Cross-Curricular Integrated Practice for Statistics | 统计学跨学科综合题型训练

📚 Cross-Curricular Integrated Practice for Statistics | 统计学跨学科综合题型训练

Statistics is not just a subject on its own – it is a toolkit you use in science experiments, geography investigations, PE lessons and even when playing games. This article is designed for Year 8 CCEA students who want to strengthen their ability to tackle statistics problems that cross over into different subjects. By working through real scenarios and guided examples, you will learn how to collect data, choose the right graph, find averages and spot patterns, no matter which subject area the question comes from.

统计学并不仅仅是一门独立的学科——它是在科学实验、地理探究、体育课甚至游戏中都会用到的工具。本文为Year 8 CCEA学生设计，帮助你提升解决跨学科统计问题的能力。通过真实情境和指导性例题，你将学会如何收集数据、选择合适的图表、计算平均数并发现规律，无论题目涉及哪个学科。

1. What Are Cross-Curricular Statistical Problems? | 什么是跨学科统计问题？

A cross-curricular statistical problem takes a skill you learn in maths – such as drawing a bar chart or finding the median – and applies it to a situation in another subject. For example, you might be asked to analyse temperature readings from a geography case study or compare jump distances in a PE lesson. The numbers and contexts change, but the statistical thinking stays the same.

跨学科统计问题将你在数学中学到的技能（例如绘制条形图或求中位数）应用到另一门学科的情境中。比如，你可能需要分析地理案例研究中的温度读数，或者比较体育课上的跳远成绩。数据和背景不同，但统计思维一脉相承。

These problems test whether you truly understand the concepts, rather than just following a recipe. You need to decide which graph to use, whether the mean or median is more appropriate, and how to explain your findings in the context of the subject. This article will build your confidence by working through examples from science, geography, PE, history and environmental studies.

这类问题考查你是否真正理解概念，而不只是照搬套路。你需要决定使用哪种图表、平均数还是中位数更合适，以及如何在学科背景下解释你的发现。本文将通过科学、地理、体育、历史和环境研究的实例逐步提升你的信心。

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2. Collecting and Organising Data in Science | 科学中的数据收集与整理

In a science investigation, you often record measurements over time. Suppose you heated a beaker of water and measured the temperature every minute. Your results are shown in the table below.

在科学探究中，你经常需要在一段时间内记录测量值。假设你加热一杯水，每分钟测量一次温度，得到如下结果。

Time (min)	0	1	2	3	4
Temperature (°C)	20	23	25	28	30

From these data, you can calculate the range and the median temperature.

根据这些数据，你可以计算温度的极差和中位数。

Step 1: To find the median, list the temperatures in order: 20, 23, 25, 28, 30. The middle value is 25 °C.

第1步：要找中位数，先按顺序列出温度值：20、23、25、28、30。中间值是25 °C。

Step 2: The range is the difference between the highest and lowest values: 30 – 20 = 10 °C. This tells you how much the temperature varied during the experiment.

第2步：极差是最高值与最低值之差：30 – 20 = 10 °C。它告诉你实验期间温度变化了多少。

Being able to pick out these summaries helps a scientist describe their results clearly. Remember, the median is not affected by extreme values, which makes it useful when data are skewed.

能够提取这些汇总指标有助于科学家清晰描述实验结果。记住，中位数不受极端值影响，因此在数据偏斜时很有用。

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3. Drawing and Interpreting Bar Charts in Geography | 地理中的条形图绘制与解读

Geography often presents rainfall or population data that are best displayed in a bar chart. Imagine you have collected the average annual rainfall for four different cities.

地理学中经常需要展示降雨量或人口数据，最适合用条形图呈现。假设你收集了四个不同城市的年均降雨量。

City	Rainfall (mm)
Belfast	950
Cardiff	1150
Edinburgh	670
London	580

Task: Draw a bar chart and find the mode of the rainfall data.

任务：绘制条形图，并找出降雨量数据的众数。

When you draw the bar chart, each city gets a bar with height equal to its rainfall. The mode is the value that appears most often. Look carefully – Belfast and London have unique values, but does one rainfall amount repeat? In this set every value is different, so there is no mode. Sometimes the mode can be taken from the tallest bar, but only if the data contain repeats. Always check the raw numbers before stating the mode.

绘制条形图时，每个城市对应一个条形，高度等于降雨量。众数是出现次数最多的值。仔细观察——贝尔法斯特和伦敦的数值都独一无二，是否有某个降雨量重复出现？这组数据中每个值都不同，因此没有众数。有时众数可以从最高的条形推断，但前提是数据中有重复值。在确认众数之前务必检查原始数据。

This example reminds you not to assume there is always a mode just because you have drawn a chart. Statistical thinking requires looking at the data, not just the picture.

这个例子提醒你，不要因为画了图就认为一定存在众数。统计思维要求你审视数据本身，而不仅仅是图片。

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4. Using Mean, Median and Mode in PE | 体育中的平均数运用

PE teachers often use statistics to track performance. Seven students measured their standing long jump distance (in metres): 3.2, 3.5, 3.0, 3.5, 3.4, 3.6, 3.5.

体育老师常用统计数据来追踪表现。七名学生测量了立定跳远距离（单位：米）：3.2、3.5、3.0、3.5、3.4、3.6、3.5。

Let’s calculate all three averages and see what they tell us.

我们来计算所有三种平均数，看看它们揭示什么。

Step 1: Mean. Add the values: 3.2 + 3.5 + 3.0 + 3.5 + 3.4 + 3.6 + 3.5 = 24.7. Divide by 7:

Mean = 24.7 ÷ 7 ≈ 3.53 m (to 2 d.p.)

第1步：均值。将所有值相加：3.2 + 3.5 + 3.0 + 3.5 + 3.4 + 3.6 + 3.5 = 24.7。除以7：

均值 = 24.7 ÷ 7 ≈ 3.53 米（保留两位小数）

Step 2: Median. Order the data: 3.0, 3.2, 3.4, 3.5, 3.5, 3.5, 3.6. The fourth value is 3.5, so the median is 3.5 m.

第2步：中位数。将数据排序：3.0、3.2、3.4、3.5、3.5、3.5、3.6。第四个值是3.5，因此中位数为3.5米。

Step 3: Mode. The value 3.5 appears three times, more than any other, so the mode is 3.5 m.

第3步：众数。3.5出现了三次，次数最多，因此众数为3.5米。

In this case the mean is slightly higher than the median and mode. If the coach wants to know a typical performance, the median or mode might be better because they are less affected by a low score like 3.0 m.

在这种情况下，均值略高于中位数和众数。如果教练想知道典型成绩，中位数或众数可能更好，因为它们受3.0米这种低分的影响较小。

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5. Climate Graphs and Line Graphs in Geography | 地理中的气候图和折线图

A climate graph uses a line to show temperature and bars for rainfall across months. This time we focus on interpreting a line graph of average monthly temperatures in a coastal town.

气候图通常用折线表示温度，用条形表示各月降雨量。这次我们重点解读某个沿海小镇各月平均气温的折线图。

Month	J	F	M	A	M	J	J	A	S	O	N	D
Temp (°C)	5	6	8	11	14	17	19	19	16	12	8	6

Question: Which month has the highest average temperature, and what is the temperature range across the year?

问题：哪个月份的平均气温最高？全年的温度极差是多少？

Scan the table to find the maximum value: July and August both record 19 °C, so the warmest months are July and August. The range is 19 – 5 = 14 °C. A line graph would make it easy to see the gradual rise and fall and to spot the plateau in summer. When describing the trend, you could say “temperatures increase from January to July, remain steady in July and August, then decrease.”

浏览表格找到最大值：七月和八月都是19 °C，因此最温暖的月份是七月和八月。极差为19 – 5 = 14 °C。折线图能直观地展示缓慢的升降和夏季的平台期。描述趋势时，你可以说“气温从一月到七月逐渐上升，七八月保持平稳，然后下降。”

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6. Pie Charts in Environmental Studies | 环境研究中的饼图

Environmental studies often use pie charts to show proportions. A school carried out a waste audit and found: paper 40%, plastic 30%, food waste 20%, other 10%.

环境研究常使用饼图来展示比例。某学校进行了一次垃圾审计，发现：纸类40%、塑料30%、厨余20%、其他10%。

Question: If the total waste collected was 250 kg, calculate the weight of each category. What fraction of the waste is recyclable if paper and plastic can be recycled?

问题：如果收集的垃圾总量为250千克，计算每类的重量。如果纸类和塑料可回收，可回收物占总垃圾的几分之几？

Step 1 – Paper: 40% of 250 kg = 0.40 × 250 = 100 kg.

第1步 – 纸类：250千克的40% = 0.40 × 250 = 100千克。

Step 2 – Plastic: 30% of 250 kg = 0.30 × 250 = 75 kg.

第2步 – 塑料：250千克的30% = 0.30 × 250 = 75千克。

Step 3 – Food waste: 20% of 250 kg = 0.20 × 250 = 50 kg.

第3步 – 厨余：250千克的20% = 0.20 × 250 = 50千克。

Step 4 – Other: 10% of 250 kg = 0.10 × 250 = 25 kg. Always check your totals add up: 100+75+50+25 = 250 kg.

第4步 – 其他：250千克的10% = 0.10 × 250 = 25千克。务必检查总和：100+75+50+25 = 250千克。

Recyclable material = Paper + Plastic = 40% + 30% = 70%. As a fraction, 70% = 70/100 = 7/10. So 7/10 of the waste can be recycled. This kind of calculation helps a school set environmental targets.

可回收物 = 纸类 + 塑料 = 40% + 30% = 70%。以分数表示，70% = 70/100 = 7/10。因此十分之七的垃圾可以回收。这种计算有助于学校设定环境目标。

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7. Probability in Games and Random Events | 游戏与随机事件的概率

Probability is the branch of mathematics that deals with chance, and it appears in board games, weather forecasts and science experiments. Consider a bag containing 3 red marbles and 5 blue marbles. You pick one marble at random.

概率是研究机会大小的数学分支，出现在棋盘游戏、天气预报和科学实验中。考虑一个袋子，装有3个红色弹珠和5个蓝色弹珠。你随机抽取一个。

Question: What is the probability that the marble is red? Express your answer as a fraction, a decimal and a percentage.

问题：抽到红色弹珠的概率是多少？请用分数、小数和百分数表示。

Total outcomes = 3 + 5 = 8. The number of ways to pick a red marble is 3. So the probability is:

P(red) = 3/8

As a decimal: 3 ÷ 8 = 0.375. As a percentage: 0.375 × 100% = 37.5%. Always make sure the probability is between 0 and 1 inclusive. A probability of 0 means impossible, 1 means certain.

总结果数 = 3 + 5 = 8。抽出红色弹珠的方式有3种。因此概率为：

P(红色) = 3/8

化为小数：3 ÷ 8 = 0.375。化为百分数：0.375 × 100% = 37.5%。务必确保概率值在0到1之间（含端点）。概率为0表示不可能，1表示必然发生。

Understanding probability helps you predict how often an event might happen if you repeat the experiment many times. For example, if you pulled a marble 80 times, you would expect about 3/8 × 80 = 30 red marbles.

理解概率有助于预测重复多次实验时事件发生的频率。例如，如果你抽80次弹珠，预计大约会有 3/8 × 80 = 30 次是红色的。

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8. Comparing Data Using Statistics Across Subjects | 跨学科数据比较

When you have two sets of data, statistics let you compare them fairly. A teacher recorded the times (in seconds) that two Year 8 classes took to complete a 200 m sprint: Class A: 28, 30, 29, 31, 32; Class B: 26, 33, 28, 30, 31.

当你有两组数据时，统计可以帮助你公平地比较。一位老师记录了两个8年级班级完成200米短跑的时间（秒

Published by TutorHao | Year 8 统计 Revision Series | aleveler.com

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