📚 Year 7 CCEA Statistics: Summer Prep & Bridging Course | CCEA 七年级统计：暑期预习与衔接课程
Welcome to your Year 7 CCEA Statistics summer preparation programme. This bridging course is designed to reinforce the handling data skills you developed in Key Stage 2, while giving you a confident head start for the more formal statistical methods you will meet in Year 8 and beyond. Through clear explanations and plenty of examples, you will revise how to collect, organise, display and interpret data, and begin to explore the basics of probability.
欢迎参加 CCEA 七年级统计暑期预习课程。这个衔接课程旨在巩固你在 Key Stage 2 阶段掌握的数据处理技能，同时让你自信地提前接触 Year 8 及以后更规范的统计方法。通过清晰的讲解和丰富的例题，你将复习如何收集、整理、展示和解读数据，并开始探索概率的基础知识。
1. What is Statistics? | 什么是统计？
Statistics is the branch of mathematics that deals with collecting, organising, analysing, interpreting and presenting data. Whenever you carry out a survey, measure temperatures over a week or record your favourite sports team’s scores, you are working with statistics. It helps us make sense of numbers and information we see every day.
统计学是数学的一个分支，涉及数据的收集、整理、分析、解读和展示。每当你进行一项调查、记录一周的气温或者记录你最喜欢运动队的得分时，你就在和统计打交道。统计学帮助我们理解每天看到的数字和信息。
In CCEA Key Stage 2, you learned to ask questions, gather information and draw simple conclusions. Now we will build on those foundations, learning to use precise vocabulary, choose the right type of graph and calculate averages. By the end of this course, you will feel ready to handle any data problem Year 8 throws at you.
在 CCEA Key Stage 2 中，你已经学会了提出问题、收集信息并得出简单的结论。现在我们将在此基础上继续发展，学习使用准确的词汇、选择合适的图表类型并计算平均数。通过本课程的学习，你将准备好应对 Year 8 中遇到的任何数据问题。
2. Collecting Data | 收集数据
All statistical work begins with a question. For example, ‘What is the most common way pupils travel to school?’ or ‘How many hours do Year 7 students spend on homework each week?’ Once you have a clear question, you need to plan how to collect your data. Data can be collected through surveys, questionnaires, observations or experiments.
所有的统计工作都从一个问题开始。比如，“学生最常用的上学方式是什么？”或者“七年级学生每周花多少小时做作业？”一旦有了明确的问题，你就需要规划如何收集数据。数据可以通过调查、问卷、观察或实验来收集。
A good data collection plan must be fair and avoid bias. For instance, if you only ask your friends about their favourite football team, your results will not represent the whole class. In CCEA assessments, you may be asked to design a simple data collection sheet or a tally chart. Tally marks make counting easy: each group of five is shown as four vertical strokes and one diagonal stroke crossing them.
一个好的数据收集计划必须公平并避免偏差。例如，如果你只问你的朋友他们最喜欢的足球队，结果将不能代表全班。在 CCEA 的测试中，你可能会被要求设计一个简单的数据收集表或画正字计数表。画正字使得计数变得容易：每五笔为一组，用四竖一横来表示。
Tally example: |||| represents 4, and |||| represents 5.
画正字示例： 四个竖线表示 4，四竖加一横表示 5。
3. Types of Data | 数据类型
Understanding the type of data you are dealing with helps you choose the best way to present and analyse it. There are two main kinds: qualitative data and quantitative data.
了解你处理的数据类型有助于你选择最好的展示和分析方式。主要有两种类型：定性数据和定量数据。
Qualitative data describes qualities or categories. It is non-numerical and is often called categorical data. Examples include eye colour, favourite subject, or types of pet. Quantitative data, on the other hand, is numerical. It can be measured or counted. Quantitative data can be further split into discrete data (which can only take certain values, like number of siblings) and continuous data (which can take any value within a range, like height or mass).
定性数据描述的是品质或类别。它是非数值的，通常被称为分类数据。示例包括眼睛颜色、最喜欢的科目或宠物的种类。另一方面，定量数据是数值型的，可以测量或计数。定量数据可以进一步分为离散数据（只能取特定值，例如兄弟姐妹的数量）和连续数据（在一个范围内可以取任何值，如身高或体重）。
| Data type 数据类型 | Description 描述 | Example 示例 |
|---|---|---|
| Qualitative / Categorical | Words or categories 文字或类别 | Favourite crisp flavour 最喜欢的薯片口味 |
| Quantitative discrete | Numerical, counted 数值，可数 | Number of books read 阅读的书籍数量 |
| Quantitative continuous | Numerical, measured 数值，可测量 | Time taken to run 100 m 跑 100 米的时间 |
4. Frequency Tables | 频数表
Once you have collected raw data, you need to organise it so that patterns become visible. A frequency table shows how often each value or category appears. The frequency is simply the count of items in each group.
一旦你收集了原始数据，就需要把它整理好，让规律显现出来。频数表显示了每个值或类别出现的频率。频数就是每一组中项目的计数。
To construct a frequency table, list all categories or values in one column and tally the counts in another. Then write the total frequency at the bottom. Always give your table a clear title. In Year 7 CCEA statistics, you will often be asked to complete or interpret a frequency table and use it to create a graph.
构建频数表时，将所有的类别或数值列在一栏，在另一栏中记录计数，然后底部写下总频数。一定要给你的表格一个清晰的标题。在 CCEA 七年级统计中，你会经常被要求补全或解读频数表，并用它来创建图表。
Example: The favourite fruits of 20 students: Apple × 8, Banana × 5, Orange × 4, Grape × 3. Total frequency = 20.
示例： 20 名学生最喜爱的水果：苹果 8，香蕉 5，橙子 4，葡萄 3。总频数 = 20。
5. Bar Charts | 柱状图
A bar chart is one of the most common ways to display categorical or discrete data. The height of each bar represents the frequency. Bars must be of equal width, and there should be gaps between them to show that the categories are separate.
柱状图是展示分类数据或离散数据最常用的方法之一。每个柱子的高度代表频数。柱子的宽度必须相等，并且柱子之间应有间隙，以表明类别是分开的。
When drawing a bar chart, always label the axes clearly: the horizontal axis shows the categories, and the vertical axis shows the frequency. Choose a sensible scale so that the tallest bar fits comfortably. In CCEA exams, you may have to draw a bar chart from a frequency table or answer questions by reading information from one.
画柱状图时，一定要清楚地标记坐标轴：横轴表示类别，纵轴表示频数。选择一个合适的刻度，使最高的柱子能舒适地容纳在内。在 CCEA 考试中，你可能需要根据频数表画柱状图，或者通过读图回答问题。
Bar charts can also be drawn horizontally. The key rule is that the length of the bar represents frequency, and the bars do not touch. This distinguishes them from histograms, which you will meet later in secondary school.
柱状图也可以画成水平的。关键规则是柱子的长度代表频数，并且柱子不接触。这一点将它们与直方图区分开来，直方图你将在中学后期遇到。
6. Pictograms | 象形图
A pictogram uses pictures or symbols to represent data. Each symbol stands for a certain number of items. A key must be provided to show what one symbol represents. Pictograms are visually appealing and easy to read, making them popular in newspapers and primary school materials.
象形图使用图片或符号来表示数据。每个符号代表一定数量的项目。必须提供一个图例来说明一个符号代表什么。象形图视觉上吸引人且易于阅读，因此在报纸和小学教材中很受欢迎。
When creating a pictogram, choose a simple symbol and decide on a suitable value for it. For example, one star could represent 2 children. If 5 children chose walking, you would draw 2½ stars. You must be able to show half or quarter symbols accurately. Always check that your pictogram matches the frequency table exactly.
创建象形图时，选择一个简单的符号并为其设定合适的数值。例如，一颗星代表 2 个儿童。如果 5 个孩子选择步行，你就需要画出 2½ 颗星。你必须能够准确地表示半个或四分之一个符号。务必检查象形图是否与频数表完全匹配。
Tip: For CCEA questions, you may be asked to interpret a pictogram where a symbol represents more than one unit, or to spot mistakes such as a missing key.
提示： 在 CCEA 的问题中，你可能会被要求解读一个符号代表多个单位的象形图，或者找出错误，比如缺少图例。
7. Line Graphs | 折线图
Line graphs are used to show changes in data over time. They are particularly useful for continuous data. You plot points using two axes – often time on the horizontal axis and the measured quantity on the vertical axis – and then join the points with straight lines.
折线图用于显示数据随时间的变化。它们对连续数据特别有用。你使用两个坐标轴描点——通常横轴是时间，纵轴是测量量——然后用直线连接这些点。
When you draw a line graph, label both axes and give the graph a title. Choose scales that make the trend clear. You can plot more than one set of data on the same graph, using different colours or line styles, but always include a legend. In CCEA statistics, you might compare temperature changes over a week or a plant’s growth over several weeks.
画折线图时，标记两条坐标轴，并给图表起个标题。选择能清晰显示趋势的刻度。你可以在同一张图上绘制多组数据，使用不同颜色或线型，但要记得包含图例。在 CCEA 统计中，你可能会比较一周内的温度变化或植物几周内的生长情况。
Reading a line graph involves interpreting the slope, spotting peaks and troughs, and describing the overall trend. Always use words like ‘increase’, ‘decrease’, ‘constant’ and ‘fluctuate’ in your answers.
读折线图需要解读斜率、找出波峰和波谷，并描述整体趋势。回答时请始终使用如“增加”、“减少”、“不变”和“波动”等词语。
8. Pie Charts | 饼图
A pie chart displays data as slices of a circle. The entire circle represents the total frequency, and each slice shows a category’s proportion. Pie charts are excellent for showing how a whole is divided into parts.
饼图将数据展现为圆的扇形区域。整个圆代表总频数，每个扇形表示某个类别的比例。饼图非常适合于展示整体如何被划分为各个部分。
To construct a pie chart, you must first find the angle for each category. Since the full circle is 360°, the angle is calculated as:
要绘制饼图，你必须首先计算每个类别对应的角度。由于整圆为 360°，角度计算公式如下：
Angle = (Category frequency ÷ Total frequency) × 360°
角度 = (类别频数 ÷ 总频数) × 360°
In Year 7 CCEA, you might not have to draw a pie chart with a protractor from scratch, but you may be asked to interpret given pie charts or complete partially labelled ones. Always check that the angles sum to 360° and that each slice is correctly labelled with the category and percentage if needed.
在 CCEA 七年级中，你可能不需要用量角器从头画饼图，但可能被要求解读给出的饼图或补全部分标记的饼图。务必检查所有角度之和是否为 360°，以及每个扇形是否正确地标有类别和所需百分比。
9. Averages: Mode, Median and Mean | 平均数：众数、中位数和均值
Averages help us summarise a set of data with a single value that represents the ‘middle’ or most typical value. The three measures of average are the mode, median and mean. Each one is useful in different situations.
平均数帮助我们用单一数值来概括一组数据，这个数值代表了中间值或最典型的值。三种平均度量是众数、中位数和均值。每一种在不同情况下都有用。
The mode is the value that appears most often. A set of data can have one mode, more than one mode (bimodal or multimodal) or no mode at all if all values occur equally.
众数 是出现最频繁的值。一组数据可以有一个众数、多于一个众数（双众数或多众数），或者如果所有值出现次数相同则没有众数。
The median is the middle value when the data is arranged in order. If there is an odd number of observations, the median is the value at position (n+1) ÷ 2. If there is an even number, the median is the average of the two middle values.
中位数 是将数据按顺序排列后位于中间的值。如果数据个数为奇数，中位数是第 (n+1) ÷ 2 个位置的值。如果为偶数，中位数则是中间两个值的平均数。
The mean is the sum of all values divided by the number of values. It is often called the average.
均值 是所有值的总和除以值的个数。它通常被称为平均数。
Mean = (Sum of all values) ÷ (Number of values)
均值 = 所有值的总和 ÷ 值的个数
Example: For the data set 3, 7, 7, 2, 9: Mode = 7, ordered data 2, 3, 7, 7, 9 → median = 7 (third value), mean = (2+3+7+7+9) ÷ 5 = 28 ÷ 5 = 5.6.
示例： 数据集 3, 7, 7, 2, 9：众数 = 7，排序后 2, 3, 7, 7, 9 → 中位数 = 7（第三个值），均值 = (2+3+7+7+9) ÷ 5 = 28 ÷ 5 = 5.6。
10. The Range | 极差
While averages tell us about the centre of the data, the range tells us how spread out the data is. The range is the difference between the largest and the smallest values.
平均数告诉我们数据的中心情况，而极差则告诉我们数据的分散程度。极差是最大值与最小值之间的差。
Range = Highest value − Lowest value
极差 = 最大值 − 最小值
A small range means the numbers are close together; a large range shows they are more spread out. The range is simple to calculate, but it is affected by extreme outliers. In Year 7 CCEA, you will often be asked to compare two sets of data using the averages and the range, giving reasons for your conclusions.
极差小意味着数值相互接近；极差大则显示它们更加分散。极差计算简单，但会受到极端异常值的影响。在 CCEA 七年级中，你经常会被要求使用平均数和极差来比较两组数据，并为你的结论给出理由。
Example: Test scores: 12, 15, 11, 18, 14. Range = 18 − 11 = 7. You could say, ‘The range is 7, which shows a moderate spread of scores.’
示例： 测试分数：12, 15, 11, 18, 14。极差 = 18 − 11 = 7。你可以说：“极差为 7，表明分数有中等程度的分散。”
11. Introduction to Probability | 概率基础
Probability is the branch of mathematics that studies how likely events are to happen. It is measured on a scale from 0 to 1, where 0 means impossible and 1 means certain. You can also express probability as a fraction, decimal or percentage.
概率是研究事件发生可能性的数学分支。它用 0 到 1 的标度来度量，0 表示不可能，1 表示一定发生。你也可以把概率表示为分数、小数或百分比。
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Impossible (0): Rolling a 7 on a standard dice.
不可能 (0)： 在标准骰子上掷出 7 点。
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Even chance (½ or 0.5): Getting heads when flipping a fair coin.
等概率 (½ 或 0.5)： 抛掷均匀硬币得到正面。
-
Certain (1): The sun will rise tomorrow (in everyday terms).
一定 (1)： 太阳明天会升起（在日常生活中）。
To calculate probability theoretically, use the formula:
要计算理论概率，使用以下公式：
Probability of an event = Number of favourable outcomes ÷ Total number of outcomes
事件概率 = 有利结果数 ÷ 总结果数
In Year 7 CCEA, probability is often linked to experiments with dice, spinners or coloured counters. You may be asked to state the probability of a simple event or compare likelihoods using the probability scale. Remember that probabilities must always be between 0 and 1. If your answer is larger than 1 or negative, something has gone wrong!
在 CCEA 七年级中，概率常常与骰子、转盘或彩色筹码的实验相联系。你可能会被要求陈述一个简单事件的概率，或用概率标度比较可能性。记住，概率必须始终在 0 和 1 之间。如果你的答案大于 1 或为负数，说明肯定出错了！
12. Interpreting and Comparing Data | 数据解读与比较
Being able to read and compare statistical information is a vital skill. Whether you are looking at bar charts, line graphs or a set of averages, always read the question carefully and refer to specific numbers in your answer. Avoid vague statements such as ‘it’s bigger’; instead, quote actual values and differences.
能够阅读和比较统计信息是一项重要技能。无论你面对的是柱状图、折线图还是一组平均数，都要认真阅读问题并在回答中引用具体的数字。避免模糊的叙述，比如“它更大”；而要引用实际数值和差值。
When comparing two data sets, use both an average and the range. For example, ‘Class A has a higher mean score (14.2) than Class B (12.6), but Class B’s range is smaller, so their scores are more consistent.’ This type of reasoning is exactly what CCEA examiners look for as you progress through Key Stage 3.
比较两组数据时，要同时使用平均数和极差。例如，“A 班的平均分 (14.2) 高于 B 班 (12.6)，但 B 班的极差更小，因此他们的分数更稳定。” 随着你进入 Key Stage 3，CCEA 考官期望看到的就是这种类型的推理。
Finally, always check your conclusions make sense in the context of the problem. Could there be an outlier skewing the mean? Is the mode useful when all values are different? Asking yourself these questions will take your statistical thinking to a higher level – and prepare you beautifully for Year 8.
最后，务必检查你的结论在问题语境中是否合理。是否存在拉高均值的异常值？所有值都不同时，众数还有用吗？多问自己这些问题，会提升你的统计思维，为你顺利进入 Year 8 做好完美准备。
Published by TutorHao | Statistics Revision Series | aleveler.com
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