Collecting data
| English | Chinese | Pinyin |
|---|---|---|
| population | 总体 | zǒng tǐ |
| sample | 样本 | yàng běn |
| representative | 有代表性的 | yǒu dài biǎo xìng de |
| qualitative data | 定性数据 | dìng xìng shù jù |
| quantitative data | 定量数据 | dìng liàng shù jù |
| discrete | 离散 | lí sàn |
| continuous | 连续 | lián xù |
| histogram | 直方图 | zhí fāng tú |
Who you ask decides what you find
- A survey of your own class does not describe the school, however carefully you count.
- A population 总体 is everyone you want to describe; a sample 样本 is who you actually measure.
- The sample is representative 有代表性的 only if the way you chose it did not favour one kind of person.
Kinds of data
- Qualitative data 定性数据 are categories: colour, subject, yes or no.
- Quantitative data 定量数据 are numbers, and split again: discrete 离散 data are counted, continuous 连续 data are measured.
- Shoe size is discrete; foot length is continuous. Which one you have decides which chart is legitimate.
Match each variable to its data type.
Counted values are discrete; measured values are continuous. The type decides which chart is legitimate.
Displaying it honestly
- A bar chart compares categories; a histogram 直方图 shows the distribution of continuous data, with no gaps between bars.
- A pie chart shows parts of one whole, and only when the parts genuinely sum to that whole.
- Every axis needs a label and a unit, and this is marked in every project in the module.
Which chart suits continuous data such as height?
Continuous data has no gaps between values, so the bars should not have gaps either.
Two ways to sample students about the canteen.
Ask the queue at 12:30: you sample people who use the canteen. Everyone who avoids it is invisible, and they are exactly the ones with an opinion about it.
Ask every tenth name on the roll: everyone has the same chance of appearing, including those who never go.
The second is harder and slower. It is also the only one whose result describes the school.
You want student opinion on the canteen. Which sample describes the school?
Only that one gives everyone the same chance, including students who never use the canteen.
Bias enters before you calculate anything. Who you asked, who answered, and how you worded the question all shape the result, and no arithmetic afterwards removes it. Describing your sampling method honestly is a marked part of the report.
A larger sample removes bias caused by how the sample was chosen.
A bigger biased sample is more precisely wrong. Only the method fixes bias.
A truncated axis — one that starts at 40 instead of 0 — makes a small difference look enormous. It is not always dishonest, but it must be stated, and a chart that hides it is marked down in the project.
A bar chart's vertical axis starts at 40 rather than 0. What must you do?
A truncated axis is sometimes justified, but never unstated. Hiding it is marked down.