Two samples of delivery times are summarised below.
| Sample | Size | Median (minutes) | Interquartile range (minutes) | Mean (minutes) | Standard deviation (minutes) |
|---|---|---|---|---|---|
| A | 40 | 28 | 6 | 31.4 | 12.8 |
| B | 60 | 30 | 10 | 30.8 | 7.2 |
In this question you must show detailed reasoning.
Compare the location and spread of the two samples.
Suggest what the differences between the mean and median indicate about Sample A.
Explain why the summaries are not enough to decide whether either sample contains an outlier under the 1.5×IQR1.5\times\mathrm{IQR}1.5×IQR rule.