Interdisciplinary Integrated Question Practice for CIE Year 10 Statistics | CIE Year 10 统计：跨学科综合题型训练

📚 Interdisciplinary Integrated Question Practice for CIE Year 10 Statistics | CIE Year 10 统计：跨学科综合题型训练

Statistical concepts do not exist in isolation; they form the backbone of data analysis in biology, economics, geography, and many other fields. The CIE IGCSE Statistics syllabus includes questions that require you to apply your knowledge in unfamiliar, cross-curricular contexts, helping you see the real-world relevance of measures of central tendency, probability, correlation, and more.

统计概念并非孤立存在；它们构成了生物学、经济学、地理学等众多领域数据分析的支柱。CIE IGCSE 统计课程包含需要你在陌生的跨学科情境下应用知识的题目，帮助你认识到集中趋势、概率、相关性等指标的现实意义。

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1. Biology: Genetics and Probability | 生物学：遗传与概率

Mendelian genetics offers a rich source of probability problems. Consider a gene for flower colour with two alleles: purple (P) is dominant and white (p) is recessive. When two heterozygous plants (Pp) are crossed, the outcomes for a single offspring can be modelled by a probability tree or a Punnett square.

孟德尔遗传学为概率问题提供了丰富的素材。假设一个控制花色的基因有两个等位基因：紫色(P)为显性，白色(p)为隐性。当两株杂合植株(Pp)杂交时，单一后代的可能结果可以用概率树或庞纳特方格来建模。

Each parent produces gametes P and p with equal probability 1/2. The offspring’s genotype probabilities are: PP (1/4), Pp (1/4), pP (1/4), and pp (1/4). Since purple phenotype appears with at least one P, the probability of a purple-flowered offspring is 3/4.

每个亲本产生配子P和p的概率各为1/2。后代的基因型概率分别为：PP (1/4), Pp (1/4), pP (1/4) 和 pp (1/4)。由于只要至少有一个P就表现为紫色花，因此后代开紫花的概率为3/4。

Tree diagram: start with parent alleles, branch P and p each with probability 1/2, then from each branch repeat for the second parent. Multiplying along branches gives the combined probability for each genotype. This simple rule, the product rule for independent events, is central to genetic probability.

树状图：从亲本等位基因出发，以1/2的概率分出P和p枝，再从每一枝分出第二个亲本的等位基因。沿枝条相乘即得各基因型的联合概率。这一独立事件的乘积法则正是遗传概率的核心。

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2. Economics: Inflation and Index Numbers | 经济学：通货膨胀与指数

Index numbers are essential for comparing economic variables over time. The weighted aggregate price index (Laspeyres) uses base-year quantities to measure the change in the cost of a fixed basket of goods.

指数数字对于比较经济变量随时间的变化至关重要。加权总合价格指数（拉氏指数）使用基年数量来衡量一篮子固定商品成本的变化。

Example basket with three items in 2020 (base) and 2023:

示例篮子包含三种商品，2020年为基年，2023年数据如下：

Item	p₀ ($)	q₀	p₁ ($)	p₀q₀	p₁q₀
Food	10	50	12	500	600
Housing	200	2	230	400	460
Transport	50	10	55	500	550

Weighted Index = (Σp₁q₀ / Σp₀q₀) × 100

Σp₀q₀ = 500 + 400 + 500 = 1400, Σp₁q₀ = 600 + 460 + 550 = 1610. Index = (1610/1400) × 100 ≈ 115.0. This means the overall price level increased by 15% since the base year.

Σp₀q₀ = 500 + 400 + 500 = 1400，Σp₁q₀ = 600 + 460 + 550 = 1610。 指数 = (1610/1400) × 100 ≈ 115.0。这意味着自基年以来整体价格水平上涨了15%。

Interpreting the index: if wages do not rise proportionally, purchasing power falls. This directly links statistics to everyday economic decisions.

指数解读：如果工资没有同比例上涨，购买力就会下降。这直接将统计与日常经济决策联系起来。

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3. Geography: River Discharge and Moving Averages | 地理学：河流流量与移动平均

River discharge data often show seasonal fluctuations. A moving average smooths out short-term variations and reveals the underlying trend, which helps geographers assess flood risk.

河流流量数据通常显示出季节性波动。移动平均法能平滑短期变异并揭示潜在趋势，这有助于地理学者评估洪水风险。

Quarterly discharge (m³/s) for a river over three years: Spring, Summer, Autumn, Winter.

某河流三年内每季度的流量（m³/s）：春、夏、秋、冬。

Year	Q1	Q2	Q3	Q4
1	120	350	220	80
2	110	370	210	90
3	130	360	230	100

To calculate a 4-point moving average, average each block of four consecutive quarters: (120+350+220+80)/4 = 192.5, then (350+220+80+110)/4 = 190.0, and so on. The moving averages centre between quarters and are plotted to show the smoothed trend line.

计算4点移动平均：依次对每四个连续季度求平均：(120+350+220+80)/4 = 192.5，然后(350+220+80+110)/4 = 190.0，以此类推。移动平均值落位于季度之间，画点连线即可展示出平滑后的趋势线。

This technique is vital for identifying longer-term changes in river behaviour, such as the effect of climate change on seasonal flow patterns.

这一技术对于识别河流行为的长期变化至关重要，例如气候变化对季节性流量模式的影响。

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4. Sports Science: Correlation between Training and Performance | 体育科学：训练与成绩的相关性

Sports scientists often investigate the relationship between training load and competition performance. A scatter graph can reveal association, and the product-moment correlation coefficient r quantifies the strength of a linear relationship.

体育科学家经常研究训练负荷与比赛表现之间的关系。散点图可以揭示关联方向，而积矩相关系数 r 则量化线性关系的强弱。

Data for five athletes: weekly training hours (x) and race time in minutes (y).

五名运动员数据：每周训练小时数(x)和比赛完成时间（分钟）(y)。

Athlete	A	B	C	D	E
x (h)	10	12	8	14	9
y (min)	42	38	45	36	44

A negative correlation is expected: more training hours are associated with lower race times. First, compute the means x̄ = 10.6 and ȳ = 41.0. Then compute Σ(xᵢ – x̄)(yᵢ – ȳ) and the sum of squares Σ(xᵢ – x̄)² = 22.8, Σ(yᵢ – ȳ)² = 54.0.

预期呈负相关：训练小时数越多，比赛用时越短。首先计算均值 x̄ = 10.6，ȳ = 41.0。然后计算 Σ(xᵢ – x̄)(yᵢ – ȳ) 以及平方和 Σ(x

Published by TutorHao | Year 10 统计 Revision Series | aleveler.com

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