C9.2 Interpreting statistical data
- Syllabus
- 0580–2028–2029
- Topic
- C9.2
- Level
- Core
Learning objectives
C9.2.1Read, interpret and draw inferences from tables and statistical• Read, interpret and draw inferences from tables and statistical diagrams.C9.2.2Compare sets of data using tables, graphs and statistical measures.• Compare sets of data using tables, graphs and statistical measures.C9.2.3Appreciate restrictions on drawing conclusions from given data• Appreciate restrictions on drawing conclusions from given data. e.g. compare averages and ranges between two data sets.
Read statistical displays and make supported inferences
Reading a statistical display means extracting what it shows accurately; drawing an inference means combining those values into a conclusion that the display actually supports.
Before reading a value, check the title, category labels, units, scale intervals and key. Locate the exact category or interval, read from the correct mark or bar, and state the unit. Then calculate any required difference, total, fraction or percentage from those values.
| Month | Rainfall (mm) | Days with rain |
|---|---|---|
| January | 40 | 8 |
| February | 65 | 6 |
| March | 50 | 10 |
The table shows February has the greatest rainfall, while March has the most rainy days. Therefore 'the month with most rainfall also has most rainy days' is false for these data. A useful inference cites the values or pattern that justify it.
Do not replace one measured variable with another: rainfall amount and number of rainy days answer different questions. An inference should say 'for these data' unless the evidence justifies a wider claim.
Compare data sets using centre and spread
A fair comparison uses the same feature, unit and statistical measure for both data sets, and comments separately on typical value and variation.
| Data set | Mean | Median | Range |
|---|---|---|---|
| A | 52 | 51 | 12 |
| B | 58 | 57 | 30 |
Set B has the higher typical value because both its mean and median are higher. Name the measure and direction: 'B has a higher median by 6' is stronger than 'B is better'.
Set A is less variable because its range is smaller: 12 compared with 30. A lower range means the observed values are packed into a narrower span, but it does not say that every A value is close to every other value.
When comparing graphs, also use like-for-like features such as the modal category, peaks, gaps or overall pattern. Two comments should describe genuinely different features rather than repeat the same comparison in new words.
Do not compare a mean from one set with a median from the other, or raw frequencies when sample sizes differ and proportions are needed. Check axes and units before comparing bar heights or plotted positions.
Judge the limits of conclusions from data
A conclusion is only as strong as the data and method behind it. Before generalising, identify what the display or statistical measure leaves uncertain.
| Restriction | Why it matters | Safer conclusion |
|---|---|---|
| small or unrepresentative sample | the sample may not reflect the population | limit the claim to the sampled group |
| extreme value | it can pull the mean away from most values | compare the median or inspect the data |
| one summary measure | different distributions can share the same average | compare centre and spread together |
| different scales, units or time periods | the visual comparison is not like-for-like | standardise before comparing |
| two variables change together | association alone does not prove cause | describe the association, not a cause |
For values 24,25,26,27,98, the mean is 40 but the median is 26. The single value 98 pulls the mean upward, so calling 40 a typical value would misrepresent most observations.
Use evidence-bounded language: the data 'show', 'suggest' or 'support' a pattern. State the group and time covered, and mention the specific restriction when it affects the conclusion.
Finding a limitation does not make the data useless; it sets the boundary of what can be claimed. Do not reject a conclusion without explaining which feature of the data weakens it.