Interdisciplinary Statistics Practice | 跨学科统计综合训练

📚 Interdisciplinary Statistics Practice | 跨学科统计综合训练

Statistics is not just a branch of mathematics — it is a powerful tool used in almost every subject you study. From recording the growth of a plant in biology, to comparing rainfall across regions in geography, to analysing game scores in physical education, statistical skills help you make sense of real-world data. This article provides cross‑curricular practice problems designed for Year 7 CAIE students, strengthening your ability to collect, organise, display and interpret data in multiple contexts.

统计学不仅仅是数学的一个分支——它几乎是你在每门学科中都会用到的强大工具。从记录生物课上的植物生长，到比较地理课中各地区的降雨量，再到分析体育比赛中的得分，统计学技能能帮助你理解真实世界的数据。本文为七年级 CAIE 学生设计了跨学科综合练习，旨在提升你在多种情境中收集、整理、展示和解读数据的能力。

1. Understanding Cross-curricular Statistics | 理解跨学科统计

Cross-curricular statistics means applying the same core skills — averages, charts, tables and data comparisons — to problems from science, geography, social studies, health and sports. It shows you that the mean, median, mode and range are not just abstract ideas; they help you answer genuine questions.

跨学科统计意味着将相同的核心技能——平均值、图表、表格及数据比较——应用于科学、地理、社会科学、健康和体育等领域的问题。它让你明白，平均数、中位数、众数和极差并非抽象概念，它们能帮助你回答真实的问题。

In Year 7 you are expected to calculate mean, median, mode and range, draw and interpret bar charts, line graphs, pie charts and frequency tables, and use tally marks. When these skills appear in a biology experiment or a geography field study, you must read the context carefully to decide which measure best describes the data.

在七年级，你需要学会计算平均数、中位数、众数和极差，绘制并解读条形图、折线图、饼图以及频率表，还会使用计数符号。当这些技能出现在生物实验或地理实地考察中时，你必须仔细阅读情境，决定哪种统计量最能描述数据。

2. Collecting Data in Science Experiments | 科学实验中的数据收集

A class measures the height of bean plants every two days to see how they grow. The data must be recorded in a table with clear headings and units. For example, ‘Day’ and ‘Height (cm)’. Good organisation makes the next step — drawing a line graph — much easier.

全班同学每两天测量一次豆苗的高度，观察它们如何生长。数据必须记录在表格中，表头清晰并标明单位，例如“天数”和“高度（厘米）”。良好的数据整理会让下一步——绘制折线图——容易得多。

Always include a title for the table, such as ‘Bean Plant Growth Over 10 Days’, and keep the independent variable (the one you change, like time) in the first column. The dependent variable (the one you measure) goes in the second column.

一定要为表格加上标题，如“豆苗十天生长记录”，并将自变量（你改变的变量，如时间）放在第一列。因变量（你测量的变量）放在第二列。

3. Analysing Temperatures from Geography | 地理气温数据分析

The table below shows the average midday temperatures in two cities during one week:

下表显示了一周内两个城市的平均正午温度：

Day	City A (°C)	City B (°C)
Mon	18	22
Tue	20	21
Wed	19	23
Thu	22	24
Fri	21	25

Calculate the mean temperature for each city. For City A, add 18 + 20 + 19 + 22 + 21 = 100, then divide by 5: the mean is 20 °C. For City B, the sum is 115, so the mean is 23 °C. The range for City A is 22 − 18 = 4 °C; for City B it is 5 °C. This tells you City B is warmer on average but also slightly more variable.

计算每个城市的平均温度。对于城市 A，将 18 + 20 + 19 + 22 + 21 相加得 100，再除以 5，平均值为 20 °C。城市 B 总和为 115，平均值为 23 °C。城市 A 的极差是 22 − 18 = 4 °C；城市 B 的极差为 5 °C。这说明城市 B 平均温度更高，但变化也稍大一些。

4. Sports Statistics: Averages and Range | 体育统计：平均值与极差

A long jump competition records the following distances (in metres) for five attempts by a Year 7 student: 3.2, 3.5, 2.9, 3.8, 3.1. To find the mean, add the distances: 3.2 + 3.5 + 2.9 + 3.8 + 3.1 = 16.5, then ÷ 5 = 3.3 m. The median (middle value when sorted: 2.9, 3.1, 3.2, 3.5, 3.8) is 3.2 m. The range is 3.8 − 2.9 = 0.9 m.

一名七年级学生的五次跳远成绩（米）如下：3.2, 3.5, 2.9, 3.8, 3.1。要计算平均数，将数据相加：3.2 + 3.5 + 2.9 + 3.8 + 3.1 = 16.5，然后 ÷ 5 = 3.3 米。中位数（排序后 2.9, 3.1, 3.2, 3.5, 3.8 的中间值）是 3.2 米。极差为 3.8 − 2.9 = 0.9 米。

The PE teacher might ask: ‘Which average best represents a typical jump?’. Here the mean (3.3 m) and median (3.2 m) are close, suggesting a fairly consistent performance. However, if one jump were an unusual 5.0 m, the mean would be pulled upwards, making the median more representative.

体育老师可能会问：“哪个平均值最能代表一次典型的跳远成绩？”这里平均数（3.3 米）和中位数（3.2 米）很接近，表明表现较为稳定。然而，如果其中一次跳远出现了异常的 5.0 米，平均数就会被拉高，此时中位数会更具代表性。

5. Interpreting Bar Charts in Social Studies | 社会科学中的条形图解读

A bar chart shows the number of students in each year group who walk, cycle, take the bus or travel by car. The chart has Year groups on the horizontal axis and frequency on the vertical axis, with different coloured bars for each mode of transport. You might be asked: ‘How many Year 7 students cycle to school?’ or ‘Which mode is most popular overall?’.

一张条形图显示了各年级选择步行、骑自行车、乘公交车或乘坐小汽车的学生人数。图中横轴是年级，纵轴是频数，不同颜色的条形代表不同的交通方式。你可能会被问到：“有多少名七年级学生骑自行车上学？”或“总体来看，哪种交通方式最受欢迎？”

When reading the bar chart, check the scale on the vertical axis carefully. If each small square represents 2 students, you must count the height correctly. Also, use the key to match colours with categories.

阅读条形图时，一定要仔细查看纵轴刻度。如果每个小格代表 2 名学生，就必须正确计算条形高度。此外，还要利用图例将颜色与类别对应起来。

6. Line Graphs for Growth in Biology | 生物生长线图

Line graphs are ideal for showing change over time, such as the growth of a seedling. Points are plotted for each measurement day and joined with straight lines. The steepness of the line tells you how fast the plant grew. A flat section might mean growth has paused.

折线图非常适合展示随时间的变化，例如幼苗的生长。每个测量日的数值被描点，并用直线连接。线的陡峭程度告诉你植物生长有多快。一段平坦的线可能意味着生长暂时停止了。

To draw a line graph, label the x‑axis ‘Time (days)’ and the y‑axis ‘Height (cm)’. Choose a scale that uses most of the grid. Plot each point as a small cross, then connect them with a ruler. Do not extend the line beyond the last data point unless the question asks you to estimate.

绘制折线图时，将 x 轴标记为“时间（天）”，y 轴标记为“高度（厘米）”。选择能充分利用网格的刻度。将每个点画成小叉号，然后用直尺连线。除非题目要求你进行估算，否则不要将线条延伸到最后一个数据点之外。

7. Pie Charts and Percentages in Health | 健康领域的饼图与百分比

A survey of 60 students asked what they eat for breakfast: 15 chose fruit, 20 cereal, 10 eggs, and 15 toast. To draw a pie chart, calculate the angle for each sector. Since a full circle is 360 °, each student represents 360 ° ÷ 60 = 6 °. Fruit: 15 × 6 ° = 90 °, cereal: 20 × 6 ° = 120 °, eggs: 10 × 6 ° = 60 °, toast: 15 × 6 ° = 90 °.

一项针对 60 名学生的调查问他们早餐吃什么：15 人选水果，20 人选麦片，10 人选鸡蛋，15 人选烤面包片。要绘制饼图，首先计算各扇形的角度。因为整个圆是 360 °，每名学生代表 360 ° ÷ 60 = 6 °。水果：15 × 6 ° = 90 °，麦片：20 × 6 ° = 120 °，鸡蛋：10 × 6 ° = 60 °，烤面包片：15 × 6 ° = 90 °。

You can also describe the data using fractions and percentages. For instance, cereal accounts for 20/60 = 1/3 ≈ 33.3% of the total. Using a protractor, draw each sector carefully and label it with the category and percentage.

你也可以用分数和百分比来描述数据。例如，麦片占 20/60 = 1/3 ≈ 33.3%。使用量角器仔细画出每个扇形，并标注类别和百分比。

8. Using Tally Charts and Frequency Tables | 使用计数符号与频率表

Tally charts are a quick way to record observations in the field, such as the types of birds seen on a nature walk. Each sighting is marked with a tally stroke; every fifth stroke is drawn diagonally across the previous four to make counting in groups of five easy. The totals are then transferred to a frequency table.

计数符号表是野外记录观察结果的一种快捷方式，比如记录自然散步中看到的鸟类种类。每次观察画一个计数符号；每第五个符号横向画在之前四个上面，形成一组五个，便于计数。最后将总数填入频数表。

A frequency table lists each category and its frequency. From this you can quickly find the mode — the category with the highest tally. For example, if ‘robin’ appeared 12 times, ‘sparrow’ 8 and ‘blackbird’ 5, the mode is robin.

频数表列出每个类别及其频数。由此你可以快速找出众数——也就是计数最高的类别。例如，如果“知更鸟”出现 12 次，“麻雀”8 次，“乌鸫”5 次，那么众数就是知更鸟。

9. Comparing Two Sets of Data | 比较两组数据

In health class, you might compare the resting heart rates (beats per minute) of swimmers and non‑swimmers. An effective comparison uses both a calculated average and a measure of spread. For example, swimmers: mean 68 bpm, range 10 bpm; non‑swimmers: mean 76 bpm, range 18 bpm. This suggests swimmers have lower and more consistent resting heart rates.

在健康课上，你可能会比较游泳者和不游泳者的静息心率（每分钟心跳数）。有效的比较会同时使用计算得出的平均值和离散程度。例如，游泳者：平均 68 bpm，极差 10 bpm；不游泳者：平均 76 bpm，极差 18 bpm。这表明游泳者的静息心率更低且更稳定。

When writing a comparison, always quote figures from the data. Say ‘The average for swimmers is 8 bpm lower than for non‑swimmers, and the range is 8 bpm smaller, showing less variation.’ Never just say ‘Swimmers are better’ without evidence.

在进行比较时，务必引用数据中的具体数字。可以说“游泳者的平均值比不游泳者低 8 bpm，极差也小 8 bpm，表明变化更小”。绝不能在没有证据的情况下只说“游泳者更好”。

10. Drawing Conclusions from Real-world Data | 从真实数据中得出结论

Data analysis is only complete when you write a short conclusion linking the statistics back to the original question. For instance, after analysing temperatures in City A and City B, you might conclude: ‘City B is consistently warmer; however, its temperature fluctuates more over the week, which could affect outdoor activity planning.’

只有当你写出一段简短的结论，将统计数据与原始问题联系起来时，数据分析才算完整。例如，在分析了城市 A 和城市 B 的温度后，你可以得出结论：“城市 B 持续更温暖；然而其温度在一周内波动更大，这可能影响户外活动的安排。”

A strong conclusion uses the words ‘mean’, ‘median’, ‘range’ or refers to chart features. Avoid vague statements. Instead, say ‘The mean midday temperature was 3 °C higher in City B, with a range of 5 °C compared to 4 °C in City A.’

一个好的结论会使用“平均数”、“中位数”、“极差”等词，或提及图表的特征。避免含糊的说法。相反，要说“城市 B 的平均正午温度高出 3 °C，极差为 5 °C，而城市 A 为 4 °C”。

11. Mixed Practice Problems | 综合练习题

Try these cross‑curricular questions. They combine skills you have practised above.

尝试以下跨学科问题，它们结合了上面练习过的技能。

Question 1 (Science): A student measured the length of a spring as she added weights. Her results: 0 kg → 8 cm, 1 kg → 10 cm, 2 kg → 12 cm, 3 kg → 14 cm. Draw a line graph and describe the relationship.

问题 1（科学）：一名学生在向弹簧上加砝码时测量了弹簧长度。结果：0 kg → 8 cm, 1 kg → 10 cm, 2 kg → 12 cm, 3 kg → 14 cm。请画出折线图并描述关系。

Question 2 (Geography): The annual rainfall in Town X for four years was 600 mm, 720 mm, 580 mm, 660 mm. Calculate the mean and the range.

问题 2（地理）：X 镇四年间的年降雨量分别是 600 mm, 720 mm, 580 mm, 660 mm。计算平均值与极差。

Question 3 (Social Studies): A bar chart shows the favourite sports of 100 students: Football 40, Netball 30, Athletics 20, Other 10. What percentage chose Netball? What is the mode?

问题 3（社会科学）：一张条形图显示了 100 名学生最喜爱的运动：足球 40，无挡板篮球 30，田径 20，其他 10。选择无挡板篮球的百分比是多少？众数是哪一项？

12. Tips for Cross-curricular Exams | 跨学科考试小贴士

Always read the context of the problem first. Identify which subject the data comes from — this will help you understand what the numbers represent and what units to use. Underline key numbers and words such as ‘mean’, ‘range’, ‘most common’ or ‘compare’.

一定要先阅读问题的背景。识别数据来自哪门学科——这有助于你理解数字代表什么以及使用什么单位。在“平均数”、“极差”、“最常见”或“比较”等关键数字和词语下划线。

Show all working clearly. Even if the calculation is simple, writing down the sum and division helps you avoid careless mistakes. Include the units in your final answer. When drawing charts, use a sharp pencil, label axes and keep bars equal in width.

清晰地展示所有计算过程。即使计算很简单，写下相加和相除的过程也能帮你避免粗心错误。最终答案要包含单位。绘制图表时，使用削尖的铅笔，标记坐标轴，并确保条形宽度一致。

Check that your answer makes sense in the context. For example, if you find a mean height of 150 cm for 7‑year‑olds, that is unrealistic — you may have misread the data or made a calculation error.

检查答案是否符合实际背景。例如，如果你算出 7 岁儿童的平均身高是 150 cm，这就不切实际——你可能看错了数据或存在计算错误。

Published by TutorHao | Statistics Revision Series | aleveler.com

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Interdisciplinary Statistics Practice | 跨学科统计综合训练