Year 10 Edexcel Statistics: Unit Test Mock Paper Breakdown | 单元测试模拟卷解析

📚 Year 10 Edexcel Statistics: Unit Test Mock Paper Breakdown | 单元测试模拟卷解析

This article provides a thorough analysis of a typical Year 10 Edexcel Statistics unit test mock paper. We break down each question type, highlight key concepts, and demonstrate step-by-step solutions to help students master data handling, probability, and sampling techniques. By understanding the common pitfalls and examiner expectations, you can boost your confidence and achieve a higher grade.

本文对一份典型的 Year 10 Edexcel 统计单元测试模拟卷进行了深入解析。我们逐一剖析各类题型，强调关键概念，并展示分步解题过程，帮助学生掌握数据处理、概率和抽样方法。了解常见错误和考官期望，有助于增强信心并提高成绩。

1. Stem-and-Leaf Diagrams and Median | 茎叶图与中位数

The stem-and-leaf diagram below shows the marks (out of 50) for 24 students in a test. Key: 2|3 means 23 marks.

下面的茎叶图显示了 24 名学生在一次测试中的分数（满分 50）。图例：2|3 表示 23 分。

Question: Find the median mark and the interquartile range (IQR).

问题：求分数中位数和四分位距 (IQR)。

Step 1: List the data in order. The ordered marks are: 14, 17, 19, 20, 23, 23, 25, 28, 31, 32, 34, 36, 37, 39, 40, 42, 45, 45, 48, 50, 50. There are 24 values, so the median is the average of the 12th and 13th values.

步骤 1：将数据按顺序列出。 排序后的分数为：14, 17, 19, 20, 23, 23, 25, 28, 31, 32, 34, 36, 37, 39, 40, 42, 45, 45, 48, 50, 50。共有 24 个数值，因此中位数是第 12 和第 13 个数值的平均值。

Step 2: Calculate median. The 12th value is 36, the 13th is 37. Median = (36 + 37) ÷ 2 = 36.5 marks.

步骤 2：计算中位数。 第 12 个数值是 36，第 13 个是 37。中位数 = (36 + 37) ÷ 2 = 36.5 分。

Step 3: Find quartiles. Lower quartile (Q1) is the median of the first 12 values: (23 + 25) ÷ 2 = 24. Upper quartile (Q3) is the median of the last 12 values: (45 + 45) ÷ 2 = 45. IQR = Q3 – Q1 = 45 – 24 = 21 marks.

步骤 3：求四分位数。 下四分位数 (Q1) 是前 12 个数值的中位数：(23 + 25) ÷ 2 = 24。上四分位数 (Q3) 是后 12 个数值的中位数：(45 + 45) ÷ 2 = 45。IQR = 45 – 24 = 21 分。

2. Box Plots and Comparing Distributions | 箱线图与分布比较

Two classes, A and B, took the same test. The five-number summaries are: Class A: min=18, Q1=30, median=42, Q3=54, max=72; Class B: min=25, Q1=36, median=48, Q3=58, max=70.

两个班级 A 和 B 参加了相同的测试。五数概括为：A 班：最小值=18，Q1=30，中位数=42，Q3=54，最大值=72；B 班：最小值=25，Q1=36，中位数=48，Q3=58，最大值=70。

Question: Draw box plots for both classes and compare the distributions, commenting on central tendency and spread.

问题：绘制两个班级的箱线图，并比较分布情况，对集中趋势和离散程度进行评述。

Drawing box plots: (In the exam, you would sketch them on graph paper.) Key features: the box spans Q1 to Q3, the median line is inside the box, and whiskers extend to min and max unless there are outliers (none here).

绘制箱线图： (在考试中，你需要在方格纸上绘制。) 关键特征：箱体从 Q1 到 Q3，中位数线在箱内，触须延伸至最小值和最大值（此处无异常值）。

Comparison: The median of Class B (48) is higher than that of Class A (42), suggesting that on average, Class B performed better. The interquartile range for Class B is 58 – 36 = 22, compared to Class A’s IQR of 24, so Class B has a slightly smaller spread of the middle 50%. The range of Class A (72–18=54) is larger than Class B (70–25=45), indicating more variation overall, mainly due to a lower minimum.

比较：