📚 Year 7 CCEA Statistics: Interdisciplinary Practice Problems | Year 7 CCEA 统计：跨学科综合题型训练
Statistics is not just about numbers in a textbook – it appears in science experiments, geography investigations, sports results, and everyday decisions. This article presents a series of practice problems that combine Year 7 statistical skills with other subjects. By working through examples involving bar charts, averages, probability, questionnaires, and more, you will learn how to collect, organise, and interpret data across different contexts. Each section includes an explanation in English immediately followed by its Chinese equivalent, helping you build both statistical understanding and bilingual confidence.
统计学不只是教科书上的数字——它出现在科学实验、地理调查、体育成绩和日常决策中。本文提供了一系列将七年级统计技能与其他学科相结合的综合练习题。通过处理涉及条形图、平均数、概率、问卷设计等例题，你将学会如何在不同情境中收集、整理和解读数据。每个部分都先给出英文解释，紧接着给出对应的中文解释，帮助你在建立统计理解的同时也增强双语自信心。
1. Mean, Median, Mode and Range in Science Experiments | 科学实验中的平均数、中位数、众数和极差
In a biology investigation, a student measured the heights of bean seedlings after 14 days. The eight measurements, in centimetres, were: 12, 14, 15, 13, 14, 16, 12, 15. We can use these values to practise calculating the four key measures of central tendency and spread.
在一次生物探究中，一名学生测量了豆苗14天后的高度。八个以厘米为单位的数据为：12, 14, 15, 13, 14, 16, 12, 15。我们可以用这些值练习计算集中趋势和离散程度的四个关键指标。
To find the mean, add all the heights together: 12 + 14 + 15 + 13 + 14 + 16 + 12 + 15 = 111. Then divide the sum by the number of plants: 111 ÷ 8 = 13.875 cm. So the mean height is 13.875 cm.
求平均数：把所有高度相加：12 + 14 + 15 + 13 + 14 + 16 + 12 + 15 = 111。然后将总和除以植株数量：111 ÷ 8 = 13.875 厘米。因此平均高度为13.875厘米。
The median is the middle value when the data are arranged in order. Sorting the set gives: 12, 12, 13, 14, 14, 15, 15, 16. With eight numbers, the median is halfway between the 4th and 5th values, so (14 + 14) ÷ 2 = 14 cm.
中位数是将数据排序后的中间值。排序后得到：12, 12, 13, 14, 14, 15, 15, 16。因为有八个数，中位数位于第4个和第5个值中间，因此 (14 + 14) ÷ 2 = 14 厘米。
For the mode, look for the most frequent data point. Here 12, 14 and 15 each appear twice. This dataset has more than one mode; it is multimodal. The range is the difference between the largest and smallest values: 16 − 12 = 4 cm. A large range suggests variation in seedling growth rates.
众数即出现次数最多的数据值。这里12、14和15各出现两次。这组数据有多个众数，为多众数模式。极差是最大值与最小值之差：16 − 12 = 4 厘米。较大的极差暗示豆苗生长速率存在差异。
2. Bar Charts and Comparing Energy Consumption | 条形图与用电量比较
In a science lesson on energy, students collected data on the power used by common household appliances. The table below shows the power ratings in watts. A bar chart can easily show which appliance uses the most energy.
在关于能源的科学课上，学生们收集了常见家用电器的使用功率数据。下表显示了以瓦特为单位的功率等级。条形图可以轻松展示哪个电器耗能最多。
| Appliance | Power (W) |
| Kettle | 2200 |
| Microwave | 1000 |
| Laptop | 65 |
| Television | 150 |
| Vacuum Cleaner | 1400 |
If we draw a bar chart with appliances on the x-axis and power on the y-axis, the bar for the kettle will be the tallest. By reading the chart, we can quickly spot that the kettle has a power rating more than twenty times that of the laptop. This kind of comparison helps us decide which devices cost more to run.
如果绘制条形图，以电器为x轴、功率为y轴，水壶的条形会最高。通过读取图表，我们一眼就能发现水壶的额定功率是笔记本电脑的二十多倍。这种比较有助于我们判断哪些设备运行成本更高。
A common exam question asks: ‘How many times greater is the power of the kettle than the television?’ You would divide 2200 W by 150 W, which gives about 14.7 times. Always remember to label both axes and give the chart a clear title, such as ‘Power Ratings of Household Appliances’.
一个常见的试题会问：”水壶的功率是电视机的多少倍？”这时你需要用2200 W除以150 W，结果约为14.7倍。始终记得为两个坐标轴标注，并为图表加上清晰的标题，例如“家用电器额定功率”。
3. Pictograms and World Population Data | 象形图与世界人口数据
In geography, you often work with large populations. A pictogram uses symbols to represent a certain number of people. For example, a globe symbol 🌍 could stand for 100 million people. The key tells you what each symbol means.
在地理中，你经常需要处理庞大的人口数据。象形图用符号来代表一定数量的人。例如，一个地球符号🌍可以代表1亿人。图例会告诉你每个符号代表多少。
Suppose a pictogram shows the approximate populations of four countries using globe symbols, where each 🌍 = 100 million. Country A has 4 symbols, B has 7, C has 1.5, and D has 2. We can calculate the population of each. Country A: 4 × 100 million = 400 million. Country C has one full symbol and one half symbol, so 100 million + 50 million = 150 million. The total population across all four countries is (4 + 7 + 1.5 + 2) × 100 million = 14.5 × 100 million = 1.45 billion.
假设一个象形图使用地球符号展示四个国家的近似人口，每个🌍＝1亿。A国有4个符号，B国7个，C国1.5个，D国2个。我们可以计算每个国家的人口。A国：4×1亿＝4亿。C国有一个完整符号和一个半符号，因此是1亿＋5千万＝1.5亿。四个国家的总人口是(4＋7＋1.5＋2)×1亿＝14.5×1亿＝14.5亿。
When constructing your own pictogram, choose a suitable key so that symbols are easy to draw and read. Half and quarter symbols are often needed for more precise values. Also arrange the symbols in neat rows to make comparisons easy.
在制作自己的象形图时，要选择合适的图例，使符号易于绘制和阅读。为了表达更精确的数值，通常需要使用半个或四分之一符号。同时，把符号排成整齐的行，便于比较。
4. Line Graphs for Monthly Temperature Changes | 气温月变化的折线图
Scientists and geographers use line graphs to show how a variable changes over time. A class recorded the average monthly temperature (°C) in a coastal town: Jan 8, Feb 9, Mar 11, Apr 14, May 17, Jun 20, Jul 22, Aug 22, Sep 19, Oct 15, Nov 11, Dec 9. Plotting these points and connecting them with straight lines reveals the yearly temperature pattern.
科学家和地理学家使用折线图来展示变量随时间的变化。一个班级记录了一个沿海城镇的月平均气温（°C）：1月8、2月9、3月11、4月14、5月17、6月20、7月22、8月22、9月19、10月15、11月11、12月9。把这些点绘出并用直线连接，就能揭示全年的温度变化规律。
The line graph will rise from January to a peak in July and August, then fall again. You can use the graph to find that the highest temperature was 22°C and the lowest 8°C, giving an annual range of 14°C. The steepest increase occurs between March and April (3°C rise), showing a rapid transition into spring.
折线图将从1月开始上升，到7月和8月达到峰值，随后下降。利用图表可以找到最高气温为22°C，最低为8°C，年较差为14°C。最陡峭的上升发生在3月到4月之间（上升3°C），显示出快速进入春季。
When interpreting a line graph, pay attention to the scale on both axes. The x-axis should show months evenly spaced, and the y-axis should begin at 0 or just below the lowest data point to avoid a misleading picture. Always title the graph ‘Average Monthly Temperature in 2024’.
解读折线图时，要注意两条轴的刻度。x轴应均匀标注月份，y轴应从0开始或略低于最低数据点，以免产生误导。图表标题应写为“2024年月平均气温”。
5. Probability with Dice and Card Games | 骰子与卡牌游戏中的概率
Probability measures how likely an event is to happen, and it is often expressed as a fraction, decimal or percentage. Rolling a fair six-sided die is a classic experiment. The probability of rolling an even number is P(even) = number of even outcomes ÷ total outcomes = 3/6 = 1/2. This links to the idea of equally likely outcomes.
概率衡量一个事件发生的可能性大小，通常用分数、小数或百分数表示。投掷一枚公平的六面骰子是一个经典实验。掷出偶数的概率是 P(偶数) = 偶数结果数 ÷ 总结果数 = 3/6 = 1/2。这与等可能结果的概念关联。
In a card game, a standard deck has 52 cards. If you pick one card at random, what is the probability it is a heart? There are 13 hearts, so P(heart) = 13/52 = 1/4. You can also consider compound events: the probability of picking a king or a queen is (4 + 4)/52 = 8/52 = 2/13. Always simplify fractions where possible.
在卡牌游戏中，一副标准扑克牌有52张。如果你随机抽取一张，抽到红心的概率是多少？红心有13张，因此 P(红心) = 13/52 = 1/4。你也可以考虑复合事件：抽到一张K或一张Q的概率是 (4＋4)/52 = 8/52 = 2/13。一定要注意约分。
When a question asks whether a game is fair, compare the probabilities of winning for each player. If a player wins by throwing a number greater than 4 on a die, their probability of winning is 2/6 = 1/3. The other player wins with a 2/3 chance, so the game is not fair. A fair game requires equal winning probabilities.
当题目询问一个游戏是否公平时，需要比较各玩家获胜的概率。如果一名玩家通过掷出大于4的点数获胜，其获胜概率是2/6 = 1/3。另一名玩家有2/3的获胜机会，因此游戏不公平。公平游戏要求获胜概率相等。
6. Venn Diagrams and Classifying Animals | 韦恩图与动物分类
In biology, Venn diagrams help sort animals according to shared characteristics. Imagine two overlapping ovals: one for ‘mammals’ and one for ‘lays eggs’. Animals such as dogs and whales go in the mammal-only section. Birds and crocodiles go in the lays-eggs-only section. The platypus fits in the overlap because it is a mammal that lays eggs.
在生物学中，韦恩图有助于根据共同特征对动物进行分类。想象两个重叠的椭圆：一个代表“哺乳动物”，一个代表“产卵”。狗和鲸鱼等动物放在仅哺乳动物的区域。鸟类和鳄鱼放在仅产卵的区域。鸭嘴兽则放置在重叠区，因为它是产卵的哺乳动物。
Suppose we survey 30 animals in a zoo: 18 are mammals, 12 lay eggs, and 5 are both mammals and egg-layers (the platypus group). The Venn diagram would show 13 in mammal-only, 7 in lays-eggs-only, 5 in the overlap, and 5 animals outside both circles (perhaps reptiles that give live birth). The total adds up to 30.
假设我们调查动物园中的30种动物：18种是哺乳动物，12种产卵，5种既是哺乳动物又产卵（鸭嘴兽类群）。韦恩图将显示哺乳动物独有13种，产卵独有7种，重叠区5种，两个圆之外还有5种（可能是卵胎生的爬行动物）。合计为30种。
Venn diagrams can include three circles for more complex sorting. For example, add ‘can fly’ as a third set, and study bats, eagles, and butterflies. Always start by filling the central overlap and work outwards. This is a powerful way to organise data logically.
韦恩图还可以包含三个圆，用于更复杂的分类。例如，增加“能飞”作为第三个集合，并研究蝙蝠、鹰和蝴蝶。你应该始终先填写中心重叠区，然后逐步向外填写。这是逻辑性组织数据的有力工具。
7. Questionnaire Design and School Transport Survey | 问卷设计与上学交通方式调查
Designing a good questionnaire is an essential data-collection skill. In a citizenship project, students want to find out how their classmates travel to school. The question must be clear and offer mutually exclusive response options. For example: ‘How do you usually travel to school? A) Walk B) Bicycle C) Bus D) Car E) Other.’
设计一份好的问卷是一项基本的数据收集技能。在公民教育项目中，学生们想了解他们的同学如何上学。问题必须清晰，并提供互斥的选项。例如：“你通常怎样上学？A) 步行 B) 自行车 C) 公共汽车 D) 小汽车 E) 其他。”
Pilot the questionnaire with a small group to catch any confusing words. After collecting 50 responses, the results are: walk 18, bicycle 8, bus 15, car 7, other 2. We can summarise the data in a frequency table and then draw a pie chart. To find the angle for ‘Walk’, use the fraction (18/50) × 360° = 129.6°.
先在一小群人中试发问卷，找出任何让人困惑的用词。收集到50份回复后，结果如下：步行18人，自行车8人，公共汽车15人，小汽车7人，其他2人。我们可以用频数表汇总数据，然后绘制饼图。要计算“步行”的扇形角度，用 (18/50) × 360° = 129.6°。
A well-designed questionnaire avoids leading questions and open-ended answers if you need quantitative data. Instead of ‘Do you agree that walking is healthy?’, ask ‘What is your main travel mode to school?’ This keeps the survey objective and the responses easy to analyse.
一份设计良好的问卷应避免引导性问题，并且在需要量化数据时避免开放式回答。不要问“你是否同意步行很健康？”，而应该问“你上学的主要交通方式是什么？”。这样能保持调查客观，也便于分析回答。
8. Pie Charts and Time Management | 饼图与时间管理
A student records how she spends her 24-hour day: sleeping 8 h, school 7 h, homework 2 h, leisure 4 h, meals and travel 3 h. To display this in a pie chart, first calculate the fraction of the day for each activity. For sleep, the fraction is 8/24 = 1/3, so the angle is 1/3 × 360° = 120°.
一名学生记录了她在一天24小时中的时间分配：睡眠8小时，上学7小时，家庭作业2小时，休闲4小时，用餐与交通3小时。要在饼图中展示，首先要计算每项活动占全天的分数。睡眠的分数是8/24 = 1/3，因此扇区角度为1/3 × 360° = 120°。
Complete the angles: school 7/24 × 360° = 105°, homework 2/24 = 1/12 → 30°, leisure 4/24 = 1/6 → 60°, meals/travel 3/24 = 1/8 → 45°. The sum of angles is 120° + 105° + 30° + 60° + 45° = 360°, which is a perfect check. When drawing, label each sector clearly and maybe use different colours.
完成所有角度计算：上学 7/24 × 360° = 105°，作业 2/24 = 1/12 → 30°，休闲 4/24 = 1/6 → 60°，用餐/交通 3/24 = 1/8 → 45°。角度之和为120° + 105° + 30° + 60° + 45° = 360°，这是完美的检验。绘制时，清晰标注每个扇形，并可使用不同颜色。
Pie charts make it easy to compare proportions at a glance. You can instantly see that sleep takes up the biggest slice, while homework takes the smallest. This visual representation helps when presenting time-management plans to peers or teachers.
饼图可以一目了然地比较比例。你一眼就能看出睡眠占最大扇区，而家庭作业占比最小。这种直观表示有助于向同学或老师展示时间管理计划。
9. Scatter Graphs and the Relationship Between Height and Hand Span | 身高与手跨的散点图
In a science and PE cross-curricular project, students measure their height (cm) and hand span (cm). The first six pairs are: (150, 17), (155, 18), (162, 19), (168, 20), (172, 21), (178, 22). Plotting these on a scatter graph, with height on the x-axis and hand span on the y-axis, reveals a general pattern.
在一个科学和体育的跨学科项目中，学生们测量了自己的身高（厘米）和手跨（厘米）。前六组成对数据为：(150, 17), (155, 18), (162, 19), (168, 20), (172, 21), (178, 22)。把这些数据绘成散点图，身高放在x轴，手跨放在y轴，可以揭示出大致趋势。
All the points lie roughly along a straight line sloping upwards. This indicates a positive correlation: as height increases, hand span also tends to increase. The scatter graph does not prove that being taller causes a larger hand span, but it shows an association that can be explored further in biology.
这些点大致沿一条向上的直线分布。这表明存在正相关：身高增加，手跨也往往增大。散点图并没有证明身高更高会导致手跨更大，但它显示了一种关联，可以在生物课上进一步探究。
You might be asked to describe the correlation. Use the terms ‘positive’, ‘negative’ or ‘no correlation’. Here it is positive. You could also draw a line of best fit by eye, which goes through the middle of the points, to make predictions. For example, a student with a height of 165 cm might have a hand span of about 19.5 cm according to the line.
考试中可能会要求你描述相关性。使用“正相关”、“负相关”或“无相关”等术语。这里是正相关。你还可以用目测法画一条最佳拟合线，穿过点群的中央，用于预测。例如，根据这条线，身高165厘米的学生手跨可能约为19.5厘米。
10. Two-Way Tables and Favourite Subjects | 双向表与最喜欢的科目
A school conducted a survey on favourite core subjects among 60 Year 7 students, recording both gender and subject choice. A two-way table organises the data neatly. Below is the completed table:
一所学校对60名七年级学生进行了最喜欢的核心科目调查，同时记录性别和所选科目。双向表可以清晰地组织数据。下面是完整的表格：
| Maths | English | Science | Total | |
| Boys | 14 | 6 | 10 | 30 |
| Girls | 8 | 13 | 9 | 30 |
| Total | 22 | 19 | 19 | 60 |
From the table we can find that 14 boys chose Maths, while only 6 chose English. A total of 22 students prefer Maths, giving a proportion of 22/60 = 11/30. We can also compare conditional proportions: among boys, the fraction choosing Science is 10/30 = 1/3; among girls, it is 9/30 = 3/10.
从表中可知，14名男孩选择数学，而只有6名选择英文。共有22名学生最喜欢数学，比例为22/60 = 11/30。我们还可以比较条件比例：在男孩中，选择科学的比例是10/30 = 1/3；在女孩中，则为9/30 = 3/10。
Two-way tables help spot trends. For instance, English appears more popular with girls (13 out of 30) than with
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