📚 Year 7 Cambridge Statistics: In-Depth Analysis of Past Papers | 剑桥7年级统计：历年真题深度解析
In this comprehensive guide, we break down the most common question types found in Year 7 Cambridge Statistics papers. By working through real-style exam questions, you will gain a deep understanding of data handling, averages, charts, and basic probability. Each section pairs an English explanation with a Chinese translation to support bilingual learners and reinforce key concepts.
在本综合指南中，我们将详细解析剑桥 Year 7 统计试卷中最常见的题型。通过演练真实风格的考题，你将深入理解数据处理、平均数、图表和基础概率。每个部分都配有英文解释和中文翻译，以支持双语学习者并巩固关键概念。
1. Data Collection and Types | 数据收集与类型
Many past papers start with questions that ask students to classify data as qualitative or quantitative, and to distinguish between discrete and continuous data. For example, ‘eye colour’ is qualitative, while ‘number of siblings’ is quantitative and discrete. A common trick is asking whether ‘height in cm’ is discrete or continuous – it is continuous because height can take any value within a range. Always read the question carefully to see if it asks for the type of data or the method of collection, such as survey, observation, or experiment.
许多真题一开始会要求学生对数据进行分类，分为定性数据或定量数据，并区分离散数据与连续数据。例如，“眼睛颜色”属于定性数据，而“兄弟姐妹数量”则属于定量且离散的数据。常见的陷阱是问“身高（厘米）”属于离散还是连续——答案是连续，因为身高可以在一定范围内取任意值。务必仔细审题，看清题目是问数据类型还是收集方式，比如调查、观察或实验。
2. Frequency Tables and Bar Charts | 频率表与柱状图
A typical exam question provides a raw list of data and asks you to complete a frequency table, then draw a bar chart. Remember that the bars in a bar chart should not touch if the data is categorical. When drawing, label the axes clearly, write a title, and use a ruler. A common mistake is forgetting to put the frequency on the vertical axis and the categories on the horizontal axis. In a 2021-style question, students were given the eye colours of 30 pupils and had to construct a bar chart – marks were lost for missing axis labels.
常见的考题会给出一组原始数据列表，要求你完成频率表，然后绘制柱状图。请记住，如果数据是分类数据，柱状图的柱子之间不应接触。绘图时要清晰标注坐标轴，写上标题，并使用直尺。一个常见错误是忘记将频数放在纵轴，类别放在横轴。在一道2021风格的题目中，给出了30名学生的眼睛颜色，要求绘制柱状图——很多学生因为缺少坐标轴标签而失分。
3. Calculating the Mean | 计算平均数
Past papers frequently ask for the mean of a data set. The formula is: Mean = (sum of all values) / (number of values). For instance, if the scores in a test are 7, 9, 5, 6, and 8, the sum is 35 and the mean is 35 ÷ 5 = 7. A more challenging problem involves finding a missing value given the mean. For example: ‘The mean of four numbers is 12. Three of the numbers are 10, 14, and 9. Find the fourth number.’ Work backwards: total = 4 × 12 = 48, so missing = 48 – (10+14+9) = 15.
真题经常要求计算一组数据的平均数。公式为：平均数 = 所有数值之和 / 数值的个数。例如，如果测验成绩为7、9、5、6和8，总和为35，平均数为35 ÷ 5 = 7。更具挑战性的题目是已知平均数求缺失值。例如：“四个数的平均数为12。其中三个数为10、14和9。求第四个数。”反向推算：总和 = 4 × 12 = 48，缺失值 = 48 – (10+14+9) = 15。
4. Median and Mode | 中位数与众数
The median is the middle value when data is ordered from smallest to largest. If there are two middle numbers, find their mean. The mode is the value that appears most often – a set can have one mode, more than one, or no mode at all. In a past question, students were asked to find the median of: 3, 8, 2, 8, 5, 10. Ordering gives 2, 3, 5, 8, 8, 10; the median is the mean of 5 and 8, which is 6.5. Always check you have ordered the numbers correctly before finding the median.
中位数是将数据从小到大排序后中间的值。如果中间有两个数，则取它们的中位数。众数是出现次数最多的值——一组数据可能有一个众数、多个众数或没有众数。在一道真题中，要求找出以下数据的中位数：3, 8, 2, 8, 5, 10。排序后得到2, 3, 5, 8, 8, 10；中位数为5和8的平均数，即6.5。务必确保在找中位数之前已正确排序。
5. Range and Spread | 范围与离散程度
The range measures how spread out the data is, calculated as: Range = largest value – smallest value. A small range means the data is clustered closely; a large range suggests more variability. Exam questions often pair this with a comparison, e.g., ‘Which class had more consistent test scores?’ A Year 7 paper from 2022 showed heights of two basketball teams: Team A range = 12 cm, Team B range = 27 cm. Students then concluded Team A was more consistent in height.
范围衡量数据的离散程度，计算公式为：范围 = 最大值 – 最小值。范围小表示数据集中；范围大表示变化较大。考题常将此与比较题结合，例如：“哪个班级的测验成绩更稳定？”一份2022年的Year 7试卷显示了两支篮球队的身高数据：A队范围 = 12 厘米，B队范围 = 27 厘米。学生由此得出A队身高更一致。
6. Line Graphs and Trends | 折线图与趋势
Line graphs are used to show changes over time. When interpreting a line graph, look for trends: is it increasing, decreasing, or staying constant? You might be asked to estimate a value between plotted points (interpolation) or beyond them (extrapolation). A common exam question: ‘Between which two days did the temperature rise the most?’ Calculate the difference for each interval. Also, be careful with the scale – sometimes each small square represents more than one unit.
折线图用于显示随时间的变化。解读折线图时，要观察趋势：是上升、下降还是保持不变？你可能需要估计已标绘点之间的值（内插法）或之外的值（外推法）。常见的考题：“在哪两天之间温度上升最多？”计算每个区间的差值。此外，要注意刻度——有时每个小方格代表不止一个单位。
7. Pie Charts and Percentages | 饼图与百分比
Constructing a pie chart involves calculating the angle for each sector. Since a full circle is 360°, the angle = (frequency / total) × 360°. Past papers often give a table of favourite sports and ask students to draw the pie chart. Remember to use a protractor, label each sector, and write a title. A 2020-style question: ‘If 20 students chose football out of 80, what is the angle?’ Solution: (20/80) × 360° = 90°. Always check that your angles sum to 360°.
绘制饼图需要计算每个扇区的角度。因为整个圆为360°，所以角度 = (频数 / 总数) × 360°。真题通常会给出一个关于最喜欢的运动的表格，要求学生绘制饼图。记得使用量角器，标注每个扇区，并写上标题。一道2020风格的题目：“如果80名学生中有20人选择了足球，角度是多少？”解答：(20/80) × 360° = 90°。务必检查所有角度之和是否为360°。
8. Dual Bar Charts and Misleading Graphs | 复合柱状图与误导性图表
Dual bar charts compare two sets of data side by side. They often ask: ‘In which month was the difference between rainfall in City A and City B the greatest?’ To answer, subtract the heights visually or using given values. Some past papers include a misleading graph where the vertical axis does not start at zero or has an uneven scale. Always scrutinise the axes: does the scale exaggerate differences? A question may ask, ‘Why is this graph misleading?’ and expect you to mention the scale issue.
复合柱状图用于并列比较两组数据。常见问题：“哪个月份A市与B市的降雨量差最大？”回答时，通过目测或给定数值计算高度差。一些真题会包含误导性图表，其纵轴不从零开始或刻度不均匀。一定要仔细审视坐标轴：刻度是否夸大了差异？题目可能会问：“为什么这个图表具有误导性？”并期望你指出刻度问题。
9. Introduction to Probability | 概率入门
Probability in Year 7 is expressed as a fraction, decimal, or percentage between 0 and 1. The probability of an impossible event is 0; a certain event is 1. Questions often involve spinners, dice, or bags of coloured counters. For example: ‘A bag contains 3 red, 2 blue and 5 green counters. What is the probability of picking a blue?’ The answer is 2/10 = 1/5. If asked for ‘expected number’ in 50 trials, multiply probability by number of trials: (1/5) × 50 = 10 times.
Year 7的概率用0到1之间的分数、小数或百分比表示。不可能事件的概率为0；必然事件的概率为1。题目常涉及转盘、骰子或装有彩色筹码的袋子。例如：“袋中有3个红色、2个蓝色和5个绿色筹码。抽到蓝色的概率是多少？”答案是2/10 = 1/5。如果问“在50次试验中预计出现多少次”，用概率乘以试验次数：(1/5) × 50 = 10次。
10. Mixed Past Paper Questions | 综合真题演练
Here is a selection of mixed questions that combine several skills, typical in the final pages of a Cambridge Year 7 Statistics exam. Practice these to sharpen your problem-solving ability.
这里精选了几道综合性题目，结合了多项技能，常见于剑桥Year 7统计试卷的最后几页。练习这些题目可以提高你的解题能力。
Question 1: The stem-and-leaf diagram shows the scores of a class in a science quiz: 1|2 5 5, 2|0 3 4 8, 3|1 2 4. Find the mode, median, mean, and range.
问题1：茎叶图显示了一个班级在科学小测验中的成绩：1|2 5 5, 2|0 3 4 8, 3|1 2 4。求众数、中位数、平均数和范围。
Answer: Data: 12, 15, 15, 20, 23, 24, 28, 31, 32, 34. Mode = 15, median = (23+24)/2 = 23.5, mean = (12+15+15+20+23+24+28+31+32+34)/10 = 23.4, range = 34 – 12 = 22.
答案：数据为12, 15, 15, 20, 23, 24, 28, 31, 32, 34。众数 = 15，中位数 = (23+24)/2 = 23.5，平均数 = (12+15+15+20+23+24+28+31+32+34)/10 = 23.4，范围 = 34 – 12 = 22。
Question 2: A pie chart shows favourite fruits. Apples: 90°, Bananas: 120°, Oranges: 60°, Grapes: 90°. If 36 students chose Bananas, how many students chose Oranges?
问题2：一个饼图显示了最喜爱的水果。苹果：90°，香蕉：120°，橙子：60°，葡萄：90°。如果36名学生选择了香蕉，选择橙子的有多少人？
Solution: Banana fraction = 120/360 = 1/3 of students. So total students = 36 × 3 = 108. Orange fraction = 60/360 = 1/6. Number = 108 × 1/6 = 18 students.
解答：香蕉所占比例 = 120/360 = 1/3，因此学生总数 = 36 × 3 = 108。橙子比例 = 60/360 = 1/6，人数 = 108 × 1/6 = 18名学生。
Question 3: The line graph shows the temperature at 8am each day for a week: Mon 8°C, Tue 10°C, Wed 7°C, Thu 12°C, Fri 14°C, Sat 11°C, Sun 9°C. Between which two consecutive days was the rise in temperature the greatest?
问题3：折线图显示了一周中每天早上8点的温度：周一 8°C，周二 10°C，周三 7°C，周四 12°C，周五 14°C，周六 11°C，周日 9°C。哪两个连续日之间的温度上升最大？
Solution: Calculate differences: Mon-Tue +2, Tue-Wed -3 (drop), Wed-Thu +5, Thu-Fri +2, Fri-Sat -3, Sat-Sun -2. The greatest rise is +5°C between Wednesday and Thursday.
解答：计算差值：周一-周二 +2，周二-周三 -3（下降），周三-周四 +5，周四-周五 +2，周五-周六 -3，周六-周日 -2。最大上升是周三到周四的 +5°C。
Remember to show all your working in the exam; even if the final answer is wrong, you can earn method marks.
考试中记得展示所有解题步骤；即使最终答案错误，也能获得方法分。
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