6.17 Trend & Patterns in Experimental Data

• Graphs are used to visualise the relationship between two sets of data from two different variables
• Trends and patterns can be identified from experimental data
• Common trends are:
  • Linear
  • Directly proportional
  • Inversely proportional
  • Rate of change
• A linear graph set of data is any data that creates a straight line

An example of a linear graph

• The rate of change of a graph is how quickly a variable is increasing or decreasing with something else
  • This can be seen from the change in gradient of the graph, an increasing gradient has an increasing rate of change and a decreasing gradient has a decreasing rate of change
• A direct proportionality relationship is where as one amount increases, another amount increases at the same rate
  
  • This is represented by a straight-line graph with a positive gradient
• For two variables, y and x this looks like:

y ∝ x

• An inverse proportionality relationship is where as one amount increases, another amount decreases at the same rate
  • This is represented by a curved graph with a decreasing gradient
• For two variables, y and x this looks like:

y ∝ 

Sketched graphs show relationships between variables

• In the first sketch graph, above you can see that the relationship is a straight line going through the origin
  • This means as you double one variable the other variable also doubles so we say the independent variable is directly proportional to the dependent variable
• The second sketched graph shows a shallow curve
  • This is the characteristic shape when two variables have an inversely proportional relationship
• The third sketched graph shows a straight horizontal line,
  • This means as the independent variable (x-axis) increases the dependent variable does not change or is constant

• Stress and strain are proportional to each other, but not directly
• The graph is linear with a positive gradient up to a strain of 1.0 × 10^-3 
• After this, the rate of change of the strain with stress decreases, as the gradient of the graph decreases up to the breaking stress at 190 MPa