📚 Year 7 Cambridge Statistics: Interdisciplinary Integrated Question Training | Year 7 剑桥统计：跨学科综合题型训练
In Year 7 Cambridge Mathematics, statistics is not just about drawing graphs. It often appears in questions that combine science experiments, geographical data, sports results, and even historical records. This integrated training helps you develop the skill to move between tables, charts, and real‑world contexts confidently.
在 Year 7 剑桥数学中，统计不仅仅是画图。它常常与科学实验、地理数据、运动成绩甚至历史记录结合出题。这类跨学科训练帮助你培养在表格、图表和真实情境之间灵活转换的能力。
1. Understanding the Task: Reading Data Across Subjects | 理解任务：跨学科阅读数据
Interdisciplinary statistics questions always begin with a scenario. You might read about a biology experiment measuring plant growth, a geography topic comparing city populations, or a sports league table. Your first job is to identify what the numbers represent and decide which statistical tool or graph is most appropriate.
跨学科统计题总是从一个情境开始。你可能读到关于测量植物生长的生物实验、比较城市人口的地理课题，或者一个体育联赛积分表。你的首要任务是识别这些数字代表什么，并决定哪种统计工具或图表最合适。
For example, a science teacher asks: ‘The heights of bean plants after two weeks were recorded. Show the data in a bar chart and find the average height.’ You must extract numerical data, choose a suitable graph type, and then perform calculations. Never rush into drawing without understanding the units and labels.
例如，科学老师问：“两周后记录豆苗的高度。用条形图展示数据并求平均高度。”你必须提取出数值，选择合适的图表类型，然后进行计算。在没有理解单位和标签之前，千万不要匆忙画图。
2. Collecting and Organising Data: From Science Experiments | 收集和整理数据：来自科学实验
Imagine a Year 7 class grows cress seedlings. The heights in centimetres are: 3.2, 2.8, 3.5, 3.0, 3.1, 2.9, 3.4, 3.3, 3.2, 3.6. First, organise the raw data into a frequency table. This makes patterns easier to spot and helps when calculating the mean.
想象一个 Year 7 班级种植水芹幼苗。高度（厘米）为：3.2, 2.8, 3.5, 3.0, 3.1, 2.9, 3.4, 3.3, 3.2, 3.6。首先，将原始数据整理成频数表。这使模式更容易发现，也便于计算平均数。
| Height (cm) | Tally | Frequency |
|---|---|---|
| 2.8 – 2.9 | II | 2 |
| 3.0 – 3.1 | II | 2 |
| 3.2 – 3.3 | III | 3 |
| 3.4 – 3.5 | II | 2 |
| 3.6 | I | 1 |
To find the mean height, add all the values and divide by the total number of seedlings. Sum = 3.2 + 2.8 + 3.5 + 3.0 + 3.1 + 2.9 + 3.4 + 3.3 + 3.2 + 3.6 = 32.0. There are 10 seedlings, so mean = 32.0 ÷ 10 = 3.2 cm. This shows the central tendency of the plant growth.
要求平均高度，把所有数值相加再除以幼苗总数。总和 = 3.2 + 2.8 + 3.5 + 3.0 + 3.1 + 2.9 + 3.4 + 3.3 + 3.2 + 3.6 = 32.0。共有 10 株幼苗，因此平均数 = 32.0 ÷ 10 = 3.2 cm。这体现了植物生长的集中趋势。
3. Bar Charts and Comparative Analysis in Geography | 地理中的条形图与比较分析
Geography often asks you to compare data across regions. A typical question: The annual rainfall (mm) in four cities is: London 593, Mumbai 2200, Sydney 1217, Cairo 25. Draw a bar chart and write two sentences comparing the cities.
地理学科经常要求比较不同地区的数据。一个典型问题：四个城市的年降水量（毫米）为：伦敦 593，孟买 2200，悉尼 1217，开罗 25。绘制条形图并写两句话比较这些城市。
To draw the bar chart, label the horizontal axis with city names and the vertical axis with rainfall in mm, using a scale of 1 cm = 200 mm. The bars should be equal width and clearly separated. The tallest bar (Mumbai) shows the highest rainfall, while Cairo’s bar is barely visible, indicating an arid climate. Always include a title, e.g., ‘Annual Rainfall of Four World Cities’.
绘制条形图时，横轴标出城市名称，纵轴标出降水量（毫米），使用比例尺 1 厘米代表 200 毫米。条形应等宽且清晰分开。最高的条形（孟买）表示降水量最大，而开罗的条形几乎是平的，表明干旱气候。务必加上标题，如“四个世界城市的年降水量”。
When comparing, use phrases like ‘Mumbai receives over 88 times more rainfall than Cairo’ or ‘London’s rainfall is less than a third of Mumbai’s’. This links numerical analysis with geographical understanding.
在比较时，使用诸如“孟买的降水量是开罗的 88 倍多”或“伦敦的降水量不到孟买的三分之一”这样的表述。这把数值分析和地理理解联系了起来。
4. Line Graphs: Temperature Trends Over Time | 折线图：温度随时间变化趋势
In a combined science and mathematics task, you may record the outdoor temperature every two hours. Data: 08:00 – 12°C, 10:00 – 15°C, 12:00 – 19°C, 14:00 – 21°C, 16:00 – 20°C, 18:00 – 17°C. Plot these points on a line graph.
在科学与数学结合的任务中，你可能每两小时记录一次室外温度。数据：08:00 – 12°C，10:00 – 15°C，12:00 – 19°C，14:00 – 21°C，16:00 – 20°C，18:00 – 17°C。把这些点画在折线图上。
The graph should have time on the x‑axis and temperature on the y‑axis. Join the points with straight lines. This line graph reveals that the temperature rises until 14:00, reaching a peak of 21°C, then gradually falls. The difference between the maximum and minimum temperature is 21 – 12 = 9°C.
图中时间应在横轴，温度在纵轴。用直线连接各点。这条折线图显示温度一直上升到 14:00，达到峰值 21°C，然后逐渐下降。最高与最低温度之差为 21 – 12 = 9°C。
A cross‑curricular follow‑up might ask: ‘Explain why the temperature changed in this pattern.’ That encourages thinking about the Sun’s position — a science concept. You don’t need to write an essay, just a short sentence like ‘The Sun is highest around midday, so it heats the ground more.’
一个跨学科的后续问题可能会问：“解释为什么温度呈现这种变化模式。”这会促使你思考太阳的位置——一个科学概念。你不需要写长篇大论，只需简短一句如“正午前后太阳最高，所以对地面的加热更强。”
5. Pie Charts: Energy Sources in Environmental Studies | 饼图：环境研究中的能源来源
Environmental topics often use pie charts. Suppose a town’s electricity comes from: solar 15%, wind 25%, natural gas 40%, nuclear 20%. Construct a pie chart to represent this mix.
环境主题经常使用饼图。假设一个小镇的电力来源为：太阳能 15%，风能 25%，天然气 40%，核能 20%。画一个饼图表示这一组合。
Remember that a full circle is 360°. To find the angle for each sector, multiply the percentage by 3.6. For solar: 15 × 3.6 = 54°. Wind: 90°, natural gas: 144°, nuclear: 72°. Check that the angles sum to 360°. Draw the sectors using a protractor and label each clearly with the source and percentage.
记住整个圆是 360°。要计算每个扇形的角度，用百分比乘以 3.6。太阳能：15 × 3.6 = 54°；风能：90°；天然气：144°；核能：72°。检查角度之和为 360°。用量角器绘制扇形，并清楚标出每种来源及其百分比。
A typical question: ‘What fraction of electricity comes from renewable sources?’ Solar and wind are renewable, together 15% + 25% = 40%, which is 40/100 = 2/5. Linking percentages and fractions is a key statistical skill tested in such cross‑subject problems.
一个典型问题：“可再生能源发电量占总量的几分之几？”太阳能和风能是可再生的，合计 15% + 25% = 40%，即 40/100 = 2/5。将百分数和分数联系起来是这类跨学科问题测试的关键统计技能。
6. Mean, Median, Mode in Sports Statistics | 体育运动统计中的平均数、中位数、众数
A PE teacher records the number of goals scored by a football team in 11 matches: 2, 1, 0, 3, 2, 4, 1, 2, 3, 2, 5. Use this data set to calculate the three averages.
一位体育老师记录了足球队在 11 场比赛中的进球数：2, 1, 0, 3, 2, 4, 1, 2, 3, 2, 5。用这组数据计算三种平均数。
First, the mode: the number that appears most often. The number 2 appears four times, more than any other, so mode = 2. Next, arrange the numbers in order to find the median: 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5. With 11 values, the median is the 6th value, which is 2. Median = 2. For the mean, add all values: 0+1+1+2+2+2+2+3+3+4+5 = 25. Mean = 25 ÷ 11 ≈ 2.27 (to 2 d.p.).
首先，求众数：出现次数最多的数。数字 2 出现了四次，多于其他数字，所以众数 = 2。接着，将数字排序以找中位数：0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5。共 11 个值，中位数是第 6 个值，即 2。中位数 = 2。计算平均数，将所有值相加：0+1+1+2+2+2+2+3+3+4+5 = 25。平均数 = 25 ÷ 11 ≈ 2.27（保留两位小数）。
These three measures tell different stories: the mode and median show that scoring 2 goals is typical, but the mean is slightly higher, pulled up by the 5‑goal match. This is a gentle introduction to how outliers affect statistics.
这三个度量说明了不同的情况：众数和中位数表明进 2 球是典型表现，但平均数略高，是被那场进 5 球的比赛拉高了。这初步介绍了离群值如何影响统计量。
7. Interpreting Tables: Historical Population Data | 解读表格：历史人口数据
Historians and geographers often present population figures in tables. The table below shows the estimated population (in millions) of a country in different centuries.
历史学家和地理学家经常用表格呈报人口数据。下表显示了某国在不同世纪的估计人口（百万）。
| Year | Population (millions) |
|---|---|
| 1500 | 4.2 |
| 1600 | 5.1 |
| 1700 | 6.0 |
| 1800 | 9.3 |
| 1900 | 16.5 |
Questions might include: ‘Calculate the increase in population between 1500 and 1900.’ Subtract: 16.5 – 4.2 = 12.3 million. ‘Between which two centuries did the absolute increase become larger?’ The increase from 1800 to 1900 is 16.5 – 9.3 = 7.2 million, which is the largest jump.
问题可能包括：“计算 1500 年至 1900 年间人口的增长。”相减：16.5 – 4.2 = 12.3 百万。“哪两个世纪之间增长的绝对值更大？”从 1800 年到 1900 年的增长为 16.5 – 9.3 = 7.2 百万，是最大的一次跃升。
Such tasks reinforce subtraction of decimals and reading a timeline – a blend of history, numeracy, and data interpretation.
这类任务强化了小数的减法以及时间轴的阅读——融合了历史、算数和数据解读。
8. Scatter Graphs: Linking Two Variables in Biology | 散点图：生物学中两个变量的关联
In a biology investigation, students measure the hand span (cm) and height (cm) of ten classmates. Here is the data: (14, 150), (15, 155), (16, 162), (17, 168), (18, 170), (15, 153), (16, 160), (17.5, 172), (14.5, 148), (19, 178). Plot a scatter graph with hand span on the x‑axis and height on the y‑axis.
在生物探究中，学生测量了十位同学的手掌宽度（cm）和身高（cm）。数据如下：(14, 150), (15, 155), (16, 162), (17, 168), (18, 170), (15, 153), (16, 160), (17.5, 172), (14.5, 148), (19, 178)。绘制散点图，手掌宽度在横轴，身高在纵轴。
After plotting, you will see the points roughly sloping upwards. This suggests a positive correlation: students with larger hand spans tend to be taller. You may be asked to describe the correlation using words like ‘strong positive’ or ‘weak positive’. Never claim causation from a scatter graph alone; it only shows a relationship, not that one causes the other.
描点后，你会看到点大致呈上升趋势。这表明正相关：手掌较宽的学生往往身高也较高。你可能会被要求用“强正相关”或“弱正相关”等词语描述相关性。切勿仅从散点图断言因果关系；它只显示关联，而不表示一个变量导致另一个变量变化。
A follow‑up could ask: ‘Draw a line of best fit and predict the height of a student with a hand span of 16.5 cm.’ Extend the trend line and read off the predicted height – a skill that connects statistics with interpolation on graphs.
后续问题可能是：“画一条最佳拟合线，预测手宽为 16.5 厘米的学生的身高。”延长趋势线并读出预测身高——这一技能把统计与图表插值联系了起来。
9. Probability and Predictions in Economics | 概率与经济预测
Even in Year 7, simple probability can be tied to economic ideas like games of chance. A fair six‑sided die is rolled. What is the probability of getting an even number? There are 3 even numbers (2, 4, 6) out of 6 possible outcomes, so P(even) = 3/6 = 1/2.
即使在 Year 7，简单的概率也可以与机会游戏等经济概念相联系。掷一个公平的六面骰子。得到偶数的概率是多少？共有 3 个偶数（2, 4, 6），6 种可能结果，所以 P(偶数) = 3/6 = 1/2。
Now imagine a multi‑subject problem: ‘In a school fair, a game costs £1 to play. You toss two coins. If both show heads, you win £3. Otherwise you win nothing. Is it a fair game?’ List all outcomes: HH, HT, TH, TT. Only HH wins. Probability of winning = 1/4. Expected gain per game = (1/4 × £3) – (3/4 × £0) = £0.75, but the ticket costs £1, so on average you lose £0.25 per play. This is not fair for the player. Introducing expected value in simple terms blends economics and probability.
现在设想一个多学科问题：“在校园义卖中，一个游戏花费 £1 玩一次。你抛两枚硬币。如果两枚都是正面，你赢得 £3。否则不得奖。这是公平游戏吗？”列出所有结果：HH, HT, TH, TT。只有 HH 赢。赢的概率 = 1/4。每次游戏的期望收益 = (1/4 × £3) – (3/4 × £0) = £0.75，但门票花费 £1，因此平均每次损失 £0.25。这对玩家不公平。用简单语言引入期望值的概念融合了经济学与概率。
10. Multi-Step Word Problems: Mixed Data Forms | 多步骤应用题：混合数据形式
A rich cross‑curricular task might combine a table and a bar chart. For instance: The table below shows the number of students in each Year 7 class who recycle bottles every week. The bar chart (not shown here but described) displays the same data broken down by gender. Answer the questions that follow.
一道丰富的跨学科任务可能结合表格和条形图。例如：下表显示了每个 Year 7 班级每周回收瓶子的学生人数。条形图（此处未显示，但进行描述）按性别细分了相同数据。回答随后的问题。
| Class | Recyclers |
|---|---|
| 7A | 18 |
| 7B | 22 |
| 7C | 15 |
| 7D | 24 |
From the bar chart, we learn that in 7B, 10 boys and 12 girls recycle. In 7D, 14 boys and 10 girls recycle. Step‑by‑step, calculate the total number of recycling boys across all classes, find the fraction of recyclers who are boys, and determine which class has the highest proportion of girl recyclers. Multi‑step problems test your ability to synthesise information from two different representations.
从条形图得知，7B 有 10 名男生和 12 名女生回收；7D 有 14 名男生和 10 名女生回收。逐步计算所有班级中参与回收的男生总人数，求出回收者中男生的比例，并确定哪个班级女生回收者比例最高。多步骤问题考察你综合两种不同表现形式的信息的能力。
11. Designing a Survey: Cross-Curricular Project | 设计调查：跨学科项目
Teachers often ask you to design a simple survey that links subjects. Suppose your topic is ‘Screen Time and Sleep’. In small groups, write a questionnaire to collect data from Year 7 students. Include numerical questions like ‘How many hours of screen time do you have per day?’ and ‘How many hours do you sleep?’
老师们常常要求你设计一个连接多学科的简单调查。假设你的主题是“屏幕时间与睡眠”。以小组为单位，编写一份问卷，向 Year 7 学生收集数据。包括数值型问题，如“你每天屏幕时间是多少小时？”和“你睡多少小时？”
After collecting data, organise it into a two‑way table or draw a scatter graph. Then write a short report. This project combines statistical planning (data collection, sampling), mathematics (graphs, averages), and PSHE (health education). You learn that good surveys need clear, unbiased questions and a sensible way to record responses.
在收集数据后，将其整理成双向表或绘制散点图。然后写一份简短报告。这个项目结合了统计规划（数据收集、抽样）、数学（图表、平均数）和个人社会健康教育（健康教育）。你会懂得好的调查需要清晰、无偏见的问题以及合理的答案记录方式。
12. Common Mistakes and How to Avoid Them | 常见错误及避免方法
In interdisciplinary statistics, several errors appear again and again. One is forgetting to label axes and include units, which loses easy marks. Another is misreading the scale — if a bar chart’s vertical axis jumps by 5, a bar that reaches halfway between gridlines might be misinterpreted as 2.5 instead of the true value. Always check the scale carefully.
在跨学科统计中，有几个错误反复出现。一是忘记给坐标轴加标签和单位，这会轻易丢分。二是读错比例尺——如果条形图的纵轴以 5 为单位递增，一条处于网格线中间的条形可能被误读为 2.5 而非真实值。始终仔细检查比例尺。
When calculating the mean, many students divide by the wrong total or include the frequency count in the sum. Double‑check your divisor. In probability, mixing up ‘and’ and ‘or’ rules can lead to incorrect values. Finally, when writing conclusions, avoid saying ‘this proves’ — statistics only suggest evidence, never proof. Practice these integrated tasks to build strong cross‑curricular reasoning.
计算平均数时，许多学生会除以错误的总数，或者把频数也算进总和里。务必复核除数。在概率中，混淆“且”与“或”的规则会导致错误的值。最后，在写结论时，避免使用“这就证明了”——统计只提供证据，从不是证明。通过练习这些综合性任务，你能建立起强大的跨学科推理能力。
Published by TutorHao | Statistics Revision Series | aleveler.com
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