2.5 Vertical or horizontal bar charts?
As humans we are familiar and comfortable with ‘upright’ shapes which have their base on a level horizontal ‘floor’, bar charts are no different. We naturally want them to be vertical i.e. with upright bars as shown in Activity 6.
Piaget, a Swiss educational psychologist who studied children’s cognitive development in the mid-twentieth century, noted the most natural frame of reference is to use the vertical and horizontal axes as they are derived from the physical world (Piaget and Inhelder, 1956).
Here is the same bar chart from Activity 6 shown in a horizontal perspective.
The same ‘rules’ apply regarding good presentation:
- Values on the axes are evenly spaced and clearly labelled, including a title showing what information each axis represents, with units of measure if applicable.
- For categorical data, the bars are the same width and separated with gaps (which, again, should be the same width as one another); the length of the bars represents the frequency of occurrences.
- The chart has a title describing what it shows and, if the data has not been collected first-hand (primary data), there is a data source referenced (secondary data).
These aren’t just rules for aesthetic or traditional reasons. Accurate and helpful labelling and regular spacing enable comparison and analysis (remember presentation of data is part of the ‘analyse’ in the PCAI cycle).
Activity 7
Here are some Census 2021 data about the levels of educational qualification of residents aged 16 and over in Milton Keynes.
The ‘highest level of qualification’ is the contextual data to be presented. Imagine you are going to plot a bar chart to show pictorially how many people over the age of 16 in Milton Keynes in 2021 had each level of qualification; is there anything you would need to think about differently in presenting this data compared to the previous bar charts we have looked at?
in presenting this data compared to the previous bar charts we have looked at? Write down your thoughts.
Note: There are considerations about the different levels of qualification that should be discussed when working with this dataset. For instance, qualifications gained by those who studied overseas may be different to those listed in the census questionnaire and therefore some form of conversion of attainment level will have been made. Discussing statistics is the focus of Week 7.
Comment
The data in which we are interested is again categorical data – the level of qualification – so these would need to be spaced along one axis with gaps in between.
The main point of note is the high frequencies and how best to represent these on the frequency axis. You may decide to round the frequencies to the nearest 100, say, for ease of plotting. Here we have not done this, we have used a spreadsheet graphing function to produce the chart using the exact data. However, despite using the exact figures, only a certain level of accuracy can be read from the graph so rounding may happen at a later stage.
Notice on the frequency scale in the chart below, rather than write the frequency labels in full i.e. 10000, 20000 etc, we have added ‘in 1000s’ in the axis title. This is commonly missed by students when interpreting data in charts such as this. The numbers in units of 1000s make it easier to read and compare the values.
Here is one way in which the data could be presented in a bar chart:
This bar chart could have been produced ‘by hand’. Teachers should not avoid using real data in the classroom just because the numbers are not nice. From a learning point of view, using meaningful data is helpful.
Using computers to produce graphs is a nice way to explore different aspects of the data. Format and labelling can be quickly changed without the need to repeatedly redraw the chart. For instance, after starting with a vertical bar chart to represent the data in the activity above, we quickly moved to a horizontal option for ease of reading the important data labels i.e. the level of qualification. Below is an idea for a computer activity.
Classroom task
Provide learners each with a pre-prepared data set; perhaps 5 different datasets in a class of 30 pupils so half a dozen learners work independently on each set of data. Ask individuals to use a spreadsheet program, or similar, to present the data graphically in a format that they feel best demonstrates the data. They need to be able to give reasons for the choices made in their design. Once completed, pair the pupils or put them in threes so that pupils given the same dataset work together to discuss the choices they made in producing their own graphs. Each group can then present back to the class which format(s) and choices they think work best and why. If there are two groups presenting the same data but in a different way, this can lead to a useful class discussion about whether one pictorial representation is more appropriate than the other.
Giving learners freedom to explore and present data as they wish supports them in finding representations that are, and are not, appropriate through making their own decisions. It helps with creativity and understanding. However, if tasks are too free, or too open-ended, it can be difficult for learners to produce something which is meaningful. By incorporating well-considered constraints into a problem, the task can be simplified. For instance, in the task above, a constraint could be that students are given three graph types from which to choose; this could remove or reduce the need for them to be familiar with which graphs are appropriate for which type of data.
The ideas of ‘freedom and constraint’ are important considerations in mathematics education. More typically used to explore generalities in the context of algebra or geometry for instance, the idea can be applied to statistics in helping see the bigger picture in which a dataset sits or narrowing down the field of data variables to ensure data collection is manageable and data is relevant.