Year 11 WJEC Statistics: Interdisciplinary Integrated Question Practice | WJEC 11年级统计：跨学科综合题型训练

📚 Year 11 WJEC Statistics: Interdisciplinary Integrated Question Practice | 跨学科综合题型训练

WJEC GCSE Statistics challenges you to apply statistical methods across a wide range of real-life situations. Interdisciplinary questions combine data contexts from biology, geography, business, sports science, and many other fields. This revision guide provides integrated practice for key topics, helping you build confidence in tackling multi-step, cross-curricular problems.

WJEC GCSE 统计考试要求你将统计方法应用于各种真实场景。跨学科题目把数据背景与生物学、地理、商业、体育科学等多个领域结合起来。本复习指南提供关键主题的综合训练，帮助你更自信地解决多步骤的跨学科问题。

1. Biology: Variability and Standard Deviation | 生物学：变异与标准差

In a botany experiment, two fertilisers, X and Y, are applied to bean plants. The heights (cm) after four weeks are recorded for five plants in each group.

在一个植物学实验中，对两组豆类植物分别施用肥料 X 和 Y。四周后，每组五株植物的高度（厘米）记录如下。

First compute the mean height for each fertiliser. For X: (18+22+19+21+20)/5 = 20 cm. For Y: (15+25+16+23+21)/5 = 20 cm. Both have identical means, but the spread clearly differs.

首先计算每种肥料的平均高度。对于 X：(18+22+19+21+20)/5 = 20 cm。对于 Y：(15+25+16+23+21)/5 = 20 cm。两者均值相同，但离散程度明显不同。

Next we calculate the standard deviation using σ = √( Σ(x − x̄)² / n ). For X, deviations from the mean are: -2, 2, -1, 1, 0. Squared deviations: 4, 4, 1, 1, 0. Sum = 10. Variance = 10/5 = 2. σ = √2 ≈ 1.41 cm. For Y, deviations: -5, 5, -4, 3, 1. Squares: 25, 25, 16, 9, 1. Sum = 76. Variance = 76/5 = 15.2. σ ≈ 3.90 cm.

接着用公式 σ = √( Σ(x − x̄)² / n ) 计算标准差。对于 X，离均差为 -2, 2, -1, 1, 0；平方后为 4, 4, 1, 1, 0；总和 = 10；方差 = 10/5 = 2；σ ≈ 1.41 cm。对于 Y，离差为 -5, 5, -4, 3, 1；平方和 = 76；方差 = 15.2；σ ≈ 3.90 cm。

The coefficient of variation (CV) is CV = (σ / mean) × 100%. Fertiliser X gives (1.41/20)×100 ≈ 7.05%, while Y gives 19.5%. X produces more consistent growth, which is valuable in agriculture when uniformity is required.

变异系数 (CV) 为 CV = (σ / 均值) × 100%。肥料 X 的 CV 约为 7.05%，而 Y 为 19.5%。X 带来的生长更稳定，这在要求均匀度的农业中很有价值。

2. Geography: Stratified Sampling and Pie Charts | 地理：分层抽样与饼图

A town has the following population by age group: 0–18 years: 5 000; 19–65 years: 12 000; 66+ years: 3 000. A sample of 200 residents is needed for a travel survey, using stratified sampling proportional to age group size.

某城镇按年龄组的人口分布如下：0–18岁：5 000人；19–65岁：12 000人；66岁以上：3 000人。现需抽取200名居民进行出行调查，采用按年龄组大小比例的分层抽样。

The total population is 20 000. For the 0–18 group, sample size = (5 000 / 20 000) × 200 = 50. 19–65: (12 000 / 20 000) × 200 = 120. 66+: (3 000 / 20 000) × 200 = 30. This ensures each age group is fairly represented.

总人口为 20 000。对于 0–18 组，样本量 = (5 000 / 20 000) × 200 = 50。19–65 组：120；66+ 组：30。这样能确保每个年龄组都得到公平代表。

Sometimes we need to construct a pie chart to visualise the population distribution. The angle for each sector is calculated as (group frequency / total frequency) × 360°. 0–18 age group: (5 000/20 000)×360° = 90°. 19–65: 216°; 66+: 54°. Always check that angles sum to 360°.

有时需要用饼图展示人口分布。每部分的角度计算公式为 (组频数 / 总频数) × 360°。0–18 岁组：(5 000/20 000)×360° = 90°；19–65 岁：216°；66+ 岁：54°。务必检查角度总和为 360°。

3. Business: Time Series Analysis and Moving Averages | 商业：时间序列分析与移动平均

Quarterly sales revenue (in £1000s) for a small business over two years is recorded: Year 1 Q1=42, Q2=48, Q3=54, Q4=52; Year 2 Q1=46, Q2=51, Q3=60, Q4=58.

一家小企业的季度销售收入（单位：千英镑）记录如下：第1年 Q1=42, Q2=48, Q3=54, Q4=52；第2年 Q1=46, Q2=51, Q3=60, Q4=58。

To smooth out seasonal fluctuations, we calculate a four-point moving average. The first moving average is (42+48+54+52)/4 = 49.0, centred between Q2 and Q3. The second is (48+54+52+46)/4 = 50.0, centred between Q3 and Q4. The process continues, giving the trend values: 49.0, 50.0, 50.75, 52.25, 53.75, etc.

为消除季节性波动，我们计算四点移动平均。第一个移动平均为 (42+48+54+52)/4 = 49.0，居于 Q2 与 Q3 之间。第二个为 (48+54+52+46)/4 = 50.0，居于 Q3 与 Q4 之间。继续此过程可得趋势值：49.0, 50.0, 50.75, 52.25, 53.75 等。

The moving average trend can be plotted on the same graph as the original data. A line of best fit through these points can be used to predict future sales, for example the next quarter (Year 3 Q1) might be forecast by extending the trend, possibly around 61. Always comment on the reliability of extrapolation.

移动平均趋势可与原始数据绘制在同一图表上。通过这些点的最佳拟合线可用于预测未来销售，例如下个季度（第3年 Q1）可能通过延伸趋势预测约为 61。对向外推测的可靠性应始终加以评论。

4. Sports Science: Scatter Graphs and Spearman’s Rank Correlation | 体育科学：散点图与斯皮尔曼等级相关

A coach investigates whether training hours relate to sprint performance. Five athletes are ranked by weekly training hours and by their 100 m times (fastest time gets rank 1 for performance).

一位教练研究训练时间是否与短跑成绩相关。五名运动员按每周训练小时数和100米成绩分别排名（成绩最快者排名第1）。