Module 4 Lesson: Centre, Spread, and Distribution Shape
Classroom Explanation
The mean and the median answer the same question by different routes: the mean uses every value's size, the median only its rank. When they agree the distribution is fairly symmetric. When they disagree, the disagreement is itself the finding.
In this module, the goal is to describe numeric data with centre, spread, shape, and outlier caution. The important part is not only the calculation. The important part is the thinking before and after the calculation.
Why This Matters
The common mistake is reporting only the mean and hiding the outlier. That can make normal deliveries look slower than they usually are. This mistake can make a report sound more confident than the evidence deserves.
Key Ideas
1. The mean uses every value and is sensitive to outliers.
The mean is pulled by every observation. That is useful when all values are part of the story, but risky when one extreme value dominates the result.
2. The median is the middle value and is often safer for skewed data.
The median is the middle of the ordered values. It often describes a typical case better when the data is skewed or has outliers.
3. Spread and shape tell whether the centre is enough to understand the data.
Two groups can have the same centre but very different spreads. Shape tells whether the data is clustered, skewed, flat, or broken into separate groups.
Worked Example
South-zone delivery times include one very late order of 118 minutes. The mean is pulled upward, while the median better describes a typical South-zone order.
Here is the dataset used in this module.
| order_id | city_zone | delivery_minutes |
|---|---|---|
| D01 | North | 28 |
| D02 | North | 32 |
| D03 | North | 30 |
| D04 | North | 35 |
| D05 | North | 29 |
| D06 | North | 31 |
Look at the values before summarising them. A single extreme observation moves the mean a long way and the median hardly at all, so the gap between the two tells you something is pulling one tail — and that something usually deserves investigating rather than averaging away.
How To Think Through It
- Compute the mean and the median.
- Note the size of any gap between them.
- Find the values responsible.
- Decide whether to investigate, keep or exclude them, and say why.
- Report a centre and a spread together.
Common Mistake
The common mistake is reporting only the mean and hiding the outlier. That can make normal deliveries look slower than they usually are.
How To Write The Result
The South-zone median is more useful for a typical order, but the very late order still matters as a service-risk signal.
Practice Prompt
Compare mean and median for the South zone and explain why they differ.
Takeaway
Report the mean and the median where they disagree; the gap is information, not an inconvenience.