📚 Year 7 SQA Statistics: Summer Preparation and Bridging Course | 七年级 SQA 统计：暑期预习与衔接课程
Welcome to your summer statistics bridging course. This guide is designed to help you build confidence in data handling, averages, charts, and basic probability – exactly what you need for a smooth start in Year 7 SQA Mathematics. Work through each section at your own pace, try the examples, and you will enter Year 7 fully prepared.
欢迎来到暑期统计衔接课程。这份指南旨在帮助你建立处理数据、计算平均数、绘制图表以及基础概率的自信心——这些正是你顺利开启七年级 SQA 数学课程所需的。按照自己的节奏学习每一部分，尝试示例，你将做好充分准备迎接七年级。
1. What Is Statistics? | 什么是统计？
Statistics is the science of collecting, organising, presenting, analysing, and interpreting data. In Year 7, you will learn to turn raw facts and figures into meaningful information using tables, graphs, and summary numbers.
统计学是收集、整理、展示、分析和解读数据的科学。在七年级，你将学习如何使用表格、图表和概括性数字，将原始的事实和数据转化为有意义的信息。
Statistics helps us answer real-world questions: What is the most popular sport in our class? How does the temperature change over a week? Which supermarket offers better value? By learning statistics, you become a data detective who finds patterns and makes informed decisions.
统计学帮助我们回答现实世界的问题：我们班最受欢迎的运动是什么？温度在一周内如何变化？哪家超市更划算？通过学习统计，你将成为一名数据侦探，发现规律并做出明智的决策。
2. Types of Data | 数据类型
Data can be divided into two main types: qualitative and quantitative. Qualitative data describes qualities or categories, such as eye colour, favourite subject, or type of pet. Quantitative data consists of numbers that can be measured or counted, like height, number of siblings, or test scores.
数据可分为两大类：定性数据和定量数据。定性数据描述品质或类别，例如眼睛颜色、最喜欢的科目或宠物类型。定量数据则由可测量或可计数的数字组成，如身高、兄弟姐妹人数或考试分数。
Quantitative data is further split into discrete and continuous data. Discrete data can only take certain values – often whole numbers, like the number of students in a class or shoes in a cupboard. Continuous data can take any value within a range, for example height (1.63 m), mass (45.2 kg), or time (12.7 s).
定量数据进一步分为离散数据和连续数据。离散数据只能取特定数值——通常是整数，比如班级里的学生人数或柜子里的鞋子数量。连续数据可以取某个范围内的任何值，例如身高（1.63 米）、质量（45.2 千克）或时间（12.7 秒）。
| Data Type 数据类型 | Description 描述 | Examples 示例 |
|---|---|---|
| Qualitative 定性 | Categories or labels 类别或标签 | Hair colour, favourite film 发色、最喜欢的电影 |
| Quantitative discrete 定量离散 | Countable, whole numbers 可计数，整数 | Number of books, pupils in a group 书本数量、小组人数 |
| Quantitative continuous 定量连续 | Measurable, any value 可测量，任意值 | Temperature, length, volume 温度、长度、体积 |
Recognising data types helps you choose the right chart and the right calculations. For example, it makes no sense to find the ‘average’ hair colour, but you can calculate the mean height.
认识数据类型有助于你选择合适的图表和计算方法。例如，寻找头发颜色的“平均数”没有意义，但你可以计算平均身高。
3. Collecting Data | 收集数据
Before you can work with data, you need to collect it properly. Data can be gathered through surveys, questionnaires, experiments, observations, or from existing records. A good survey asks clear, unbiased questions – avoid leading questions like ‘Don’t you agree that football is the best sport?’
在你处理数据之前，需要正确地收集数据。数据可以通过调查、问卷、实验、观察或已有记录来收集。好的调查会提出清晰、不带偏见的问题——避免诱导性问题，例如“你难道不认为足球是最好的运动吗？”
You will often use tally charts to record data as it is collected. A tally mark is made for each item, and the fifth mark crosses the previous four to make groups of five easy to count. Tally charts help you organise data before making frequency tables or diagrams.
你经常会使用计数表在收集数据的同时进行记录。每出现一项就画一个计数符号，第五个符号画一条横线穿过前四个，以便五个一组容易计数。计数表帮助你在制作频数表或图表之前整理数据。
Example: Tally for favourite fruit: Apple ||||, Banana ||, Orange |||| ||. This shows 5 for apple, 2 for banana, and 7 for orange.
示例：最受欢迎水果的计数：苹果 ||||，香蕉 ||，橙子 |||| ||。这表示苹果 5 票，香蕉 2 票，橙子 7 票。
4. Organising Data: Frequency Tables | 整理数据：频数表
A frequency table is a simple way to summarise data. It lists each category or data value and the number of times it appears (the frequency). Frequencies can be counted from raw data or from a tally chart.
频数表是一种概括数据的简单方法。它列出每个类别或数据值以及出现的次数（频数）。频数可以从原始数据或计数表中数出。
For discrete data, you may list individual values. For continuous data, you will group the values into class intervals, such as 0 ≤ h < 10, 10 ≤ h < 20, and so on, where h represents height in centimetres. Grouping makes large sets of continuous data easier to handle.
对于离散数据，你可以列出每个单独数值。对于连续数据，你将把数值分组到区间中，例如 0 ≤ h < 10，10 ≤ h < 20，依此类推，其中 h 代表厘米为单位的身高。分组使得大量连续数据更易于处理。
Always check that your frequency total matches the number of data items – this is a quick way to spot mistakes.
务必检查频数总和是否与数据项总数一致——这是发现错误的快速方法。
5. Bar Charts and Pictograms | 条形图与象形图
Bar charts display categorical or discrete data using rectangular bars. The length or height of each bar represents the frequency. Bars should be evenly spaced, of equal width, and clearly labelled with a title and axis labels.
条形图使用矩形条来展示类别数据或离散数据。每个条的长度或高度代表频数。条形之间应均匀间隔，宽度相等，并有清晰的标题和坐标轴标签。
A pictogram uses small pictures or symbols to represent data. Each picture stands for a certain number of items – for example, one book icon might represent 5 books. A key must always explain what one symbol equals. Pictograms are eye-catching but can be harder to read accurately when partial symbols are used.
象形图使用小图片或符号来代表数据。每个图片代表一定数量的项目——例如，一个书本图标可能代表 5 本书。必须始终用图例说明每个符号代表什么。象形图引人注目，但当使用部分符号时，可能较难准确读取。
When drawing bar charts or pictograms, always use a ruler and a sharp pencil. Neat presentation helps others understand your data quickly.
绘制条形图或象形图时，请始终使用尺子和削尖的铅笔。整洁的呈现有助于他人快速理解你的数据。
6. Line Graphs and Pie Charts | 折线图与饼图
Line graphs are used to show how data changes over time. Time is placed on the horizontal x-axis, and the quantity being measured goes on the vertical y-axis. Points are plotted and joined with straight lines. Line graphs make trends and patterns easy to spot, such as rising or falling temperatures.
折线图用于显示数据随时间的变化。时间放在水平 x 轴上，被测量的量放在垂直 y 轴上。标出数据点并用直线连接。折线图使趋势和模式一目了然，例如温度的上升或下降。
Pie charts represent data as slices of a circle. The whole circle stands for the total, and each slice shows a proportion, usually as a fraction or percentage. The angle of each slice is calculated by: (frequency ÷ total) × 360°. Pie charts are excellent for comparing parts to a whole, but not for precise values.
饼图用圆形的扇形代表数据。整个圆代表总体，每一扇形显示一个比例，通常用分数或百分比表示。每个扇形的角度通过计算得到：（频数 ÷ 总数）× 360°。饼图非常适合比较部分与整体的关系，但不适合精确数值。
Slice angle = (Frequency ÷ Total frequency) × 360°
扇形角度 =（频数 ÷ 总频数）× 360°
7. Mean, Median, and Mode | 平均数、中位数与众数
These three measures are called ‘averages’ and each summarises a data set in a different way.
这三种度量被称为“平均数”，各自以不同方式概括数据集。
The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode at all. The mode is the only average that can be used with qualitative data.
众数是出现次数最多的值。一个数据集可以有一个众数、多个众数，或没有众数。众数是唯一可用于定性数据的平均数。
The median is the middle value when the data are arranged in order. If there are two middle numbers, the median is the number halfway between them. The median is not affected by extremely high or low values.
中位数是将数据按大小顺序排列后位于中间的值。如果有两个中间数，则中位数是两者正中间的数。中位数不受极高或极低数值的影响。
The mean is found by adding all the values together and dividing by the number of values. It is the ‘fair share’ average, but it can be distorted by outliers.
平均数是把所有的值加在一起再除以数值的个数得到的。它是“公平分享”的平均数，但可能受异常值影响而失真。
Mean = Sum of all values ÷ Number of values
平均数 = 所有数值之和 ÷ 数值的个数
8. Range | 极差
The range measures how spread out the data are. It is simply the difference between the largest and smallest values.
极差衡量数据的离散程度。它只是最大值与最小值之间的差。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
A small range tells you the data are closely grouped; a large range indicates greater variability. The range is easy to calculate, but it only considers the two extreme values and ignores the rest.
极差小说明数据集中在一起；极差大说明变异性大。极差计算简单，但它只考虑两个极端数值而忽略了其余部分。
Always include the range when you summarise data – giving just an average can be misleading. For example, two classes with the same mean test score can have very different ranges, telling you about the consistency of performance.
在概括数据时务必包含极差——只给出平均数可能产生误导。例如，两个班级的平均测试分数相同，但极差可能差异很大，这说明成绩的一致性不同。
9. Introduction to Probability | 概率入门
Probability is a branch of mathematics that measures how likely an event is to happen. It is expressed as a number between 0 and 1. An impossible event has probability 0, a certain event has probability 1, and all other events lie in between.
概率是数学的一个分支，衡量事件发生的可能性大小。它用一个介于 0 和 1 之间的数字表示。不可能发生的事件概率为 0，必然发生的事件概率为 1，其他所有事件的概率介于两者之间。
The probability of an event A is often written as P(A) and calculated by:
事件 A 的概率通常写作 P(A)，并通过以下方式计算：
P(A) = Number of favourable outcomes ÷ Total number of possible outcomes
P(A) = 有利结果的数量 ÷ 所有可能结果的总数
For example, when you roll a fair six-sided dice, the probability of rolling a 3 is 1/6. The probability of rolling an even number is 3/6 = 1/2. All outcomes must be equally likely for this formula to work.
例如，掷一枚均匀的六面骰子时，掷出 3 点的概率是 1/6。掷出偶数的概率是 3/6 = 1/2。所有结果必须是等可能的，这个公式才适用。
10. Probability Scale and Simple Events | 概率尺与简单事件
A probability scale is a visual line from 0 to 1 that helps us place the likelihood of events. Words such as ‘impossible’, ‘unlikely’, ‘even chance’, ‘likely’, and ‘certain’ can be placed along the scale.
概率尺是一条从 0 到 1 的可视线条，帮助我们标明事件的可能性。诸如“不可能”、“不太可能”、“等可能性”、“很可能”和“必然”等词语可以沿尺标出。
Simple events involve a single action, like flipping one coin or spinning one spinner. When listing outcomes, a systematic approach prevents missing any. Use a list or a two-way table for combined events.
简单事件涉及单个动作，比如抛一枚硬币或转一次转盘。在列举结果时，采用系统方法可避免遗漏。对于组合事件，使用列表或双向表。
The sum of probabilities of all possible outcomes of an experiment is always 1. So if the probability of winning a game is 0.3, the probability of not winning is 1 − 0.3 = 0.7. This is called the complement rule.
一个实验中所有可能结果的概率之和始终为 1。因此，如果赢一场游戏的概率是 0.3，那么不赢的概率就是 1 − 0.3 = 0.7。这称为互补规则。
11. Interpreting Statistical Diagrams | 解读统计图表
Reading charts accurately is just as important as drawing them. Always start by checking the title, axis labels, and scale. Look for any misleading features, such as a y-axis that doesn’t start at zero, which can exaggerate differences.
准确读取图表与绘制图表同等重要。开始读取时总是先查看标题、坐标轴标签和刻度。留意任何误导性的特征，例如未从零开始的 y 轴可能夸大了差异。
When comparing two data sets from a chart, use numbers and data ranges, not just visual impressions. For instance, ‘The median mark in Class A is 6 marks higher than in Class B’ is more precise than ‘Class A did better’.
在从图表中比较两组数据时，使用具体数字和数据范围，而不仅仅是视觉印象。例如，“A 班的中位数成绩比 B 班高 6 分”比“A 班考得更好”更精确。
Practice interpreting real-life data: weather charts, sports statistics in newspapers, or popularity polls online. Every chart tells a story – your job is to find it and back up your findings with evidence from the data.
练习解读现实生活中的数据：天气图、报纸上的体育数据或网络上的受欢迎度投票。每张图表都在讲述一个故事——你的任务就是找到它并用数据中的证据支持你的发现。
12. Summary and Bridging to Year 7 | 总结与升入七年级衔接
You have now covered the core statistical ideas that will form the foundation of your Year 7 SQA course. Remember to keep practising these concepts over the summer: tally a week’s weather, calculate the mean screen time, or draw a bar chart of your family’s favourite fruits.
你已经掌握了构成七年级 SQA 课程基础的核心统计思想。记得在暑期继续练习这些概念：记录一周天气的频数、计算平均屏幕时间，或者绘制一张家人最爱水果的条形图。
In Year 7, you will extend these skills further: working with larger data sets, comparing distributions using averages and range, constructing more complex charts, and exploring experimental probability. The confidence you build now will make those topics much easier to tackle.
在七年级，你将进一步拓展这些技能：处理更大的数据集、使用平均数和极差比较分布、构建更复杂的图表，以及探索实验概率。你现在建立的信心将使那些课题变得更易掌握。
If you find any concept tricky, revisit the section, try the examples again, and explain it in your own words. Statistics is a practical subject – the more you do, the better you become.
如果你觉得某个概念困难，请重温该节，再次尝试示例，并用你自己的话加以解释。统计是一门实践性学科——你做得越多，就会越熟练。
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