Year 7 Edexcel Statistics: Cross-curricular Integrated Practice | 跨学科综合题型训练

📚 Year 7 Edexcel Statistics: Cross-curricular Integrated Practice | 跨学科综合题型训练

Statistics is not just a set of techniques for handling numbers – it is a powerful language that connects almost every subject you study. When you collect plant growth data in science, compare population sizes in geography, record historical events in a timeline, or analyse your own sports performance, you are applying statistical thinking. This article presents a series of cross-curricular integrated tasks designed for Year 7 Edexcel Statistics. Each task blends statistical skills with real-world scenarios from other disciplines, helping you see how averages, charts, tables and data comparisons bring meaning to facts and figures. By working through these examples, you will strengthen both your mathematical understanding and your ability to use statistics as a tool for investigation in any subject.

统计学不仅仅是一套处理数字的方法，它还是一种强大的语言，几乎能连接你学习的每一个学科。当你在科学课上收集植物生长数据，在地理课上比较人口规模，在历史课中记录事件时间线，或者分析自己的运动成绩时，你都在运用统计思维。本文为 Year 7 Edexcel 统计课程设计了一系列跨学科综合任务。每个任务都把统计技能与来自其他学科的真实场景结合起来，帮助你看到平均数、图表、表格和数据比较如何赋予事实和数字以意义。通过这些练习，你将同时加深数学理解，并提高把统计学用作任何学科研究工具的能力。

1. Science Experiments: Plant Growth and Measurement | 科学实验：植物生长与测量

In a biology investigation, a Year 7 class planted bean seeds under four different light conditions: full sunlight, partial shade, artificial light, and no light. After 21 days, they measured the height of each plant in centimetres. The results for full sunlight were: 12, 14, 15, 11, 14, 16, 14, 13. The challenge is to organise this raw data, calculate the mean height, and choose the most suitable chart to compare the conditions. First, you must recognise that these eight numbers form a data set. Sorting them from smallest to largest (11, 12, 13, 14, 14, 14, 15, 16) helps you see the spread. The mean is found by adding all values (sum = 109) and dividing by the count (8), giving 13.625 cm. Because you are comparing categories of light, a bar chart is the ideal choice, with light condition on the horizontal axis and mean height on the vertical axis. Always label axes and give the chart a title.

在一次生物探究中，一个七年级班级在四种不同光照条件下种植了豆子：充足阳光、半阴、人工光和无光。21天后，他们测量了每株植物的高度（厘米）。充足阳光组的结果是：12, 14, 15, 11, 14, 16, 14, 13。任务是将这些原始数据整理好，计算平均高度，并选择最合适的图表来比较不同条件。首先你要认识到这八个数字构成一个数据集。从小到大排序（11, 12, 13, 14, 14, 14, 15, 16）有助于观察分布。平均数算法：所有值相加（总和=109）除以个数（8），得到13.625厘米。由于你要比较不同光照类别，条形图是最理想的选择，横轴为光照条件，纵轴为平均高度。务必标注坐标轴并给出图表标题。

A further step could be finding the median and mode. For this data set, the median (the middle value when ordered) is 14 cm, and the mode (most frequent value) is also 14 cm. Notice that the mean is slightly lower than the median, which suggests a small left skew – useful when discussing reliability of data in science. You could also discuss how to deal with anomalous results, such as a plant that might have been accidentally broken.

进一步可找出中位数和众数。对于这组数据，中位数（排序后中间值）是14厘米，众数（出现最频繁的值）也是14厘米。注意到平均数略低于中位数，说明数据有轻微左偏——这在科学中讨论数据可靠性时很有用。你还可以讨论如何处理异常结果，比如一株可能意外折断的植物。

2. Geography: Comparing City Populations | 地理：城市人口比较

A geography project asks students to compare the populations of five UK cities: London (8.9 million), Birmingham (1.1 million), Leeds (0.8 million), Glasgow (0.6 million), and Cardiff (0.36 million). Instead of just looking at raw numbers, a statistician would ask: what is the best way to present this data? A bar chart with population on the y-axis makes it easy to see that London dominates. However, the difference is so large that the other bars would look tiny. One solution is to use a pictogram, where one symbol represents, say, 0.2 million people. London would have 44.5 symbols, Birmingham 5.5, and so on. This visual approach makes comparisons more engaging. The class could also calculate the range of the data: 8.9 million minus 0.36 million equals 8.54 million, showing huge variation. Another useful diagram is a pie chart, but only if the total population is known. Here the total is 11.76 million, so London’s sector is (8.9 ÷ 11.76) × 360° ≈ 272°, a massive slice that highlights its dominance.

一个地理项目要求学生比较五个英国城市的人口：伦敦（890万）、伯明翰（110万）、利兹（80万）、格拉斯哥（60万）和卡迪夫（36万）。统计学家会问：呈现这些数据的最佳方式是什么？以人口为纵轴的条形图很容易看出伦敦的主导地位，但差异如此之大，其他柱子会显得极小。一种解决方案是使用象形图，每个符号代表20万人，伦敦将有44.5个符号，伯明翰5.5个，依此类推。这种视觉方法使比较更有吸引力。学生还可以计算数据的全距：890万减去36万等于854万，显示巨大差异。另一种有用的图表是饼图，但需要已知总人口。这里总人口为1176万，因此伦敦的扇区角度为 (890 ÷ 1176) × 360° ≈ 272°，一大块扇形突出了其主导地位。

For a deeper cross-curricular link, you could then research why populations differ so much: historical trade, industrialisation, and modern services. Statistics becomes a starting point for geographical enquiry, not just a number-crunching exercise.

为了更深入的跨学科联系，你可以接着研究人口差异为何如此之大：历史贸易、工业化以及现代服务业。统计学成为地理探究的起点，而不仅仅是数字运算练习。

3. History: Frequency of Inventions by Century | 历史：各世纪发明频率

A history lesson on the Industrial Revolution lists key inventions and their dates. Students convert these into a frequency table grouped by century. For example, between 1700 and 1799: spinning jenny (1764), steam engine improvements (1765), cotton gin (1793). Between 1800 and 1899: electric light bulb (1879), telephone (1876), automobile (1885). They record the frequency of inventions per century and draw a line graph to show how inventive activity changed. This kind of time series line graph is new to many Year 7s but vital. The horizontal axis marks the centuries (17th, 18th, 19th, 20th), and the vertical axis the number of inventions. If there are zero inventions in the 17th century but six in the 18th, the line rises sharply. Students must be careful to plot points accurately and use a ruler to join them. They should also discuss why frequencies increase – better education, funding, scientific method. This task merges chronological thinking with statistical plotting.

一节关于工业革命的历史课列出了关键发明及其日期。学生将这些转换成按世纪分组的频数表。例如，1700年至1799年间：珍妮纺纱机（1764）、蒸汽机改进（1765）、轧棉机（1793）。1800年至1899年间：电灯泡（1879）、电话（1876）、汽车（1885）。他们记录每个世纪的发明频数，并绘制折线图来展示发明活动的变化。这种时间序列折线图对许多七年级学生来说较新但至关重要。横轴标示世纪（17、18、19、20世纪），纵轴标示发明数量。如果17世纪发明数为零，18世纪为六项，则线条急剧上升。学生须小心准确标点，并用直尺连接。他们还应讨论频率为何增加——更好的教育、资金、科学方法。这一任务将时序思维与统计绘图融为一体。

An extension could be calculating the mean number of inventions per century over the whole period, or comparing the mode of invention types (transport, communication, manufacturing). This encourages categorisation of data, much like in data handling cycles.

拓展练习可以计算整个时期每世纪的平均发明数量，或比较发明类型的众数（交通、通信、制造）。这鼓励了数据分类，类似于数据处理循环中的操作。

4. Physical Education: Analysing Sprint Times | 体育：分析短跑成绩

Your PE teacher records the 100-metre sprint times (in seconds) for ten students: 14.2, 15.1, 13.8, 16.0, 14.5, 14.2, 15.6, 13.9, 14.8, 14.2. The task is to calculate the mean time, find the median and mode, and decide which average best represents the class’s performance. The mean is (sum 145.3) ÷ 10 = 14.53 s. The sorted list (13.8, 13.9, 14.2, 14.2, 14.2, 14.5, 14.8, 15.1, 15.6, 16.0) shows the median is between the 5th and 6th values – (14.2 + 14.5) ÷ 2 = 14.35 s. The mode is 14.2 s, as it appears three times. Notice the mean is pulled higher by the slowest time of 16.0 s. In sport, the median is often preferred because it is unaffected by one very slow runner. This is a great illustration of choosing the right average for a context. A stem-and-leaf diagram could also be used to display the times compactly, with stems 13, 14, 15, 16.

你的体育老师记录了十名学生的100米短跑时间（秒）：14.2, 15.1, 13.8, 16.0, 14.5, 14.2, 15.6, 13.9, 14.8, 14.2。任务是计算平均时间，找出中位数和众数，并确定哪个平均数最能代表班级表现。平均数 = (总和145.3) ÷ 10 = 14.53秒。排序后列表 (13.8, 13.9, 14.2, 14.2, 14.2, 14.5, 14.8, 15.1, 15.6, 16.0) 显示中位数位于第5和第6个值之间——(14.2 + 14.5) ÷ 2 = 14.35秒。众数为14.2秒，出现三次。注意到平均数被最慢的16.0秒拉高了。在体育中，中位数往往更受欢迎，因为它不受个别极慢选手的影响。这很好地说明了如何根据情境选择合适的平均数。也可使用茎叶图紧凑地显示时间，茎为13,14,15,16。

You could also calculate the range (16.0 – 13.8 = 2.2 s), showing the spread of ability. For a cross-curricular challenge, link to biology by investigating how heart rate and muscle fatigue affect times, and design a follow-up experiment with statistical analysis.

你还可以计算全距（16.0 – 13.8 = 2.2秒），显示能力的差异。作为跨学科挑战，联系生物学探究心率和肌肉疲劳如何影响成绩，并设计一个带有统计分析的后续实验。

5. Environmental Science: Monthly Rainfall Patterns | 环境科学：月降水量模式

Environmental science classes often collect weather data. Suppose a school weather station recorded monthly rainfall (in mm) over a year: Jan 72, Feb 55, Mar 48, Apr 41, May 43, Jun 38, Jul 45, Aug 52, Sep 67, Oct 79, Nov 85, Dec 88. The question is: which graph best reveals the seasonal pattern? A bar chart is possible, but a line graph is better for showing trends over time. By plotting the months on the x-axis and rainfall on the y-axis, we see a U-shaped curve: higher rainfall in winter, lower in spring/summer. Students can then compute the total annual rainfall (sum = 713 mm) and the mean monthly rainfall (713 ÷ 12 ≈ 59.4 mm). They might also identify the driest month (June, 38 mm) and wettest (December, 88 mm) and calculate the range (88 – 38 = 50 mm). This task links data presentation with climate interpretation. You could next compare the data with another city’s rainfall pattern, using dual line graphs on the same axes – a key skill.

环境科学课上常收集天气数据。假设学校气象站记录了一年的月降水量（毫米）：一月72，二月55，三月48，四月41，五月43，六月38，七月45，八月52，九月67，十月79，十一月85，十二月88。问题在于：哪种图表最能揭示季节模式？条形图可以，但折线图更能显示随时间变化的趋势。以月份为横轴、降水量为纵轴，我们得到一个U形曲线：冬季降水多，春夏季较少。然后学生可计算年总降水量（总和=713毫米）和月平均降水量（713÷12≈59.4毫米）。他们还可找出最干燥的月份（六月，38毫米）和最潮湿的月份（十二月，88毫米），并计算全距（88–38=50毫米）。这一任务将数据呈现与气候解读联系起来。接下去可以比较另一座城市的降水模式，在同一坐标轴上绘制双折线图——这是一项关键技能。

For an extended investigation, students can discuss outliers – maybe June had unusually low rain because of a heatwave – and how that affects the mean. This builds critical thinking about data reliability.

作为扩展探究，学生可以讨论异常值——也许六月因热浪而异常少雨——以及这如何影响平均数。这建立了关于数据可靠性的批判性思维。

6. Economics: Pocket Money Survey | 经济学：零花钱调查

You decide to survey 30 classmates about their weekly pocket money and present the results in a pie chart. The responses (in £) were: 1, 2, 2, 1.5, 3, 2, 2.5, 1, 2, 3, 4, 2, 2.5, 1, 1.5, 2, 3, 2, 1, 1.5, 2, 2, 5, 2.5, 2, 3, 1.5, 2, 4, 2. First, create a frequency table with categories: £1, £1.5, £2, £2.5, £3, £4, £5. Count the tallies: £1 (4), £1.5 (4), £2 (11), £2.5 (3), £3 (4), £4 (2), £5 (1). The mode is £2, which is important for understanding typical pocket money. For a pie chart, calculate the angle for each sector. Total frequency = 29? Wait, recount: 4+4+11+3+4+2+1 = 29. We need 30, so assume one is missing – check data. Let’s adjust: add one £2 to make 12, total 30. Then £2 sector is (12 ÷ 30) × 360° = 144°. This visual will show that over a third of students receive exactly £2. The mean can also be calculated by multiplying each value by its frequency, summing, and dividing by 30, leading to approximately £2.18. This shows the mean is slightly above the mode, suggesting some higher values pull it up.

你决定调查30位同学的每周零花钱，并用饼图呈现结果。回答（单位：英镑）为：1, 2, 2, 1.5, 3, 2, 2.5, 1, 2, 3, 4, 2, 2.5, 1, 1.5, 2, 3, 2, 1, 1.5, 2, 2, 5, 2.5, 2, 3, 1.5, 2, 4, 2。首先创建频数表，类别为：£1, £1.5, £2, £2.5, £3, £4, £5。计数：£1(4), £1.5(4), £2(11), £2.5(3), £3(4), £4(2), £5(1)。众数为£2，对了解典型零花钱很重要。为饼图计算每个扇区角度。总频数=29？重新计算：4+4+11+3+4+2+1=29。需要30，假设遗漏一个——数据调整：加一个£2使成12，总数30。则£2扇区为 (12÷30)×360°=144°。这张图将显示超过三分之一的学生恰好得到£2。还可以计算平均数：每值乘以频数再求和，除以30，约得£2.18。表明平均数略高于众数，一些较高值拉高了平均数。

Linking to economics, you could discuss how inequality in pocket money might reflect family income and budgeting. Statistics thus provides evidence for social discussion. Also, ensure students know how to interpret a pie chart: large sectors mean common categories, while small sectors mean rare ones.

联系经济学，可以讨论零花钱不平等如何反映家庭收入和预算安排。因此统计学为社会讨论提供了证据。同时，确保学生知道如何解读饼图：大扇区表示常见类别，小扇区表示罕见类别。

7. Health & Nutrition: Calorie Intake and Exercise | 健康与营养：卡路里摄入与运动

A health project asks students to record their daily calorie intake and minutes of exercise for each of seven days. The data for one student is shown in a paired table:

Day	Calories (kcal)	Exercise (min)
Mon	2100	30
Tue	2300	20
Wed	1950	45
Thu	2500	10
Fri	2200	25
Sat	2600	5
Sun	2400	15

The task is to investigate whether there is a relationship between calorie intake and exercise. A scatter graph is the correct tool. Plot each day as a point, with exercise minutes on the x-axis and calories on the y-axis. The points might show a negative correlation: as exercise increases, calorie intake tends to be slightly lower, perhaps because the student was less hungry or more careful on active days. Students should draw a line of best fit – roughly showing the trend – but not expect perfect correlation. They can compute the mean calories (≈ 2293 kcal) and mean exercise (≈ 21.4 min) to understand the centre of the data. This combines scatter diagrams, correlation, and mean calculations, linking directly to Biology and PSHE topics on balanced lifestyles.

一个健康项目要求学生记录一周七天每天的热量摄入和运动分钟数。某学生的数据成对列于表中。任务是探究热量摄入和运动之间是否存在关系。散点图是正确的工具。将每一天作为一个点，横轴为运动分钟数，纵轴为卡路里。这些点可能显示出负相关：随着运动增加，热量摄入往往稍低，可能是因为学生在活跃的日子里不那么饿或更注意饮食。学生应画出一条最佳拟合线——大致显示趋势——但不期望完美相关。他们可以计算平均热量（≈2293千卡）和平均运动时间（≈21.4分钟）以了解数据的中心。这结合了散点图、相关性和平均数计算，与生物学和PSHE关于平衡生活方式的主题直接相连。

Careful interpretation is needed: a scatter graph does not prove cause and effect; it only suggests an association. This is a key statistical lesson for Year 7.

需要仔细解读：散点图不能证明因果关系，只能提示关联。这对7年级而言是一个关键的统计学认知。

8. Languages: Word Frequency in a Short Text | 语言：短文本中的词频

In English or a modern foreign language lesson, students count the frequency of words in a paragraph. Let’s take a simple English paragraph: “The cat sat on the mat. The cat was happy. The mat was soft. The cat and the mat were clean.” By tallying, we get: The – 6, cat – 3, mat – 3, sat – 1, on – 1, was – 2, happy – 1, soft – 1, and – 1, were – 1, clean – 1. A frequency table and bar chart quickly reveal that ‘the’ is most common. The mode is ‘the’. What about average word length? Count letters per word and create a grouped frequency table: 1–3 letters, 4–6 letters, etc. This links to literacy and helps understand vocabulary complexity. Students could compare word frequency in different texts – for example, a science textbook vs a story – and spot that academic texts use longer, less frequent words. The statistical skills here are tallying, designing frequency tables, and choosing appropriate class intervals for grouping data.

在英语或外语课上，学生统计一段文字中的词频。以一段简单英文为例：”The cat sat on the mat. The cat was happy. The mat was soft. The cat and the mat were clean.” 通过画记，我们得到：The – 6, cat – 3, mat – 3, sat – 1, on – 1, was – 2, happy – 1, soft – 1, and – 1, were – 1, clean – 1。频数表和条形图很快显示‘the’是最常见的。众数是‘the’。平均词长呢？计算每个单词的字母数并创建分组频数表：1–3字母，4–6字母等。这关联到读写能力，帮助理解词汇复杂性。学生可以比较不同文本中的词频——例如科学课本与故事——并发现学术文本使用更长、出现频率更低的词。这里涉及的统计技能有画记、设计频数表，以及为数据分组选择适当的组距。

For an extension, ask pupils to find the median word length from the raw list, reinforcing the difference between raw and grouped data. This task demonstrates how statistics applies to humanities, not just mathematics.

作为拓展，要求学生从原始单词列表中找出词长的中位数，以此强化原始数据与分组数据的区别。这个任务展示了统计学如何应用于人文学科，而不仅仅是数学。

9. Art & Design: Colour Preferences Survey | 艺术与设计：颜色偏好调查

In an art lesson, students conduct a survey on favourite colours from a list of five: red, blue, green, yellow, purple. They ask 25 classmates and record the frequency: red 5, blue 8, green 6, yellow 4, purple 2. The challenge is to display this data using a pictogram, where one coloured circle represents one student. This makes a visually appealing chart that links directly with artistic design. Next, they calculate the fraction and percentage of students liking blue: (8 ÷ 25) × 100% = 32%. They can then draw a pie chart, first finding each angle: blue 8/25 × 360° ≈ 115°, red 72°, green 86°, yellow 58°, purple 29°. The pie chart must be labelled or given a key. Students might also discuss the mode (blue) and why blue might be popular – linking to colour psychology. The statistical learning covers categorical data, frequency, percentage, angle calculation, and effective visual representation. To connect with design, they can create a poster presenting their findings artistically.

在艺术课上，学生从五种颜色（红、蓝、绿、黄、紫）中进行最喜欢颜色的调查。他们询问了25位同学，记录频数：红5，蓝8，绿6，黄4，紫2。挑战是用象形图展示数据，每个彩色圆圈代表一个学生。这将形成一张与艺术设计直接相关的吸引人的图表。接着，他们计算喜欢蓝色的分数和百分比：(8÷25)×100%=32%。然后可以绘制饼图，先求每个角度：蓝8/25×360°≈115°，红72°，绿86°，黄58°，紫29°。饼图必须标注或给出图例。学生还可以讨论众数（蓝色）以及为什么蓝色可能受欢迎——联系颜色心理学。该统计学习涵盖了分类数据、频数、百分比、角度计算和有效的视觉呈现。为了与设计联系，他们可以制作一张艺术化地呈现结果的海报。

An additional layer could involve comparing preferences between boys and girls using a dual bar chart, introducing the idea of comparing data sets – a foundational skill for advanced statistics.

另一个层次可以涉及使用复式条形图比较男生和女生的偏好，引入比较数据集的理念——这是高级统计学的基础技能。

10. Technology: Screen Time Analysis | 科技：屏幕使用时间分析

Many Year 7 students track their daily screen time (in hours) for a week. The data for one student: 2.5, 3.0, 1.5, 4.0, 3.5, 2.0, 5.0. The teacher suggests grouping the data into intervals: 1.0–2.0, 2.1–3.0, 3.1–4.0, 4.1–5.0. The frequency counts become: 1.0–2.0: 2, 2.1–3.0: 2, 3.1–4.0: 2, 4.1–5.0: 1. Students then draw a histogram-like block graph (with equal width bars) representing grouped data. They can estimate the mean by using the midpoint of each interval: midpoint 1.5 for 1.0–2.0, 2.55 for 2.1–3.0, 3.55 for 3.1–4.0, 4.55 for 4.1–5.0. Multiply each midpoint by its frequency, sum, and divide by total frequency (7): (1.5×2 + 2.55×2 + 3.55×2 + 4.55×1) ÷ 7 = (3 + 5.1 + 7.1 + 4.55) ÷ 7 = 19.75 ÷ 7 ≈ 2.82 hours, close to the true mean of actual data (21.5 ÷ 7 ≈ 3.07). Discuss why grouping loses precision. This task ties into digital citizenship discussions about healthy technology use while teaching grouped frequency and approximation.

许多七年级学生跟踪自己一周的每日屏幕使用时间（小时）。某学生的数据为：2.5, 3.0, 1.5, 4.0, 3.5, 2.0, 5.0。老师建议将数据分组为以下区间：1.0–2.0, 2.1–3.0, 3.1–4.0, 4.1–5.0。频数统计为：1.0–2.0: 2, 2.1–3.

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Year 7 Edexcel Statistics: Cross-curricular Integrated Practice | 跨学科综合题型训练