Scatter Graphs

Key Facts and Exam Tips

• A scatter graph is used to explore whether two sets of numerical data are related to each other.
  
• Corresponding pairs of values are plotted as points. Examination questions usually give the pairs of values in a table and include the graph on which to plot them.
  
• Take care to read the scale on each axis accurately when plotting your points.
  
• Your points may be scattered all over the graph or they may appear to form a pattern showing a possible relationship between the values.
  
• If the points appear to cluster on or are very near to a straight line, this indicates a correlation between the two sets of data. Correlation is a measure of the strength of the association between the two variables.
  
• If the line has a positive gradient (ie it slopes upwards from left to right) then the correlation is positive. As the values in one set of data increase, the corresponding values in the other set tend to increase as well.
  
• If the line has a negative gradient (ie it slopes downwards from left to right) then the correlation is negative. As the values in one set of data increase, the corresponding values in the other set tend to decrease.
  
• If the points are scattered randomly, forming no pattern, then the correlation is zero. Another way of describing this is to say there is no linear correlation between the two sets of data.
  
• Questions often ask you to draw a line of best fit on the graph. This means that you draw in the line that your points seem to be following. Placing the line is a matter of judgement but there are some guidelines to follow:
  a) Try to get the line as close to, or through, as many points as possible (it may be that none of your points lie exactly on the line).
  b) Try to get an equal number of points on either side of your line.
  c) Ignore any extreme points that don't appear to follow the general pattern (these are called 'outliers').
  d) Don't assume that the line will go through the origin.
  
• The tendency for the data to show a linear correlation may be strong or weak. The strength of the correlation depends on how near the majority of points lie to the line of best fit.
  
• Some examination questions ask you to describe the correlation shown on a scatter graph (ie positive or negative, or none). Other questions ask you to describe the relationship between the two sets of data. This means that you have to explain what happens to one set of values as the other set increases or decreases.