Data Presentation
Introduction
Data needs to be summarised. This is so it can be made easier to understand or to see any possible patterns.
A range of diagrams can be used for data presentation for statistical information.
Data Presentation - Bar Charts and Vertical Line Charts
Bar charts are best used for categorical data and line charts are best used for discrete data. The height of the bar is used to represent frequency.
Consider the following information that looks at the pain levels during a drug trial:
A bar chart is shown below:
One thing that is straightforward about the bar chart is that it is very easy to read off the frequencies.
As mentioned, vertical line charts are best used to represent discrete data, however it is also possible to use a vertical line chart instead of a bar chart. This is sometimes a better option because quite often the width of a bar chart is misunderstood to represent a range of possible values whereas in fact it only represents just one discrete value.
There are many different ways of drawing bar charts and they can be horizontal as well as vertical. Bar charts can also be subdivided also known as a compound bar chart.
Consider the data below which shows the pain levels during a drug trial using a pain killer and a placebo drug which has no actual active ingredients:
A compound bar chart is shown below:
Consider the frequency table below which shows the results for a six sided dice being thrown:
Below is a vertical line chart which shows that the scores are discrete and that there can be no other values such as 3.2, 3.5, etc.
Data Presentation - Pie Charts
Pie charts can be used to show categorical data or can also be used to show discrete or grouped continuous data.
One advantage of using par charts is that the data is automatically scaled to fractions of 360° and this can be very useful when wishing to compare two sets of data.
Consider the data below which shows the pain levels during a drug trial using a pain killer and a placebo drug which has no actual active ingredients:
From these two pie charts you could argue that the actual pain killer provides better results.
Data Presentation – Histograms
A histogram is used to illustrate continuous data. The bars of a histogram may have different widths and the area of each column is proportional to the frequency.
Unlike a bar chart there are no gaps between columns because where one class ends another begins.
The vertical axis is labelled the frequency density which is calculated as:
\frac{\text { frequency of class width }}{\text { width of class interval }}Example
Draw a histogram to illustrate the following data:
Solution
The frequency density has been calculated as shown below:
It is now possible to draw the histogram as shown:
At A Level, it is very unlikely that you will be asked to draw anything such as a histogram. What is required at A Level is interpretation and analysis of data and determining values such as median and standard deviation.
However, having said this, you should still be aware of the construction of a histogram, or box plat or drawing a cumulative frequency for instance.
If needed, you can always revisit these questions from your GCSE notes or view some of the GCSE articles on this website to help you recap these topics.
We will be posting other blog articles on data very soon, but remember, that most of the calculations that you are required to perform can be performed on your calculator. Make sure that you have a calculator that can be used for A Level Maths especially one that has all the required statistical features that you need.