Discussing results - WJECDrawing inferences and conclusions

Graphical representations of data are common in today’s society. Understanding and interpreting graphs correctly is a vitally important skill useful in different walks of life.

Part ofMaths Numeracy (WJEC)Statistics

Drawing inferences and conclusions

Scientists often use graphs to represent a relationship between two variables. Generally, if there is a correlation between two variables, then they are usually related in some way.

In an exam, you will be required to describe and explain graphs.

Example

A graph showing how the average adult body mass index (BMI) among Americans is increasing over time

A BMI of 18-25 is considered healthy while a of greater than 25 means the individual is overweight. The above graph shows how the average BMI among Americans is changing with time. Describe and explain the trend from the graph.

Solution

Firstly we describe the graph:

  1. There is a positive correlation – the graph starts low on the left and ends high on the right
  2. Since 1980 the gradient or rate of change has increased

Then we try to explain what our descriptions mean:

  1. Because there is a positive correlation this shows that BMI is increasing over time. The fact that there is a correlation means that the two variables are likely linked. An explanation for this would be that people have become less active and that their attitudes to food have gotten worse as time has gone on.
  2. The increasing rate of change means that the problem is getting worse.

Just because there is correlation does not mean that there is causation. In other words, just because a graph has a correlation, it does not mean that the two variables are directly linked.

Look at this graph. It clearly shows that as organic food sales have increased so have instances of autism. The graph is suggesting that organic food is causing autism. However, the correlation does not provide any evidence for this; it only shows that the number of cases of autism is increasing over the measured period as well as sales of organic food.

A graph showing how as sales of organic food have increased so has the number of individuals diagnosed with autism

Question

Tom thinks that this graph proves that ice cream causes shark attacks. He is wrong.

Explain why there is a correlation between the two variables.

A graph showing the correlation between ice cream sales and the number of shark attacks.