Year 11 CIE Statistics: Core Concepts Summary | 十一年级 CIE 统计：核心知识点梳理

📚 Year 11 CIE Statistics: Core Concepts Summary | 十一年级 CIE 统计：核心知识点梳理

The Year 11 CIE Statistics syllabus builds a solid foundation in data collection, analysis, probability, and inference. Mastering the core concepts is essential for tackling exam problems confidently. This revision guide summarises key definitions, graphical techniques, numerical measures, probability models, and time‑series tools, with bilingual explanations to support deep understanding.

十一年级 CIE 统计课程为数据的收集、分析、概率和推断奠定了坚实基础。掌握核心知识点对于自信地应对考试题目至关重要。本复习指南梳理了关键定义、图形技巧、数字度量、概率模型和时间序列工具，并提供中英双语解释以加深理解。

1. Data Types and Collection | 数据类型与收集

Data can be qualitative (categorical) – such as colours, types of car – or quantitative (numerical). Quantitative data is further split into discrete (countable, e.g. number of students) and continuous (measurable, e.g. time, height). Recognising the data type determines which chart and summary statistics are appropriate.

数据可以是定性（分类）数据，如颜色、汽车类型，也可以是定量（数值）数据。定量数据又分为离散型（可计数，如学生人数）和连续型（可测量，如时间、身高）。识别数据类型决定了选用哪种图表和汇总统计量。

Primary data is collected firsthand by the researcher; secondary data has been gathered by others. Common sampling methods include: simple random sampling (every member has an equal chance), stratified sampling (population divided into groups, then random samples proportional to group size are taken), and systematic sampling (selecting every k‑th individual after a random start). Bias is reduced by using a proper sampling frame and careful question design.

原始数据由研究者直接收集，二手数据则由他人收集。常见的抽样方法有：简单随机抽样（每个个体被抽中的概率相等）、分层抽样（将总体分组，然后从每组中抽取与组规模成比例的随机样本）和系统抽样（随机起点后每隔 k 个抽取一个）。使用合适的抽样框和精心的问卷设计可以减少偏差。

In CIE exams, you may be asked to suggest a sampling method and justify it by referring to practicality or representativeness.

在 CIE 考试中，可能要求你提出一种抽样方法，并根据实际操作性或代表性进行论述。

2. Graphical Representation of Data | 数据的图形表示

Data can be displayed using bar charts (for categorical data), pie charts (to show proportions), histograms (for continuous data with frequency density), frequency polygons, stem‑and‑leaf diagrams, and box‑and‑whisker plots. For a histogram, frequency density = frequency ÷ class width; the area of each bar is proportional to the frequency, not its height.

数据可以用条形图（分类数据）、饼图（显示比例）、直方图（连续数据，使用频数密度）、频数多边形、茎叶图和箱线图表示。在直方图中，频数密度 = 频数 ÷ 组距；每个长方形的面积与频数成比例，而非它的高度。

A cumulative frequency curve (ogive) is drawn by plotting cumulative frequency against the upper class boundary. It is used to estimate the median, quartiles and percentiles. On a box‑and‑whisker plot, the five‑number summary (minimum, Q1, median, Q3, maximum) allows quick comparison of distributions and reveals skewness

Published by TutorHao | Year 11 统计 Revision Series | aleveler.com

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