Introducing Statistics: What Can We Learn from Data? · 引入统计学：我们能从数据中学到什么？
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| data/ˈdeɪtə/ | 数据 | shù jù |
| Statistics/stəˈtɪstɪks/ | 统计学 | tǒng jì xué |
| uncertainty/ʌnˈsɜːtənti/ | 不确定性 | bù què dìng xìng |
| individuals/ˌɪndɪˈvɪdʒuːəlz/ | 个体 | gè tǐ |
| variables/ˈveərɪəblz/ | 变量 | biàn liàng |
| statistical question/stəˈtɪstɪkl ˈkwestʃn/ | 统计问题 | tǒng jì wèn tí |
Learning from data that varies
- Every day the world throws numbers at us — test scores, prices, heights. Statistics 统计学 is the science of learning from them.
- The catch: real data 数据 vary. No two people are identical, so answers come with wiggle room.
- Statistics is about finding patterns in that variation — and being honest about the uncertainty 不确定性 that remains.
- This whole course is a toolkit for turning messy data into trustworthy conclusions.
从变化的数据中学习
- 每天世界都向我们抛来数字——考试分数、价格、身高。统计学是从它们中学习的科学。
- 陷阱是:真实数据会变化。没有两个人完全相同,所以答案带有余地。
- 统计学就是在那种变化中找规律——并诚实面对残留的不确定性。
- 整门课是一套工具箱,把杂乱的数据变成可信的结论。
Data that varies · 具有变异性的数据
Real data spread out across values — statistics finds the pattern in that variation. · 真实数据在不同值上分布——统计学在这些变异性中寻找规律。
Individuals and variables
- A data set records individuals 个体 (the cases — people, animals, objects) and their variables 变量 (the characteristics measured).
- Rows are usually individuals; columns are variables.
- Example: a class roster — each student is an individual; their height, grade, favorite subject are variables.
- Identifying who and what is the first step of any analysis.
个体与变量
- 一个数据集记录个体(案例——人、动物、物体)和它们的变量(所测量的特征)。
- 行通常是个体;列是变量。
- 例:一份班级名单——每个学生是一个个体;他们的身高、年级、最喜欢的科目是变量。
- 认清"谁"和"什么"是任何分析的第一步。
In a data set of $200$ students' commute times, the individuals are... · 在$200$名学生通勤时间的数据集中，个体是……
Individuals are the cases (students); commute time is the variable. · 个体即案例（学生）；通勤时间是变量。
In a typical data table, the columns usually represent... · 在典型的数据表中，列通常代表……
Rows = individuals, columns = variables. · 行 = 个体，列 = 变量。
Asking a statistical question
- A statistical question 统计问题 anticipates variability — it expects the answers to differ.
- "How tall is Ana?" is not statistical (one answer). "How tall are students in this school?" is (many varying answers).
- A good statistical question can be answered with data and accounts for spread.
- Framing the right question shapes everything that follows.
提出统计问题
- 统计问题会预期变化——它期望答案各不相同。
- "安娜多高?"不是统计问题(一个答案)。"这所学校的学生有多高?"是(许多变化的答案)。
- 一个好的统计问题能用数据回答,并考虑到分散。
- 提对问题决定了后续的一切。
Which is a statistical question? · 哪一个是统计问题？
It anticipates variability — many differing answers. · 它预期存在变异性——会有许多不同的答案。
A question with a single definite answer is a statistical question. · 只有一个确定答案的问题不是统计问题。
Statistical questions anticipate variability. · 统计问题预期存在变异性。
Patterns vs. uncertainty
- Patterns in data let us generalize — to make claims beyond the exact cases we measured.
- But variability means those claims carry uncertainty: we're rarely $100\%$ sure.
- The art is drawing useful conclusions while honestly reporting how uncertain they are.
- Statistics never says "definitely"; it says "very likely, within this margin."
规律 vs 不确定性
- 数据中的规律让我们推广——做出超越所测量的确切案例的论断。
- 但变化意味着那些论断带有不确定性:我们很少 $100\%$ 确定。
- 艺术在于得出有用的结论,同时诚实报告有多不确定。
- 统计学从不说"一定";它说"很可能,在这个范围内"。
Because data vary, conclusions drawn from them carry . · 由于数据存在变异性，从中得出的结论带有。
Variability means we are rarely $100\%$ certain. · 变异性意味着我们很少$100\%$确定。
Select all · 所有 true statements about statistics. · 选择关于统计学的所有正确陈述。
Statistics generalizes with uncertainty; it never claims certainty. · 统计学在不确定性中进行推广；它从不声称确定性。
A statistical question anticipates variability — a question with a single definite answer ("What is the capital of France?") is not statistical. And beware overreach: a pattern in data supports a generalization with uncertainty, never a claim of certainty. Data can mislead if you forget the variability behind it.
统计问题预期变化——有单一确定答案的问题("法国首都是哪里?")不是统计问题。并当心过度推断:数据中的规律支持带不确定性的推广,绝非确定性论断。若你忘了数据背后的变化,它会误导你。
A survey records $200$ students' commute times.
- Individuals: the $200$ students. Variable: commute time (a number that varies).
- Statistical question: "What is the typical commute time, and how much does it vary?"
- A conclusion like "most students commute $15$–$30$ min" generalizes, but with uncertainty from the sample.
一项调查记录了 $200$ 名学生的通勤时间。
- 个体: 那 $200$ 名学生。变量: 通勤时间(一个会变化的数)。
- 统计问题: "典型通勤时间是多少,它变化多大?"
- 像"大多数学生通勤 $15$–$30$ 分钟"这样的结论是推广,但带有来自样本的不确定性。
Statistics is the science of learning from data that vary. A data set has individuals (cases) and variables (measurements). A statistical question anticipates variability and is answered with data. Patterns let us generalize, but variability always leaves uncertainty — report it honestly.
统计学是从变化的数据中学习的科学。数据集有个体(案例)和变量(测量值)。统计问题预期变化,并用数据回答。规律让我们推广,但变化总留下不确定性——要诚实报告它。