Drawing Inferences and Conclusions from Data
After data has been collected, summarised and represented, the final step is to draw inferences and conclusions. This involves explaining what the data shows, what it suggests about the situation and how it answers the original problem.
What an Inference Is
An inference is a reasoned statement based on evidence from the data.
Inferences go beyond simply stating values. They explain what the results suggest or indicate.
For example, if one group has a higher median than another, you may infer that typical values for that group are higher.
Inferences must always be supported by the data.
An inference is not a guess
Using Summary Measures
Summary measures include:
• measures of central tendency such as the mean, median or mode
• measures of spread such as the range or interquartile range
When drawing conclusions from summary measures:
• compare values clearly
• state which is higher or lower
• explain what this means in context
For example, a higher median may suggest better typical performance, while a larger interquartile range may suggest greater variation.
Using Data Representations
Graphs and diagrams help reveal patterns that support conclusions.
When using data representations:
• refer to features such as trends, clusters or spread
• use correct statistical terms
• describe what the diagram shows, not what you expect
For example, a box and whisker diagram can be used to compare typical values and variability between groups.
Scatter diagrams may suggest a relationship between variables, but not cause and effect.
Relating Results to the Original Problem
Conclusions must always be linked back to the original question or problem.
A good conclusion:
• directly answers the question asked
• uses evidence from the data
• refers to summary measures or graphs
• stays within the limits of the data
Avoid introducing new ideas that are not supported by the data collected.
The conclusion should match the question
Considering Reliability and Limitations
When drawing conclusions, it is important to consider:
• sample size
• possible bias
• anomalies
• whether results are estimates
Limitations should be acknowledged to avoid over generalising.
For example, results from a small or biased sample may not represent the whole population.
Drawing Balanced Conclusions
Strong conclusions:
• describe what the data shows
• include supporting evidence
• acknowledge limitations
• avoid overstatement
Weak conclusions:
• ignore spread or anomalies
• claim cause and effect without evidence
• do not link back to the problem
Balance and clarity are essential.
Key Points to Remember
Inferences are based on evidence from data.
Summary measures help describe typical values and spread.
Data representations reveal patterns and trends.
Conclusions must relate directly to the original problem.
Limitations should always be considered.
Drawing clear inferences and well supported conclusions ensures that data analysis answers the original question accurately and responsibly.