2.4 Formatting bar charts
The bar chart is one of the most familiar and intuitive ways of representing data graphically. Nonetheless, pupils often make mistakes when drawing bar charts, giving rise to learning opportunities.
Activity 5
A young pupil has counted the number of times different letters appear in the word ‘STATISTICS’. They have gone on to draw this diagram.
How many errors or opportunities for improvement can you see? Write them down. Which are the most important? Perhaps you would like to draw your own bar chart for this data and compare it to the pupil’s version.
Comment
There are multiple presentation issues here, most of which would be easy to fix:
- the pupil has not used a ruler
- the axis values are not evenly spaced
- the bars have different widths
- the bars should be separated by gaps
- there is no title or axis labels to explain what the chart represents
Bar charts should almost always be drawn with gaps between the bars, because of the type of data involved. In Activity 5, the contextual data are the letters in the word ‘statistics’ and the number of times each letter appears is the frequency. It is the data type of the contextual data (in this case, the letters) which determines if a bar chart is an appropriate way of representing the results. The letter data is categorical data, which means it can take a fixed number of distinct values: the letters of the alphabet. The gaps between the bars reflect the clear-cut (separable) nature of the categories.
Bar charts should almost always be drawn with gaps between the bars, because of the type of data involved. In Activity 5, the contextual data are the letters in the word ‘statistics’ and the number of times each letter appears is the frequency. It is the data type of the contextual data (in this case, the letters) which determines if a bar chart is an appropriate way of representing the results. The letter data is categorical data, which means it can take a fixed number of distinct values: the letters of the alphabet. The gaps between the bars reflect the clear-cut (separable) nature of the categories.
There are typically two types of categorical data:
- Nominal data - categories are named to give them some meaning such as breed of dog or hair colour or political party. ‘Nominal’ means to give something a name.
- Ordinal data - data are on an ordered scale in which the ordering has some meaning such as the ordering of clothes sizes (S, M, L,…) or a ‘Likert’ scale used to assess attitudes e.g. strongly disagree, disagree, neither agree nor disagree, agree, strongly agree.
Activity 6
Based on what you learnt from the discussion in Activity 5, draw your own bar chart to represent the number of times (frequency) each letter appears in the word ‘STATISTICS’.
You may find it helpful to organise your data in a frequency table like the one below before drawing.
Comment
The completed frequency table should look like this:
Here is one way in which the data could be presented in a bar chart:
Include animation linked to picture below Wk4_Act_6_Animation.mp4 https://openuniv.sharepoint.com/:v:/r/sites/TeachingstatisticsBOC/Shared Documents/General/Supporting Files/Wk4_Act_6_Animation.mp4?csf=1&web=1&e=NPRg17&nav=eyJyZWZlcnJhbEluZm8iOnsicmVmZXJyYWxBcHAiOiJTdHJlYW1XZWJBcHAiLCJyZWZlcnJhbFZpZXciOiJTaGFyZURpYWxvZy1MaW5rIiwicmVmZXJyYWxBcHBQbGF0Zm9ybSI6IldlYiIsInJlZmVycmFsTW9kZSI6InZpZXcifX0%3DWhilst looking at the number of times a letter occurs in a word may seem like a trivial exercise, this is a method used in cryptography, the art of writing or solving codes. Frequency analysis looks at how often certain letters or symbols appear in a code and compares those that are most frequent with the most used letters in a language, such as English, to try and ‘break’ the code. See the link to the fun code breaker activity in the further reading section.