IGCSE CAIE Statistics: Unit Test Mock Paper Walkthrough | IGCSE CAIE 统计：单元测试模拟卷解析

📚 IGCSE CAIE Statistics: Unit Test Mock Paper Walkthrough | IGCSE CAIE 统计：单元测试模拟卷解析

This walkthrough covers a mock unit test featuring ten representative questions from the CAIE IGCSE Statistics syllabus (0479). You will see how to approach data classification, find measures of central tendency and spread, construct cumulative frequency charts, work with probability and tree diagrams, apply the binomial and normal distributions, interpret scatter graphs, and calculate moving averages. Each solution includes examiner insights to help boost your marks.

本文解析一份涵盖 CAIE IGCSE 统计（0479）考纲的单元测试模拟卷，共十道典型题目。你将看到如何处理数据分类、计算集中趋势和离散度、绘制累积频率图、解决概率与树图问题、应用二项分布和正态分布、解读散点图以及计算移动平均值。每道题的解析均附带评分要点，助你提分。

1. Question 1: Classifying Data Types | 第1题：数据分类

Problem: Classify each of the following variables as qualitative or quantitative. For quantitative variables, state whether they are discrete or continuous.
(i) Height of students in centimetres.
(ii) Favourite colour.
(iii) Number of siblings.
(iv) Time taken to complete a puzzle.

题目：将下列每个变量分为定性或定量。若为定量变量，说明是离散还是连续。
（i）学生身高（厘米）。
（ii）最喜欢的颜色。
（iii）兄弟姐妹数量。
（iv）完成拼图所需的时间。

Height is quantitative continuous – it is measured on a continuous scale and can take any value within a range. Favourite colour is qualitative (categorical) because it describes a non‑numerical attribute. Number of siblings is quantitative discrete – you count siblings and the values are whole numbers. Time is quantitative continuous – time can be measured to any level of precision.

身高是定量连续变量——它在连续尺度上测量，可取范围内任意值。最喜欢的颜色是定性（分类）变量，因为它描述非数值属性。兄弟姐妹数是定量离散变量——你数兄弟姐妹，只能是整数。时间是定量连续变量——时间可以测量到任意精度。

Examiner tip: Always specify ‘continuous’ or ‘discrete’ when the question asks for it – simply saying ‘quantitative’ may lose marks.

评分提示：当题目要求说明时，务必指出“连续”或“离散”——仅写“定量”可能丢分。

2. Question 2: Mean, Median, Mode and Range | 第2题：均值、中位数、众数与极差

Problem: For the dataset 15, 22, 18, 22, 30, 18, 22, 25, calculate the mean, median, mode and range.

题目：对于数据集 15, 22, 18, 22, 30, 18, 22, 25，计算均值、中位数、众数和极差。

First, arrange the data in ascending order: 15, 18, 18, 22, 22, 22, 25, 30.

首先，按升序排列数据：15, 18, 18, 22, 22, 22, 25, 30。

Mean: sum = 15+18+18+22+22+22+25+30 = 172; there are 8 values, so x̄ = 172 / 8 = 21.5.

均值：总和 = 15+18+18+22+22+22+25+30 = 172；共8个值，因此 x̄ = 172 / 8 = 21.5。

Median: with 8 values the median lies between the 4th and 5th ordered values. (22 + 22) / 2 = 22.

中位数：有8个数值，中位数位于第4和第5个有序值之间。(22 + 22) / 2 = 22。

Mode: 22 appears three times, more than any other value, so mode = 22.

众数：22出现三次，次数最多，因此众数 = 22。

Range: maximum (30) − minimum (15) = 15.

极差：最大值（30）− 最小值（15）= 15。

3. Question 3: Quartiles and Box Plot | 第3题：四分位数与箱线图

Problem: Using the same ordered data (15, 18, 18, 22, 22, 22, 25, 30), find the lower quartile (Q₁), upper quartile (Q₃) and interquartile range (IQR). Then construct a box plot.

题目：使用相同的排序数据（15, 18, 18, 22, 22, 22, 25, 30），找出下四分位数（Q₁）、上四分位数（Q₃）和四分位距（IQR），并绘制箱线图。

For Q₁, take the lower half of the data (excluding the median): 15, 18, 18, 22. The median of this half is (18+18)/2 = 18, so Q₁ = 18. For Q₃, take the upper half: 22, 22, 25, 30. Its median is (22+25)/2 = 23.5, so Q₃ = 23.5. IQR = Q₃ − Q₁ = 23.5

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