Year 7 Cambridge Statistics: Winter Break Intensive Revision Plan | Year 7 Cambridge 统计：寒假强化复习计划

📚 Year 7 Cambridge Statistics: Winter Break Intensive Revision Plan | Year 7 Cambridge 统计：寒假强化复习计划

The winter break is a perfect opportunity to consolidate your understanding of Year 7 Statistics and build confidence before the next term. This intensive revision plan will guide you through the core topics of the Cambridge syllabus, helping you practise data handling, averages, graphs, and probability in a structured way. By following the weekly schedule and working through each section carefully, you can eliminate weak spots and enter the new term thoroughly prepared.

寒假是巩固七年级统计学知识并为新学期建立信心的绝佳时机。这份强化复习计划将带你梳理剑桥大纲的核心主题，帮助你以结构化的方式练习数据处理、平均数、图表和概率。跟随每周计划并认真完成每个部分，你可以消灭薄弱环节，在开学时做到充分准备。

1. Understanding the Cambridge Year 7 Statistics Syllabus | 理解剑桥七年级统计教学大纲

The Cambridge Year 7 Statistics syllabus introduces the fundamental building blocks of data handling. Key topics include: types of data (qualitative and quantitative), methods of data collection, representing data with tally charts and frequency tables, constructing and interpreting bar charts, pictograms and pie charts, calculating averages (mean, median, mode), finding the range, and a basic introduction to probability. Familiarising yourself with these areas will help you see how statistics is applied in everyday situations.

剑桥七年级统计大纲介绍了数据处理的基本模块。关键主题包括：数据类型（定性和定量）、数据收集方法、用计数图和频率表表示数据、构建和解读条形图、象形图和饼图、计算平均值（均值、中位数和众数）、求范围以及概率入门。熟悉这些领域将帮助你理解统计在日常生活中的应用。

2. Creating a Weekly Revision Timetable | 制定每周复习时间表

A well-structured timetable prevents last-minute cramming and ensures all topics receive attention. Spread your revision over four weeks during the winter break, dedicating around 1–1.5 hours each day to statistics. The table below offers a suggested schedule.

结构良好的时间表可以避免考前突击，确保每个主题都得到关注。将复习分散在寒假的四周内，每天投入1–1.5小时给统计学。下面的表格提供了一个建议时间安排。

Week	Focus Areas	Daily Study Time
1	Data types, tally charts, frequency tables	1–1.5 hours
2	Bar charts, pictograms, pie charts	1–1.5 hours
3	Averages (mean, median, mode) and range	1–1.5 hours
4	Probability, mixed exam-style practice, review	1.5 hours

Try to study at the same time each day to build a routine. Start each session by reviewing the previous day’s key points, then work through examples and finish with a few practise questions. Include short breaks and reward yourself when you complete a week’s goals.

尽量每天在同一时间学习以养成习惯。每次学习开始时先回顾前一天的关键点，然后完成例题，最后做几道练习题。包括短暂休息，并在完成一周目标后奖励自己。

3. Data Collection and Types of Data | 数据收集与数据类型

All statistical work begins with data. You need to be able to classify data as qualitative (categorical) or quantitative (numerical).

所有统计工作都从数据开始。你需要能区分数据是定性（分类）还是定量（数值）。

Qualitative data describes qualities or categories, such as favourite colour, type of pet, or mode of transport.
Quantitative data involves numbers that can be measured or counted, such as height, number of siblings, or test scores.

定性数据描述性质或类别，比如最喜欢的颜色、宠物类型或交通方式。
定量数据涉及可测量或计数的数字，比如身高、兄弟姐妹数量或考试成绩。

Quantitative data can be further split into discrete (countable, whole numbers, like number of books) and continuous (measurable, any value within a range, like height or mass).

定量数据还可以进一步分为离散型（可数的整数，如图书的数量）和连续型（可测量，一定范围内的任何值，如身高或质量）。

Understanding how data is collected is equally important. Data can be collected through surveys, questionnaires, experiments, or observation. When designing a question, make sure it is clear, unbiased, and offers appropriate response options.

理解数据的收集方式同样重要。数据可以通过调查、问卷、实验或观察来收集。设计问题时，确保问题清晰、无偏见，并提供合适的回答选项。

4. Frequency Tables and Tally Charts | 频率表和计数图

One of the first steps in organising data is creating a frequency table. A tally chart helps you count occurrences quickly using groups of five strokes. The fifth stroke crosses the previous four to make a gate 卌, which makes counting easier.

组织数据的第一步之一是创建频率表。计数图通过五个一组的方式帮助你快速计数。第五画穿过前四画形成“正”字的一部分（英文环境常用卌形），使计数更容易。

Once you have finished counting, the frequency is recorded in the table. For example, if you surveyed 20 students about their favourite fruit and found 8 chose apples, the frequency for apples is 8. Always include a total frequency row at the bottom to check your counts.

计数完成后，将频数记录在表格中。例如，如果你调查了20名学生最喜欢的水果，发现8人选择苹果，那么苹果的频数就是8。务必在底部添加总频数行，以核对你的计数。

When working with grouped data for continuous measurements (e.g., heights 150 cm ≤ h < 160 cm), intervals must be of equal width and non-overlapping.

处理连续测量的分组数据时（如身高150厘米 ≤ h < 160厘米），组距必须等宽且不重叠。

5. Bar Charts and Pictograms | 条形图和象形图

Bar charts are used to display discrete data. Each bar represents a category, and the height of the bar shows the frequency. Important rules: label both axes clearly, use a sensible scale on the frequency axis, leave equal gaps between bars, and give the chart a title.

条形图用于显示离散数据。每个条形代表一个类别，条形的高度表示频数。重要规则：清晰标注两轴，频数轴使用合理的刻度，条形之间留相等间隙，并给图表加上标题。

Pictograms use symbols to represent data. Each symbol stands for a certain number of items, and the key explains this. For example, one smiley face might represent 2 students. When a frequency is not an exact multiple of the symbol’s value, you may show a fraction of the symbol (like half a smiley). Always check that your pictogram is easy to read and the key is clear.

象形图使用符号来表示数据。每个符号代表一定数量的项目，图例对此进行说明。例如，一个笑脸符号可能代表2名学生。当频数不是符号值的整数倍时，可以显示符号的一部分（如半个笑脸）。始终确保象形图易于阅读且图例清晰。

6. Pie Charts: Angles and Interpretation | 饼图：角度与解读

A pie chart shows proportions of a whole as sectors of a circle. Each sector’s angle is calculated using the formula:

sector angle = (frequency ÷ total frequency) × 360°

饼图将整体比例显示为圆的扇区。每个扇区的角度通过以下公式计算：

扇区角度 = (频数 ÷ 总频数) × 360°

For example, if 15 out of 60 students walk to school, the angle for ‘walk’ is (15 ÷ 60) × 360° = 90°. Always use a protractor accurately and label each sector with the category and percentage or frequency. Double-check that all your angles add up to 360°.

例如，如果60名学生中有15人步行上学，“步行”对应的角度为(15 ÷ 60) × 360° = 90°。始终准确使用量角器，并在每个扇区上标注类别及百分比或频数。再次检查所有角度之和是否为360°。

When interpreting a pie chart, you should be able to identify the largest and smallest sectors, compare proportions, and use proportional reasoning to find frequencies if the total is known.

解读饼图时，你应该能够识别最大和最小的扇区，比较比例，并在已知总数的情况下利用比例推理求出频数。

7. Averages: Mean, Median and Mode | 平均数：均值、中位数和众数

The three main measures of average describe the centre of a data set in different ways.

三个主要的平均数度量以不同方式描述数据集的中心。

Mode: The value that appears most often. A data set can have no mode, one mode, or more than one mode.
Median: The middle value when the data are ordered from smallest to largest. For an even number of values, the median is the mean of the two middle numbers.
Mean: The sum of all values divided by the number of values.

众数：出现次数最多的值。一个数据集可能没有众数、有一个众数或多个众数。
中位数：将数据从小到大排序后位于中间的值。若数据个数为偶数，中位数是中间两个数的均值。
均值：所有值之和除以值的个数。

mean = (sum of all values) ÷ (number of values)

For the set: 2, 3, 5, 5, 7, 8, the mode is 5, the median is 5, and the mean is (2+3+5+5+7+8) ÷ 6 = 30 ÷ 6 = 5.

对于数据集：2, 3, 5, 5, 7, 8，众数是5，中位数是5，均值为(2+3+5+5+7+8) ÷ 6 = 30 ÷ 6 = 5。

Know when to use each: the mode is good for non-numeric data, the median is unaffected by extreme values, and the mean uses all data values but can be distorted by outliers.

了解何时使用每个指标：众数适用于非数值数据，中位数不受极端值影响，均值使用了所有数据但可能被异常值拉偏。

8. Range and Comparing Data Sets | 范围与数据集比较

The range measures the spread or consistency of a data set. It is calculated as:

range = largest value – smallest value

范围衡量数据集的离散度或一致性。计算公式为：

范围 = 最大值 – 最小值

A smaller range means the data are more consistent, while a larger range indicates greater spread. When comparing two sets of data, use both an average and the range to give a complete picture. For instance, two classes might have the same mean test score, but the class with the smaller range performed more uniformly.

范围越小表示数据越一致，范围越大说明离散程度越高。比较两个数据集时，同时使用平均数与范围才能提供完整的信息。例如，两个班级可能有相同的平均考试分数，但范围较小的班级表现更均衡。

Always order the data before finding the range, and never forget to include units in your answer when comparing real-world quantities like heights or temperatures.

在求范围之前务必排序数据，并且在比较实际量如身高或温度时，不要忘记在答案中包含单位。

9. Introduction to Probability | 概率入门

Probability describes how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means impossible and 1 means certain.

概率描述事件发生的可能性大小，用一个介于0和1之间的数表示，0代表不可能，1代表必然发生。

Probability of an event = number of favourable outcomes ÷ total number of equally likely outcomes

事件的概率 = 有利结果的数量 ÷ 所有等可能结果的总数

For a fair six-sided die, the probability of rolling a 4 is 1/6. For rolling an even number, the favourable outcomes are 2, 4, 6, so the probability is 3/6 = 1/2.

对于一个公平的六面骰子，掷出4的概率是1/6。掷出偶数的有利结果是2、4、6，因此概率为3/6 = 1/2。

Probability can be shown on a probability scale, often represented as a line from 0 to 1 with events placed on it. Make sure you list all possible outcomes systematically, using a sample space diagram if needed. The sum of probabilities of all mutually exclusive outcomes of an experiment is 1.

概率可以用概率尺度表示，通常是一条从0到1的线，事件被标在上面。确保系统地列出所有可能结果，必要时使用样本空间图。一个实验中所有互斥结果的概率之和为1。

10. Common Mistakes and How to Avoid Them | 常见错误及如何避免

Even small slips can cost marks in statistics. Watch out for these frequent errors:

即使是小疏忽也可能在统计题中丢分。注意以下常见错误：

Forgetting to order the data before finding the median – always arrange from smallest to largest.
Calculating the mean incorrectly by including the wrong total or forgetting to divide.
Using the wrong scale on graphs – check that each grid unit represents the correct value.
Pie chart angles not multiplying by 360° – recalculate carefully.
Confusing bar charts (gaps between bars) with histograms (no gaps for continuous data, but not needed at Year 7 level; just keep gaps for discrete categories).
Probability fractions not simplified or denominator not equal to total outcomes.
Range calculation using non-ordered list – subtract only after ordering.

求中位数前忘记排序数据 – 始终从小到大排列。
计算均值时使用了错误的总和或忘记除以数据个数。
图表使用错误刻度 – 检查每个网格单位所代表的值。
饼图角度忘记乘以360° – 仔细重新计算。
将条形图（条间有间隙）与直方图混淆（七年级阶段无需深究，记得离散类别保留间隙）。
概率分数未化简或分母不等于总结果数。
计算范围时未排序列表 – 排序后再相减。

The best way to avoid these is to show all steps clearly in your working, double-check with a different method if possible, and read every question twice to understand what is required.

避免这些错误的最佳方法是：在演算过程中清晰展示所有步骤，尽可能用不同方法双重检查，并仔细阅读题目两遍以明确要求。

11. Exam-style Questions and Practice | 考试题型练习

Regular practice with exam-style questions builds familiarity with wording and time management. Here is a typical multi-part question to work through:

通过练习考试题型，你能够熟悉题目的措辞并掌握时间管理。下面是一道典型的多步骤问题可以试做：

The heights (in cm) of 10 Year 7 students are: 152, 148, 155, 150, 149, 152, 153, 147, 151, 150.

10名七年级学生的身高（单位：厘米）为：152, 148, 155, 150, 149, 152, 153, 147, 151, 150。

(a) Calculate the mean height. (b) Find the median height. (

Published by TutorHao | Year 7 统计 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Year 7 Cambridge Statistics: Winter Break Intensive Revision Plan | Year 7 Cambridge 统计：寒假强化复习计划