High-Frequency Exam Topics and Common Mistakes Analysis for Year 13 CIE Statistics | Year 13 CIE 统计：高频考点与易错题分析

📚 High-Frequency Exam Topics and Common Mistakes Analysis for Year 13 CIE Statistics | Year 13 CIE 统计：高频考点与易错题分析

Year 13 CIE Statistics (S2) covers a wide range of topics that frequently appear in the exam and carry significant weight. This article highlights the key concepts that are tested most often and analyses the common pitfalls students encounter, helping you maximise marks through awareness and practice. By understanding both the core content and typical errors, you can approach your revision and the final paper with greater confidence.

Year 13 CIE 统计（S2）涵盖了大量高频考点，这些内容在考试中反复出现且占分较重。本文聚焦于最常考的核心概念，并分析考生常见的易错点，旨在通过提升认知与强化练习帮助你争取更高分数。只有深入理解核心内容与典型错误，才能在复习和正式考试中更加从容。

1. Continuous Random Variables and Probability Density Functions | 连续随机变量与概率密度函数

A continuous random variable X is described by its probability density function (PDF) f(x), which must satisfy f(x) ≥ 0 and the total area under the curve over the defined domain equalling 1: ∫₋∞∞ f(x) dx = 1. In exam questions, you are often asked to find an unknown constant k by setting the definite integral of f(x) over its support equal to 1. The median m is the value such that ∫₋∞ᵐ f(x) dx = 0.5. The mode occurs where f(x) attains its maximum within the interval.

连续随机变量X由其概率密度函数（PDF）f(x) 描述，f(x) ≥ 0 且定义域内的总面积等于1：∫₋∞∞ f(x) dx = 1。考试常要求通过令f(x)在有效区间上的定积分等于1来求未知常数k。中位数m满足 ∫₋∞ᵐ f(x) dx = 0.5。众数则位于区间内f(x)取最大值的位置。

A very common mistake is using incorrect integration limits, especially when the PDF is defined piecewise. Students sometimes integrate over (−∞, ∞) without realising the function is non‑zero only on a finite interval. Another slip is forgetting to check that f(x) ≥ 0 after finding k. When solving for the median, always verify that the solution lies within the range of X.

最常见的错误是积分上下限使用不当，尤其是当PDF分段定义时。一些同学在整条实轴上积分，却没有意识到函数仅在有限区间内非零。另一个疏忽是求出k后忘记验证f(x) ≥ 0。在求中位数时，切记检查解是否落在X的取值范围内。

2. Cumulative Distribution Functions | 累积分布函数

The cumulative distribution function (CDF) is given by F(x) = P(X ≤ x) = ∫₋∞ˣ f(t) dt. The CDF increases from 0 to 1. To find probabilities such as P(a < X < b), we compute F(b) − F(a). The median can also be obtained by solving F(m) = 0.5. When a PDF is defined piecewise, the CDF must be built up carefully, adding the accumulated probability from the previous piece.

累积分布函数（CDF）定义为 F(x) = P(X ≤ x) = ∫₋∞ˣ f(t) dt。CDF从0递增到1。求形如P(a < X < b)的概率只需计算F(b) − F(a)。中位数也可通过解F(m) = 0.5得到。当PDF分段定义时，CDF必须仔细构造，并累加此前区间已累积的概率。

A typical error is forgetting the constant of integration when finding

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