical||Bar graph, pie chart, dot plot|
|Numerical (discrete)||Bar graph, histogram, line graph, box and whisker plot, stem and leaf plot, age pyramid|
|Numerical (continuous)||Histogram, line graph, box and whisker plot, stem and leaf plot|
Bar graphs – Figure 3
A bar graph is used to represent categorical or discrete numerical data. A bar graph has a gap between each bar or set of bars and the widths of the gaps and bars are consistent. The length of the bars in a bar graph is also important: the greater the length, the greater the value. A bar graph can be either horizontal or vertical – vertical bar graphs are also known as column graphs.
Horizontal bar graphs – Figure 4
The advantage of using a horizontal bar graph over a column graph is that the category labels in a horizontal bar graph can be fully displayed making the graph easier to read.
Side by side bar or column graphs – Figure 5
Side by side bar graphs are useful to compare two or more groups for the same data.
Stacked bar or column graphs – Figure 6
Stacked or segmented bar graphs are sometimes used to display a breakdown of data for a particular group – for example, the breakdown of types of internet use by sex. They are most useful when the data is shown as a percentage value and the number of categories is very small. If there are too many categories, the frequency of the datasets can be difficult to read and compare.
Histograms – Figure 7
A histogram is similar to a column graph, however, there are no gaps between columns. Histograms are used for numerical data only. Data can be either discrete or continuous and grouped or ungrouped. A histogram should have equal width columns when possible.
Line graphs are used for numerical data. They show how one variable changes in relation to another. The independent variable is always displayed on the horizontal axis. It is important to use a consistent scale on each axis so you can get an accurate sense of the data.
Time Series – Figure 8
Time series graphs are line graphs that display a trend or a pattern in data over time. The slope can be upward or negative. Patterns can be seasonal (over a short period), or cyclic (over a longer period). Alternately, a time series can show a random variation.
To use a times series to make predictions, you can smooth fluctuations by using a suitable smoothing process such as deseasonalising the data.
Pie Charts – Figure 9
Pie charts, often called pie graphs, sector graphs or sector charts, show how much each sector contributes to the total. Pie charts are useful when there are only a few categories as more than five categories can make them difficult to read.
It is very important to label each sector with its value to make comparison easier.
Dot Charts – Figure 10
A dot chart can convey a lot of information in a simple, uncluttered way. Each dot can represent one or many.
Box and Whisker Plots – Figure 11
Box and whisker plots display 5 figure summary statistics: minimum, quartile 1, median, quartile 3 and maximum for a set of numerical data.
Box and whisker plots are useful for looking at the shape of a data set. In particular, parallel box and whisker plots are used to compare two data sets and are drawn on the same number line. To help identify possible outliers, 'fences' can be drawn at 1.5 x, the IQR above Q3 and below Q1. For more information, see summarising Data, Measures of Spread.
Stem and Leaf Plots – Figure 12
Stem and leaf plots are an efficient way of recording numerical data because numbers in the stem apply to all values in the leaves. They are also very useful to show the shape of a distribution and, since they order data, can be used to identify median and quartiles.
Back to back stem and leaf plots are used to compare the distribution of two data sets.
Age Pyramids – Figure 13
Age pyramids are used to represent a population age structure. Age pyramids are a very effective way of showing change in a country’s age structure over time or for comparing different countries. Estimates and projections of Australia's population from 1971 to 2050 are available on the ABS Animated Age Pyramid page.
Figure 3: Bar graph showing importance of conserving water.
Input from 0 (Not Important) to 999 (Very Important)
Source: 2010 C@S National summary table 28.
Figure 4: A horizontal bar graph
Figure 5: A side by side column graph
Figure 6: A stacked bar graph
Figure 7: A histogram showing data with grouped intervals
Figure 8: A time series graph
Figure 9: A pie chart
Figure 10: A dot plot with many to one correspondence
Figure 11: Parallel box and whisker plots
Figure 12: A back to back stem and leaf plot of arm span
Figure 13: An age pyramid (Source: Australian Bureau of Statistics Education Services)