E9.2 Interpreting statistical data
- Syllabus
- 0580–2028–2029
- Topic
- E9.2
- Level
- Extended
Learning objectives
E9.2.1Read, interpret and draw inferences from tables and statistical• Read, interpret and draw inferences from tables and statistical diagrams.E9.2.2Compare sets of data using tables, graphs and statistical measures.• Compare sets of data using tables, graphs and statistical measures.E9.2.3Appreciate restrictions on drawing conclusions from given data• Appreciate restrictions on drawing conclusions from given data. e.g. compare averages and measures of spread between two data sets.
Read statistical displays and make supported inferences
Reading a statistical display means extracting values accurately; an inference combines those values into a conclusion that the display supports.
Check the title, variables, units, axis intervals and key before reading. Locate the relevant value, quartile, interval or category, then calculate any required total, difference, fraction, percentage or estimate. State the unit and show which values support the conclusion.
| Group | Lower quartile | Median | Upper quartile | Number in group |
|---|---|---|---|---|
| A | 145 | 162 | 178 | 136 |
| B | 138 | 154 | 170 | 144 |
For Group A, half the values are above the median 162. Therefore an estimate of the number above 162 is 0.5×136=68. This is an estimate because a box plot summarises positions rather than listing every value.
Do not infer about a different variable or a wider population than the display describes. An evidence-backed statement names the statistic or pattern used and is qualified as an estimate when the diagram cannot give an exact count.
Compare data sets using centre and spread
A complete comparison describes both a typical value and the variation, using the same statistical measures and units for both data sets.
| Data set | Median | Interquartile range | Range |
|---|---|---|---|
| P | 56 | 18 | 42 |
| Q | 49 | 35 | 61 |
Set P has the higher typical value because its median is 56, compared with 49 for Q. Name the statistic and direction; 'P is better' is not a statistical comparison.
Set P is more consistent because its interquartile range is smaller: 18 compared with 35. The IQR compares the spread of the middle half; the range compares the full span and is more affected by extreme values.
Make like-for-like comparisons: mean with mean, median with median, and the same measure of spread for both groups. Two useful comments usually address different features—one centre and one spread—not the same feature twice.
Judge the limits of conclusions from data
A statistical conclusion is limited by the data collected and by what its summary measures leave hidden.
| Restriction | Why it matters | Safer response |
|---|---|---|
| small or unrepresentative sample | it may not reflect the intended population | limit the claim to the sampled group |
| extreme value | it can pull the mean and enlarge the range | inspect the data and compare median or IQR |
| one average or spread measure | different distributions can share the same summary | compare centre and spread together |
| different units, scales or time periods | the comparison is not like-for-like | standardise before comparing |
| association between variables | another factor may explain the pattern | describe association, not cause |
For 24,25,26,27,98, the mean is 40 but the median is 26. The single extreme value makes the mean look much larger than most observations, so the median better represents the centre of this set.
A lower median but larger IQR means one group is typically lower yet more variable; neither statement cancels the other. Conclusions should identify the exact statistic and avoid turning a summary comparison into a claim about every individual.
A limitation does not make data useless. It defines what can be claimed safely: state the group and period covered, the measures compared and the specific uncertainty that remains.