Tutor’s Toolkit: Application of Number

Interpreting Results and Presenting Findings

P2	Construct and use graphs, charts and diagrams and
follow accepted conventions for labelling these

Useful Web Links:

BBC Bitesize Revision: Drawing pie charts and frequency diagrams
http://www.bbc.co.uk/schools/gcsebitesize/maths/datahandlingih/piechartsi_rev3.shtml

P2.1	Graph and chart conventions

Scope: 

Students need to be able to:
•	understand titles [NOE],
•	label axes for discrete and continuous data [NOE],
•	understand how graphs and charts can be misleading.

What students need to know:

Titles

There are various conventions for a properly drawn graph. Make sure you include these features:

Put a title

Arrow

Label the axis and put the units

Make one smooth line

Label and units

Arrow

Arrow

Label and units

Labelling axes for discrete and continuous data
When you draw a bar chart it is important to decide if the you are using discrete or continuous data. 

Discrete data describes the situation when each category is separate from the others. Examples would be colours, chocolate bars or even number data such as shoe sizes or bus numbers. The important thing is that numbers in between have no meaning – you can have shoe size 6½ but you cannot have size 6¼!

Continuous data describes the situation when you are using a quantity where the gaps in between always mean something. Normally, anything that you measure is continuous, like time, or height

With discrete data it is common to put a small gap between the bars. The labels for the bars go in the middle, underneath the bar.

With continuous data, you must not leave a gap. The labels go under the tick marks at the beginning and end of the bars. 

How graphs and charts can be misleading
Advertisers want to make a product look good. Sometimes they bend the good graph rules a bit to make their product look better than it should. Here are examples of the tricks they use:

Wizzo looks like it got better ratings than Superbright because its pie chart is larger. However, in a pie chart, it is only the angle for each slice that matters. Wizzo’s ratings are actually slightly worse! 
Good practice: if you compare two pie charts, make them the same size.

It looks like the share value for Wizzo PLC is shooting up. However the increase is very small. Normally, the vertical scale should start at 0 and go up in equal intervals.
Good practice: It is sometimes OK to have a vertical scale that doesn’t start at 0, but you should show it with a little break before the first number mark.

Another way of cheating with a bar chart is to inflate the size of one of the bars. It looks as if the fourth quarter was much more significant than the others. There are no justifications for this!
Good practice: Make the bars the same width if the categories are the same size.

P2.2	Draw statistical charts

Scope: 

Students need to be able to:
•	draw bar charts and column graphs [NOE], 
(Have a look at Interpreting Information, Section I2 and Interpreting Results and Presenting Findings. Section P2.1 for guidance on this)
•	understand how graphs and charts can be misleading.

What students need to know:

Calculate the slice angles in a pie chart
To draw a pie chart, you must calculate the size of the slice for each category. The chart itself can be any convenient size. A good trick is to draw around the outside of a circular (360) protractor. You can then start at 0 and mark each slice of as you go round the scale. If you get back to 0 with the last slice, then it must be correct!

The idea is that we work out the fraction of a circle each slice needs (divide the quantity for the slice by the total quantity), then multiply by 360 to get the angle.

Example:
A company is preparing a chart to show how many employees they have in different categories. The data is as follows:

Management	
12	

Clerical	
11	

Sales	
4	

Ancillary	
1	

Add up the total number of people. 2 + 11 + 4 + 1 = 18.

Note: it is very common for the total to be an easy factor or multiple of 360. This makes the calculations possible without a calculator (i.e. possible in the exam). In this case, we need to divide each number by 18, then multiply by 360. Since 360  18 = 20, the calculation has the same affect as multiplying each number by 20.

Make a new column for the angle:

	
Angle	

Management	
12	
2  18  360 = 40	

Clerical	
11	
11  18  360 = 220	

Sales	
4	
4  18  360 = 80	

Ancillary	
1	
1  18  360 = 20	

Check	
40 + 220 + 80 + 20 = 360