Module 4 Lesson: Centre, Spread, and Distribution Shape
Classroom Explanation
Imagine we are in class and someone puts a small table on the board. The table looks simple, so it is tempting to jump straight to the answer. In statistics, we slow down first. We ask what question the table can answer, what question it cannot answer, and what kind of claim would be safe.
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 |
Read the table slowly. First name the unit. Then name the variables. Then name the comparison or pattern. Only after that should you write the conclusion.
How To Think Through It
- State the question in one sentence.
- Name the unit of analysis.
- Identify the outcome and comparison.
- Check the denominator, sample, uncertainty, or assumption.
- Write only what the data supports.
- Add one limit so the result does not overclaim.
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
When a statistical result feels obvious, pause and ask: what exactly was measured, compared, and assumed?