This page is an overview of the section.
A frequency table counts the number of items in a population that are in different groups.
Other quantities such as money or production may be partitioned into several categories. The total of the values in the categories is meaningful in such tables.
For frequency tables and other partitions, a column of percentages is often added.
An example shows a simple table whose values are not a partition of a meaningful total.
In simple tables, the categories may be reordered, related categories can be combined and it may be informative to restrict attention to a subset of categories.
Larger published tables often consist of a set of smaller simple tables in different columns. Two examples are presented.
This page is an overview of the section.
Never use gridlines to box all values in a table. In large multi-column tables, reading across rows is easier with occasional hairlines of light shading, but otherwise consider using white space to separate associated groups of rows or columns.
Use white space to group related rows and columns. Rearranging rows or columns may bring values that should be compared closer. Summarise and interpret in the body of a report but do not simply repeat values.
The meaningful information is 'signal'. Information that does not help understanding of the data is 'noise'. Noise includes data noise and unnecessary embellishments to the table. Decreasing the significant digits displayed often decreases data noise.
Showing proportions in a multi-column table instead of frequencies makes it easier to compare groups. Ratios of variables can be easier to interpret than their raw values.
It is easier to compare values down rows than across columns. Interchanging the rows and columns of a table can make it easier to make comparisons.
Rearranging the rows (or columns) may make the information in large tables stand out better.
An example shows a published table whose presentation can be improved in many ways.
This page is an overview of the section.
The simplest graphical display of a table of values is a bar chart. The bars can be drawn either vertically or horizontally. If the values are partitions of a total, a second axis with percentages can be added.
If there is no natural ordering of the categories in a bar chart, it is often informative to arrange them in decreasing order of the values. If the values are partitions of a total, cumulative percentages can be added.
If possible, all bars should start at zero, so bar length is proportional to the values. If the axis does not include zero, this should be clearly indicated with zig-zags on the bars or axis. Negative values can be represented with bars hanging below the axis.
Three-dimensional representations of bar charts should be avoided.
It is misleading to replace simple bars with 2- or 3-dimensional objects whose height represents the values since the visual impression depends on the area or volume of the objects.
For frequency tables describing the distribution of continuous measurements, the bars of a bar chart have their heights equal to the frequencies if all classes have the same width. However this is misleading if the class widths vary and the bar heights must be defined differently.
This page is an overview of the section.
The bars in a bar chart are sometimes stacked on top of each other. An alternative display is to represent the values by segments of a circle. These displays must only be used when the values are partitions of some total.
Individual categories can be compared more easily in a bar chart. The combined contribution of the total of several categories is displayed better in a pie chart.
Three-dimensional pie charts should be avoided.
Avoid splitting a picture into segments to form a stacked bar chart. The resulting picture often misrepresents the values for the different categories.
Colour is helpful to distinguish the categories in a pie chart. If it must be printed with shades of grey, care must be taken with the labelling of the categories.
This page is an overview of the section.
Data for comparing groups are often displayed in a two-way table with either the rows or columns corresponding to the different groups.
If the values in each group are partitions of a group total such as a frequency table, a table or bar chart of percentages within the groups highlights the differences.
The bars can be clustered together by group or by category.
If there are many groups, stacking the bars often makes it easier to compare the groups.
If there are only two categories in each group, there is no need to present both proportions. A simple bar chart of one proportion is sufficient and allows the scale to be expanded if the proportion is small for all groups.
Three-dimensional versions of clustered and stacked bar charts make it harder to understand the data and can be misleading.
This page is an overview of the section.
A scatterplot displays the values of two measurements from each region or other 'individual'.
Scatterplots show whether particular values of one measurement are associated with particular values of the second measurement. The strength of the relationship is important. Crosses that do not conform to the same relationship as the rest of the data are also important.
The crosses on a scatterplot can be coloured to distinguish different groups, or differing symbols can be used.
Scatterplots are often used when the crosses correspond to different geographical regions. If these differ in size, the crosses can be replaced by circles whose area is proportional to the size -- e.g. area, population or GDP.
Economic measurements from countries often contain many small values, but a few very large values (usually corresponding to rich countries). In order to distinguish the small values (often poor countries), a nonlinear scale can be used on a scatterplot.
This page is an overview of the section.
The geographic distribution of a measurement can be displayed using different colours on a map.
The choice of colours to represent numerical measurements on a map is important. A continuous graduation involving three contrasting colours or a grouping into classes is usually best.
Shading regions on a map can only represent a single measurement. Drawing a circle on each region can represent both a 'size' measurement with the circle area and another measurement with its colour.
Maps can have other simple bar and pie charts superimposed on each region. Only simple information about each region should be displayed in this way.
In most conventional maps, the areas of the regions are proportional to their land areas. The shapes of the regions can be distorted to make their areas proportional to their populations.
It is sometimes informative to distort a map to make the areas of regions proportional to other measurements. These measurements must be partitions of a meaningful total so that the combined measurement for two regions would be their total.
This page is an overview of the section.
Changes to a single numerical measurement over time can be displayed in a scatterplot of the measurement against time with successive values joined by lines.
If the measurement is a quantity, an alternative display is a bar chart with a bar for each successive value.
If the values at each time point form a partition of some total, such as a frequency table, a series of stacked bar charts of the values or proportions provides an effective display.
Simple time series are sometimes drawn in 3 dimensions as a ribbon chart. This may look more artistic, but makes the information in the data harder to see.
When presented on a computer, simple diagrams such as pie and bar charts can be animated to show how they change over time. However when the individual diagrams are simple, it is often possible to display all data in a static diagram more effectively.
Frequency tables of numerical measurements such as ages are usually displayed in histograms. They too can be animated to show changes over time.
A particularly useful type of display to animate is a scatterplot, either of crosses or circles of varying sizes. When the crosses represent countries or regions, it is often possible to pick out ones that behave differently from the rest.
Maps can also be animated to show changes over time. The measurement of interest can be displayed with either the shading of countries on the map or of circles that are superimposed on it.
This page is an overview of the section.
Information may be published in executive reports, for archival purposes or in documents for the general public. Publication is increasingly done electronically rather than on paper. Resolution, availability of colour, production cost and ease of formatting are issues that should be considered.
Reports generally only summarise the most important features of the available data. Identifying the important features is subjective and is similar to extracting the signal from a noisy electronic communication.
Reports should contain a balance of tables, graphs and text. Annotations on graphs can highlight important features.
Several simple graphs can sometimes be linked together in a single display. They should usually be either drawn on a common time axis or a map.
Most reports only contain simple graphs such as the general-purpose ones described in this chapter. More advanced graphs are needed to effectively display some specific types of data but they are generally too complex for reports intended for the general public.
Some excellent graphics have been devised to display particular data sets. There is still scope for innovation.