Year 11 Eduqas Statistics: Unit Test Mock Paper Analysis | 英国11年级Eduqas统计：单元测试模拟卷解析

📚 Year 11 Eduqas Statistics: Unit Test Mock Paper Analysis | 英国11年级Eduqas统计：单元测试模拟卷解析

Welcome to this detailed walkthrough of a typical Year 11 Eduqas Statistics unit test mock paper. Designed to mirror the style and content of the actual assessment, this analysis covers sampling, data presentation, averages, dispersion, probability, and time series. By working through each question, you will strengthen your exam technique and deepen your understanding of key statistical concepts.

欢迎阅读这篇详细的英国11年级Eduqas统计单元测试模拟卷解析。该模拟卷旨在反映真实考试的风格和内容，本文分析涵盖了抽样方法、数据展示、平均数、离散度、概率和时间序列。通过逐一剖析每道试题，您将提升应试技巧并加深对统计核心概念的理解。

1. Sampling Strategies | 抽样方法

Question: A school has 600 students: 200 in Year 9, 250 in Year 10, and 150 in Year 11. A stratified sample of 60 students is to be surveyed about lunch preferences. Calculate the number of students to be selected from each year group.

问题：某学校有600名学生：九年级200人，十年级250人，十一年级150人。计划抽取60名学生进行分层抽样以调查午餐偏好。请计算每个年级应抽取的学生人数。

Stratified sampling ensures each subgroup is represented proportionally. The sampling fraction is 60/600 = 0.1 (10%). Multiply each year group size by this fraction: Year 9 gets 200 × 0.1 = 20, Year 10 gets 250 × 0.1 = 25, Year 11 gets 150 × 0.1 = 15. Hence the sample requires 20, 25, and 15 students respectively.

分层抽样确保各子群按比例代表。抽样比例为60/600 = 0.1（10%）。将各年级人数乘以该比例：九年级需抽200×0.1=20人，十年级250×0.1=25人，十一年级150×0.1=15人。因此样本应分别包含20、25和15名学生。

It is important to remember that stratified sampling is not about taking equal numbers from each group, but proportional representation. Then, within each stratum, you should use simple random sampling to select the actual individuals, avoiding bias.

需要记住，分层抽样并非从每个组抽取相同数量，而是按比例抽取。在每个年级（层）内，再采用简单随机抽样选择具体学生，以避免偏倚。

2. Frequency Tables and Bar Charts | 频数表与条形图

Question: A survey of 40 households recorded the number of cars they own. The incomplete frequency table is shown below. The total frequency is 40.

(a) Find the missing frequency f. (b) Draw a bar chart to represent the data.

（a）求缺失的频数f。（b）绘制条形图以展示该数据。

The total is 40, so f = 40 − (8 + 12 + 5 + 3) = 12. The completed frequency for 2 cars is 12. When drawing the bar chart, place the number of cars on the horizontal axis (discrete) and frequency on the vertical axis. Use bars of equal width with clear gaps between them to show separate categories. Label the axes and give the chart a title, such as ‘Number of cars per household’. A convenient scale could be 1 cm representing 2 households.

总频数为40，因此f = 40 − (8 + 12 + 5 + 3) = 12，即2辆车的户数为12。绘制条形图时，横轴表示汽车数量（离散变量），纵轴表示频数。条形等宽，之间留有间隔以体现类别独立。标明坐标轴，并给图表加上标题，例如“家庭拥有汽车数量”。合适的比例尺可以是1厘米代表2户。

3. Averages and Range | 平均数与极差

Question: Using the completed frequency table from Question 2, calculate the mean, median, mode(s) and range of the number of cars per household.

问题：利用第2题中补全的频数表，计算每户汽车数量的平均数、中位数、众数以及极差。

To find the mean, multiply each car number by its frequency and sum: (0×8)+(1×12)+(2×12)+(3×5)+(4×3) = 0+12+24+15+12 = 63. Then divide by 40: mean = 63 ÷ 40 = 1.575 cars (often rounded to 1.6).

计算平均数：将每个汽车数量乘以对应的频数再求和：(0×8)+(1×12)+(2×12)+(3×5)+(4×3) = 0+12+24+15+12=63。然后除以总数40：平均数 = 63 ÷ 40 = 1.575 辆（通常四舍五入为1.6）。

For the median with 40 values, we locate the 20th and 21st ordered values. Cumulative frequencies: up to 0 cars → 8; up to 1 car → 20 (so the 9th–20th values are 1). Thus the 20th value is 1. The 21st value belongs to the next group (2 cars), so it is 2. The median is (1 + 2) ÷ 2 = 1.5 cars.

中位数：因共有40个数据，需找出第20和第21个值。累积频数：到0辆为8；到1辆为20（即第9至第20个值均为1）。因此第20个值为1。第21个值落入下一组（2辆），即为2。中位数 = (1 + 2) ÷ 2 = 1.5 辆。

The frequencies for 1 car and 2 cars are both 12, so the data is bimodal with modes at 1 and 2 cars. The range is the largest value minus the smallest: 4 − 0 = 4 cars.

1辆和2辆的频数均为12，因此数据呈双众数，众数为1和2。极差为最大值减最小值：4 − 0 = 4 辆。

Notice that the mean (1.575) is slightly above the median (1.5), suggesting a minor positive skew caused by a few families owning 3 or 4 cars. Both measures are useful for describing the centre of the data.

可以看到平均数（1.575）略高于中位数（1.5），说明由于少数家庭拥有3或4辆车，数据呈轻微正偏态。这两个指标都有助于描述数据中心。

4. Cumulative Frequency and Box Plots | 累积频数与箱线图

Question: The grouped frequency table below shows the time (minutes) taken by 30 students to complete a maths test.