📚 Year 7 Cambridge Statistics: Interdisciplinary Integrated Question Training | Year 7 剑桥统计：跨学科综合题型训练
Statistics is the language of data, appearing in every subject from science experiments to geographical surveys. This article trains Year 7 learners to apply statistical skills across the curriculum, interpreting charts, calculating averages, and thinking critically. Through worked examples and structured practice, you will become confident in handling real-world problems.
统计学是数据的语言，出现在从科学实验到地理调查的每一个学科中。本文训练Year 7学生跨课程应用统计技能，解读图表、计算平均数并进行批判性思考。通过范例讲解和结构化训练，你将自信地处理现实世界的问题。
1. Data Collection and Survey Design | 数据收集与调查设计
Imagine a geography project: ‘How do students travel to school?’ First, you must decide on data collection methods. A well-designed questionnaire captures categorical data that can be tallied into a frequency table.
设想一个地理项目：“学生们怎样去上学？”首先，你必须确定数据收集方法。一份设计良好的问卷能捕捉到可归类并整理成频率表的分类数据。
Example: Year 7 pupils recorded these transport choices: Bus, Walk, Car, Bus, Walk, Bus, Cycle, Bus, Car, Walk, Bus, Bus, Cycle, Walk, Walk, Bus, Car, Walk, Bus. Organise the data into a frequency table, then identify the mode.
示例：Year 7学生记录了这些交通方式选择：公交车，步行，小汽车，公交车，步行，公交车，自行车，公交车，小汽车，步行，公交车，公交车，自行车，步行，步行，公交车，小汽车，步行，公交车。将数据整理成频率表，然后确定众数。
Step 1: Count the tally for each category.
步骤1：为每个类别计数。
| Transport type | Tally | Frequency |
|---|---|---|
| Bus | |||| ||| | 8 |
| Walk | |||| | | 6 |
| Car | ||| | 3 |
| Cycle | || | 2 |
The mode is ‘Bus’ with frequency 8. This helps geographers suggest better bus services.
众数是“公交车”，频数为8。这帮助地理学家建议改善公交服务。
Now try: Design a survey about favourite leisure activities. Collect data from 20 friends, create a frequency table, and write one conclusion.
现在尝试：设计一份关于最喜欢的休闲活动的调查。从20位朋友那里收集数据，创建频率表，并写出一个结论。
2. Frequency Tables and Bar Charts in Science | 科学中的频率表与条形图
In a science lab, you test the pH of 15 water samples from different ponds. The results, rounded to whole numbers, are: 6, 7, 7, 8, 6, 7, 9, 7, 6, 7, 8, 7, 6, 7, 8. A frequency table and bar chart reveal patterns in acidity.
在科学实验室中，你测试了15份不同池塘水样的pH值。结果四舍五入到整数为：6, 7, 7, 8, 6, 7, 9, 7, 6, 7, 8, 7, 6, 7, 8。频率表和条形图揭示了酸度的分布模式。
Construct the frequency table:
构建频率表：
| pH value | Frequency |
|---|---|
| 6 | 4 |
| 7 | 7 |
| 8 | 3 |
| 9 | 1 |
Draw a bar chart with pH on the horizontal axis (labelled ‘pH value’) and frequency on the vertical axis (labelled ‘Number of samples’). Bars must not touch, and axes need clear scales.
绘制条形图，横轴为pH值（标注“pH值”），纵轴为频率（标注“样本数量”）。条形之间不能接触，坐标轴需要清晰的刻度。
Interpretation question: ‘Which pH is most common? What does this suggest about the pond water quality?’ The mode is pH 7, indicating neutral water, typical for healthy ponds.
解读问题：“哪个pH值最常见？这对池塘水质有什么启示？”众数是pH 7，表明中性水，是健康池塘的典型特征。
Practice: Collect your own data from a simple experiment, such as counting the number of seeds that germinate each day over a week. Draw a bar chart and describe the pattern.
练习：从简单的实验中收集你自己的数据，例如统计一周内每天发芽的种子数量。绘制条形图并描述其规律。
3. Pie Charts and Proportions in Nutrition | 营养学中的饼图与比例
Pie charts show proportions of a whole. A nutritionist recommends a daily intake of 2000 kcal. The recommended breakdown is: Carbohydrates 50%, Protein 20%, Fats 30%. To draw a pie chart, convert each percentage to an angle: Angle = (percentage ÷ 100) × 360°.
饼图显示整体的比例。营养学家建议每日摄入2000千卡。推荐分布为：碳水化合物50%，蛋白质20%，脂肪30%。要绘制饼图，将每个百分比转换为角度：角度 = (百分比 ÷ 100) × 360°。
Calculations: Carbohydrates: 50% → 0.50 × 360° = 180°. Protein: 20% → 0.20 × 360° = 72°. Fats: 30% → 0.30 × 360° = 108°.
计算：碳水化合物：50% → 0.50 × 360° = 180°。蛋白质：20% → 0.20 × 360° = 72°。脂肪：30% → 0.30 × 360° = 108°。
Use a protractor to draw these sectors. A common exam question: ‘If a person consumes 3000 kcal, how many kcal come from protein?’ Answer: 20% of 3000 = 600 kcal. This links percentages to real diets.
用量角器绘制这些扇形。常见考题：“如果一个人摄入3000千卡，来自蛋白质的热量有多少？”答案：3000的20% = 600千卡。这便把百分比与实际饮食联系起来。
Try yourself: A school canteen records lunch choices: Pasta 45%, Salad 25%, Sandwich 30%. Draw a pie chart and find the angle for Pasta. Then, if 200 meals were served, how many were Pasta?
自己尝试：学校食堂记录午餐选择：意面45%，沙拉25%，三明治30%。绘制饼图，求意面的角度。然后，如果供应了200份餐，其中意面有多少份？
4. Line Graphs and Time Series in Geography | 地理中的折线图与时间序列
Line graphs are perfect for showing change over time. A geography student recorded the average monthly temperature (°C) in Cambridge: Jan 4, Feb 5, Mar 8, Apr 10, May 13, Jun 16, Jul 18, Aug 18, Sep 15, Oct 11, Nov 7, Dec 5. Plot these on a line graph.
折线图非常适合显示随时间的变化。一名地理学生记录了剑桥的月平均气温（°C）：一月4，二月5，三月8，四月10，五月13，六月16，七月18，八月18，九月15，十月11，十一月7，十二月5。将这些数据绘制成折线图。
Draw axes: month on the x-axis (categorical but ordered), temperature on the y-axis (from 0 to 20°C). Plot points and connect with straight lines. Analyse the trend: ‘In which month does the temperature peak? How much does the temperature increase from January to July?’
绘制坐标轴：x轴为月份（分类但有序），y轴为温度（从0到20°C）。描点并用直线连接。分析趋势：“哪个月温度最高？从一月到七月温度上升了多少？”
The peak is July at 18°C; the increase is 18 − 4 = 14°C. Such graphs help geographers describe climate patterns.
最高点在七月，18°C；上升幅度为18 − 4 = 14°C。这样的图帮助地理学家描述气候模式。
Practice: Find monthly rainfall data for your region and produce a line graph. Write two sentences comparing the wettest and driest months.
练习：查找你所在地区的月降雨量数据，绘制折线图。写两句话比较最湿和最干的月份。
5. Stem-and-Leaf Diagrams in Sports | 体育中的茎叶图
Stem-and-leaf diagrams organise numerical data while preserving each value. After a long jump competition, distances (in cm) for 15 athletes are recorded: 312, 326, 335, 342, 348, 355, 360, 365, 370, 378, 385, 390, 395, 402, 410. Use the hundreds and tens as the stem, and the units as the leaf.
茎叶图在组织数值数据的同时保留每个值。一次跳远比赛后，记录了15名运动员的成绩（厘米）：312, 326, 335, 342, 348, 355, 360, 365, 370, 378, 385, 390, 395, 402, 410。以百位和十位为茎，个位为叶。
Stem-and-leaf display:
茎叶图：
31 | 2
32 | 6
33 | 5
34 | 2 8
35 | 5
36 | 0 5
37 | 0 8
38 | 5
39 | 0 5
40 | 2
41 | 0
Key: 31 | 2 means 312 cm. Now it is easy to find the median: the 8th value in order is 365 cm. The diagram also shows the shape of the distribution.
键：31 | 2 表示312厘米。现在很容易找到中位数：排序后第8个值是365厘米。该图还展示了分布的形状。
Question: ‘What is the range?’ Range = 410 − 312 = 98 cm. Ask yourself: Which jump length occurred most frequently? (No mode, all different, but clustering around 360–390 cm).
问题：“极差是多少？”极差=410−312=98厘米。问问自己：哪个跳远长度出现得最频繁？（没有众数，所有值都不同，但集中在360–390厘米附近）。
6. Mean, Median and Mode in Science Experiments | 科学实验中的平均数、中位数与众数
When you repeat a measurement, averages help describe the typical result. In a physics experiment, the time for a pendulum to swing 10 times was recorded five times: 12.4 s, 12.1 s, 11.9 s, 12.3 s, 12.2 s. Find the mean, median and mode.
当你重复测量时，平均数帮助描述典型结果。在一次物理实验中，记录了一个摆锤摆动10次所用的时间，重复五次：12.4秒，12.1秒，11.9秒，12.3秒，12.2秒。求平均数、中位数和众数。
Order the data: 11.9, 12.1, 12.2, 12.3, 12.4. Median is the middle value: 12.2 s. There is no mode. Mean = (11.9+12.1+12.2+12.3+12.4) ÷ 5 = 60.9 ÷ 5 = 12.18 s.
排序数据：11.9, 12.1, 12.2, 12.3, 12.4。中位数是中间值：12.2秒。没有众数。平均数=(11.9+12.1+12.2+12.3+12.4)÷5=60.9÷5=12.18秒。
In a lab report, you might write: ‘The mean time was 12.18 s, close to the median, suggesting a symmetric distribution.’ Understanding which average to use in science is crucial: if there is an outlier, the median is better.
在实验报告中，你可以写：“平均时间为12.18秒，与中位数接近，表明分布对称。”理解在科学中使用哪种平均数至关重要：如果存在异常值，中位数更佳。
Try: Measure the length of 10 leaves from the same plant. Calculate the mean, median, mode and range. Discuss which measure best represents the leaf size.
尝试：测量同一株植物上10片叶子的长度。计算平均数、中位数、众数和极差。讨论哪种度量最能代表叶子的大小。
7. Range and Variability in Biology | 生物中的极差与变异性
Range shows the spread of data. A biologist measured the heights (cm) of two types of bean plants after 4 weeks. Variety A: 15, 18, 20, 22, 25. Variety B: 17, 19, 19, 21, 24. Compare their growth using range and mean.
极差显示数据的散布程度。一位生物学家在4周后测量了两种豆类植物的高度（厘米）。品种A：15, 18, 20, 22, 25。品种B：17, 19, 19, 21, 24。用极差和平均数比较它们的生长。
Mean A = (15+18+20+22+25) ÷ 5 = 20 cm. Mean B = (17+19+19+21+24) ÷ 5 = 20 cm. The means are equal, but range A = 25 − 15 = 10 cm, range B = 24 − 17 = 7 cm. Variety B’s heights are more consistent, while A has greater variability.
品种A的平均数=(15+18+20+22+25)÷5=20厘米。品种B的平均数=(17+19+19+21+24)÷5=20厘米。平均数相等，但品种A的极差=25−15=10厘米，品种B的极差=24−17=7厘米。品种B的高度更一致，而品种A的变异性更大。
Question: ‘If you wanted uniform crop height for easier harvesting, which variety would you choose?’ Answer: Variety B, due to its smaller range.
问题：“如果你需要均匀的作物高度以便于收割，你会选择哪个品种？”答案：品种B，因为其极差较小。
Practice: Measure hand spans of students in your class. Calculate the range and mean for boys and girls separately. Write a brief comparison.
练习：测量你班上学生的手掌跨度。分别计算男生和女生的极差与平均数。写一个简短的比较。
8. Interpreting Charts Critically – Media Examples | 批判性解读图表——媒体案例
Charts can be misleading. A bar chart shows the sales of two brands: Brand X bar height is 5 units, Brand Y is 4 units. But the vertical axis starts at 3, not 0. This exaggerates the difference, making Brand X appear twice as popular.
图表可能具有误导性。一张条形图显示两个品牌的销量：品牌X的条形高5单位，品牌Y高4单位。但纵轴的起点是3而不是0。这夸大了差异，使品牌X看起来比品牌Y受欢迎一倍。
What is the real ratio? If axis starts at zero, both bars would show heights proportional to actual values. Always check the scale and axis labels. In a pie chart, ask: does it total 100%? In a line graph, are the intervals equal?
真实比例是多少？如果纵轴从零开始，两个条形的高度将与实际值成比例。务必检查刻度和轴标签。在饼图中要问：它加起来是100%吗？在折线图中，间隔是否相等？
Task: Find a chart in a newspaper or online. Identify the title, axes, scale. Write one reason it could be misinterpreted. For instance, a 3D pie chart can distort sector sizes.
任务：在报纸或网上找一张图表。识别标题、坐标轴、刻度。写出一个可能被误解的原因。例如，3D饼图会扭曲扇形的大小。
Being a critical reader of statistics helps in subjects like media studies and economics, as well as everyday decision-making.
成为统计学的批判性读者对媒体研究和经济学等学科以及日常决策都有帮助。
9. Introduction to Probability in Weather and Games | 天气与游戏中的概率初步
Probability is the chance of an event happening, measured between 0 (impossible) and 1 (certain). Meteorologists say: ‘Probability of rain tomorrow is 0.3.’ This means 3 in 10 chance. If you flip a fair coin, P(Head) = 1/2.
概率是事件发生的可能性，介于0（不可能）和1（必然）之间。气象学家说：“明天下雨的概率是0.3。”这意味着十分之三的可能性。如果你抛一枚公平硬币，P(正面) = 1/2。
Experiment: Roll a six-sided die 30 times, record outcomes. Calculate the experimental probability of rolling a ‘4’. Compare with the theoretical probability (1/6 ≈ 0.167). Where would you place these on a probability scale: ‘Sun will rise tomorrow’ (1), ‘Snow in the Sahara’ (near 0)?
实验：掷一个六面骰子30次，记录结果。计算掷出“4”的实验概率。与理论概率（1/6 ≈ 0.167）比较。你会将这些事件放在概率尺度的哪个位置：“明天太阳会升起”（1），“撒哈拉沙漠下雪”（接近0）？
In geography, probability appears in risk assessment: ‘The chance of a flood this year is 5%.’ Linking probability to data from frequency tables reinforces understanding.
在地理中，概率出现在风险评估中：“今年发生洪水的可能性是5%。”将概率与频率表中的数据联系起来可以加深理解。
10. Integrated Problem-Solving Across Subjects | 多学科综合问题解决
Combine all skills in a cross-curricular task. Scenario: A school environmental club monitors recycling. Data collected over one week: Paper (kg): 5, 7, 6, 8, 9; Plastic (kg): 3, 4, 4, 5, 6; Glass (kg): 2, 1, 3, 2, 2. Answer these:
在一个跨课程任务中综合所有技能。情景：学校环保俱乐部监测回收情况。一周收集的数据：纸（公斤）：5, 7, 6, 8, 9；塑料（公斤）：3, 4, 4, 5, 6；玻璃（公斤）：2, 1, 3, 2, 2。回答以下问题：
a) Calculate the mean weight of paper recycled per day. (Mean = (5+7+6+8+9)÷5 = 35÷5 = 7 kg).
a) 计算每天回收纸张的平均重量。(平均数 = (5+7+6+8+9)÷5 = 35÷5 = 7 kg)。
b) Find the total weight of all recyclables on Wednesday if the data days are Mon–Fri. (Wed: Paper 6, Plastic 4, Glass 3 → total 13 kg).
b) 如果数据日为周一至周五，求周三所有可回收物的总重量。(周三：纸6，塑料4，玻璃3 → 总计13 kg)。
c) Create a double bar chart comparing the total paper and plastic for each day.
c) 创建一个比较每天纸和
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