📚 Year 7 WJEC Statistics: Summer Preview and Bridging Course | Year 7 WJEC 统计：暑期预习与衔接课程
Welcome to your summer statistics adventure! Statistics is the art of turning numbers and facts into clear stories that answer real-world questions. Whether you are predicting a rainy day, analysing your favourite football player’s performance, or understanding survey results, statistics gives you the power to find meaning in data. This bridging course will gently introduce the key ideas you need for Year 7 WJEC Statistics, so you can start the term with confidence and curiosity.
欢迎来到暑期统计冒险！统计学是把数字和事实变成清晰故事、回答真实世界问题的一门艺术。无论是预测雨天、分析你最喜欢的足球运动员的表现，还是看懂调查结果，统计都能帮你从数据中找出意义。本衔接课程会温和地介绍 Year 7 WJEC 统计的关键知识，让你带着信心和好奇心开启新学期。
We will explore how to collect, organise, and display data, learn about averages and probability, and even design your own mini survey. Every section pairs an English explanation with a Chinese one, so you can build your mathematical vocabulary in both languages. Let’s begin!
我们将探索如何收集、整理和展示数据，学习平均值与概率，甚至设计你自己的小调查。每个小节都用英文和中文双语解释，帮助你在两种语言中建立数学词汇。我们开始吧！
1. What Is Statistics? | 统计学是什么？
Statistics is the science of collecting, organising, presenting, analysing, and interpreting data to make decisions or predictions.
统计学是收集、整理、展示、分析和解释数据以做出决策或预测的科学。
Data simply means facts or numbers gathered from the world around us, such as the heights of classmates, daily temperatures, or the colours of cars passing by.
数据就是指从我们周围世界收集的事实或数字，比如同学的身高、每日温度，或者经过的汽车颜色。
A question like “Does it rain more on weekends?” can be answered by gathering rainfall data day by day and looking for a pattern. That is statistics in action.
像“周末是不是下雨更多？”这样的问题，可以通过逐日收集降雨数据并寻找规律来回答。这就是生活中的统计。
In Year 7, you will learn simple but powerful techniques to work with data, so you can find answers yourself instead of just guessing.
在 Year 7，你将学到简单却强大的数据处理方法，这样你就可以自己找到答案，而不仅仅是猜测。
2. Types of Data: Qualitative and Quantitative | 数据类型：定性与定量
All data falls into two broad families: qualitative data and quantitative data.
所有数据都分成两大类别：定性数据和定量数据。
Qualitative data describe qualities or categories that cannot be measured with numbers in a usual sense, for example favourite food, eye colour, or types of pet.
定性数据描述的是通常不能用数字测量的属性或类别，例如最喜欢的食物、眼睛颜色或宠物种类。
Quantitative data are numbers that can be measured or counted. They come in two forms: discrete data and continuous data.
定量数据是可以测量或计数的数字。它们又分为两种形式：离散数据与连续数据。
Discrete data can only take certain values, like the number of brothers (0, 1, 2, 3 …) or the number of goals scored in a match.
离散数据只能取特定的值，比如兄弟的个数（0、1、2、3……），或者一场比赛的进球数。
Continuous data can take any value within a range, like height (you could be 142.5 cm), weight, or the amount of time it takes to run 100 metres.
连续数据可以在一个范围内取任意值，比如身高（你可能是 142.5 cm）、体重，或者跑 100 米所用的时间。
Recognising data types helps you choose the right chart or calculation later. You will often collect both kinds in the same investigation.
识别数据类型有助于你之后选择合适的图表或计算方法。在同一次调查中，你常常会同时收集这两种数据。
3. Collecting Data: Surveys and Experiments | 收集数据：调查与实验
Good statistics begins with careful data collection. Two common methods are surveys and experiments.
好的统计从认真收集数据开始。两种常见的方式是调查和实验。
A survey uses questions to gather information from a group of people. You can design a questionnaire with simple tick boxes, rating scales, or open‑ended questions.
调查是指用问题从一群人那里收集信息。你可以设计一份问卷，采用简单勾选、评分量表或开放式问题。
It is important to think about your sample – the people you ask. A fair sample should represent the group you are interested in, not just your best friends.
考虑你选择的样本（你所询问的人）很重要。一个公正的样本应该代表你感兴趣的群体，而不仅仅是你的好朋友。
An experiment involves changing something and measuring the result. For example, you could drop a ball from different heights and measure the bounce height.
实验则是改变某些条件并测量结果。例如，你可以从不同高度扔下一个球，测量其反弹高度。
Recording your data neatly right away is a crucial habit. Use a table or a simple tally chart as you collect each piece of information.
立即将数据记录整齐是一个关键习惯。在收集每一条信息时，可以使用表格或简单的计数表。
4. Organising Data: Tally Charts and Frequency Tables | 整理数据：计数表与频率表
Once raw data are gathered, they need to be organised. The tally chart is one of the simplest and most useful tools.
一旦原始数据收集完毕，就需要进行整理。计数表是最简单、最实用的工具之一。
A tally mark is a straight line; every fifth mark goes across the previous four to form a gate of five, like this: |||| . This makes counting much faster.
一个计数记号是一条竖线；每第五个记号会横穿前四个，形成一个“五”的栅栏，样子如：|||| 。这样数起来快得多。
From the tally chart you can build a frequency table. Frequency simply means how many times something appears.
从计数表可以进一步做出频率表。频率就是某个事物出现的次数。
For example, if you survey 20 classmates about their favourite fruit and record their answers with tallies, the frequency table will quickly tell you which fruit is most popular.
例如，如果你调查 20 位同学最喜欢的水果并用计数符号记录，频率表就能迅速告诉你哪种水果最受欢迎。
Always remember to add a total row showing how many pieces of data you have collected. This checks that you haven’t missed any.
千万别忘记加上合计行，显示你总共收集了多少条数据。这样可以检查是否漏记。
5. Bar Charts and Pictograms | 条形图与象形图
Visualising data makes patterns leap out. Bar charts are a great first choice for comparing categories.
将数据可视化能让规律立刻显现。在比较各类别时，条形图是一个很棒的初步选择。
In a bar chart, the height or length of each bar represents the frequency. The bars must be of equal width and, for discrete categories, should not touch each other.
条形图中，每个条形的高度或长度代表频率。条形的宽度必须相等，对于离散类别，条形之间不应相互接触。
Always label your axes and give your chart a clear title. Without these, your reader cannot understand what you are showing.
始终要给坐标轴加上标签，并给图表一个清晰的标题。没有这些，读者就无法理解你在展示什么。
A pictogram uses small pictures or symbols to represent data. Each symbol could stand for one person, or for two, five, or ten units, making a key essential.
象形图用小图片或符号来代表数据。每个符号可以表示一个人，或两个、五个、十个单位，因此图例至关重要。
Pictograms are attractive, but be careful: half a symbol must only count as half of the amount it represents, so the key must match perfectly.
象形图很吸引人，但要小心：半个符号也只能算作它所代表数量的一半，因此图例必须完全匹配。
6. Pie Charts and Line Graphs | 饼图与折线图
Pie charts show how a whole is divided into parts. They are perfect for percentages or proportions, like how you spend 24 hours in a day.
饼图展示的是整体如何划分成部分。它们非常适合表现百分比或比例，比如一天 24 小时是如何度过的。
To draw a pie chart by hand, you calculate the angle for each category using the formula: angle = (category frequency ÷ total frequency) × 360°.
Angle = (Category frequency ÷ Total frequency) × 360°
要手工绘制饼图，你需要用公式计算每类的角度：角度 = （类别频率 ÷ 总频率）× 360°。
角度 = （类别频率 ÷ 总频率）× 360°
Line graphs are best for showing how something changes over time, such as temperature across a day or a plant’s height over several weeks.
折线图最适合展示数据随时间的变化情况，比如一天内温度的变化，或几周内植物的高度变化。
When plotting a line graph, place time on the horizontal axis (x‑axis) and the changing quantity on the vertical axis (y‑axis). Connect the points with straight lines.
绘制折线图时，将时间放在横轴（x 轴），将变化的量放在纵轴（y 轴），然后用直线将各点连接起来。
7. Measures of Central Tendency: Mean, Median, Mode | 集中量数：平均数、中位数、众数
An average is a single number that summarises the centre of a data set. Year 7 focuses on three types: mode, median, and mean.
平均数是用来概括一组数据中心位置的单独数值。Year 7 重点学习三种：众数、中位数和平均数。
The mode is the value that appears most often. A set can have no mode, one mode, or more than one mode.
众数是出现次数最多的数值。一组数据可以没有众数，也可以有一个或多个众数。
The median is the middle value when the numbers are arranged in order. For an odd amount of data, it is the exact centre; for an even amount, find the mean of the two middle numbers.
中位数是把数据从小到大排列后位于中间位置的数值。数据个数为奇数时，它就是正中间的数；为偶数时，则取中间两个数的平均数。
The mean is what people often call the ‘average’. Add up all the values and then divide by how many there are.
平均数就是人们常说的“平均值”。把所有数值加起来，然后除以数据的个数。
Mean = (Sum of all values) ÷ (Number of values)
平均数 = （所有数值之和）÷ （数值个数）
Each average tells a different story. The mode shows popularity, the median resists extreme values, and the mean balances all values equally.
每种平均数讲的故事都不同。众数反映流行性，中位数不易受极端值影响，而平均数平等地平衡了所有数值。
8. Range and Interpreting Statistical Diagrams | 极差与统计图解读
The range measures how spread out the data are. It is simply the difference between the largest and smallest values.
极差衡量的是数据的分散程度。它就是最大值与最小值之差。
Range = Largest value – Smallest value
极差 = 最大值 – 最小值
A small range means the numbers are close together; a large range shows they are widely spread. Always give the range alongside an average for a fuller picture.
极差小说明数字比较集中；极差大说明它们分布很广。始终在给出平均数的同时报告极差，才能得到更完整的图景。
When reading diagrams, ask questions: What do the axes show? Is the scale fair? Are there any unusual spikes? These questions help you interpret rather than just describe.
阅读统计图时，问自己几个问题：坐标轴表示什么？刻度是否合理？有没有异常尖峰？这些问题能帮助你深入解读，而不仅仅是描述。
Be alert for misleading graphs. A bar chart with a vertical scale that does not start at zero can make differences look much larger than they really are.
要警惕误导性图表。如果条形图的纵轴刻度不是从零开始，可能会让差异看起来比真实情况大得多。
9. Probability Basics: Scale and Language | 概率基础：尺度与语言
Probability is the branch of statistics that deals with how likely an event is to happen. It is measured on a scale from 0 to 1.
概率是统计学中研究事件发生可能性的分支。它用 0 到 1 之间的一个数值来测量。
An impossible event has a probability of 0. A certain event has a probability of 1. Everything else lies somewhere between.
不可能事件的概率为 0，必然事件的概率为 1。其他所有事件都介于两者之间。
We also use words: ‘unlikely’, ‘even chance’, ‘likely’, and so on. An even chance can be written as ½, 0.5, or 50%.
我们也会使用词语来描述：“不大可能”、“机会均等”、“很可能”等等。机会均等可以写作 ½、0.5 或 50%。
The probability of rolling a 3 on a fair six‑sided dice is 1/6, because there is one desired outcome out of six equally likely outcomes.
在一个均匀的六面骰子上掷出 3 的概率是 1/6，因为 6 个等可能结果中只有 1 个是目标结果。
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）
Moving fluently between fractions, decimals, and percentages for probability is a vital skill in Year 7.
在 Year 7，能够熟练地在分数、小数和百分数之间转换概率是一项重要的技能。
10. Theoretical vs Experimental Probability | 理论概率与实验概率
Theoretical probability is what we expect to happen based on equally likely outcomes, like predicting heads as ½ for a fair coin.
理论概率是我们基于等可能结果预期的结果，比如对于均匀硬币，预测正面的概率为 ½。
Experimental probability comes from actually doing an experiment and recording what occurs. If you toss a coin 50 times and get 28 heads, the experimental probability is 28/50, or 0.56.
实验概率来自真实的实验并记录发生情况。如果你抛硬币 50 次得到 28 次正面，那么实验概率为 28/50，即 0.56。
Usually, with more trials the experimental probability gets closer to the theoretical one. This is called the law of large numbers.
通常，随着试验次数增多，实验概率会越来越接近理论概率。这被称为大数定律。
Try this at home: flip a coin 10 times, 30 times, then 100 times, and watch how the experimental probability settles. Record your results in a frequency table.
在家试试看：先抛 10 次硬币，再抛 30 次，然后是 100 次，观察实验概率如何稳定下来。把你的结果记录在频率表中。
Understanding both kinds helps you realise that real life often contains variation, and statistics helps you measure that variation.
理解两种概率能让你明白，真实生活常包含变异性，而统计学正是帮助你衡量这种变异。
11. Conducting a Mini Statistical Investigation | 进行一次小型统计调查
A complete statistical investigation follows a cycle: pose a question, collect data, organise and display it, calculate summary statistics, and interpret the findings.
一个完整的统计调查遵循这样的循环：提出问题、收集数据、整理并展示数据、计算概括性统计量，然后解读结果。
Start with a clear, simple question like ‘How many hours per week do students in my class spend on homework?’ or ‘What is the most common birth month?’
从一个清晰、简单的问题开始，比如“我们班同学每周花多少个小时做家庭作业？”或“最常见的出生月份是几月？”。
Design a data‑collection sheet with rows for each person and columns for the answers. Use a tally column if you can record as you go.
设计一份数据收集表，每一行对应一个人，每一列对应答案。如果可以的话，加上一列用作计数。
Choose an appropriate chart: a bar chart for comparing categories, a line graph for time‑based data, or a pie chart for showing shares of a whole.
选择合适的图表：比较类别用条形图，呈现随时间变化的数据用折线图，展示整体中的份额用饼图。
Calculate the mode, median, mean, and range, then write a short conclusion. Did anything surprise you? Could your survey be improved next time?
计算出众数、中位数、平均数和极差，然后写一小段结论。有什么令你惊讶的地方吗？下次调查可以如何改进？
This mini investigation will help you see how all the Year 7 topics connect in a real project.
这个小型调查将帮助你看到所有 Year 7 课题是如何在一个真实项目中连接起来的。
12. Getting Ready for Year 7 Success | 为 Year 7 成功做好准备
You have now previewed the core WJEC Year 7 statistics topics: data types, tallies, charts, averages, range, probability, and investigative skills.
到目前为止，你已经预习了 WJEC Year 7 统计的核心主题：数据类型、计数表、图表、平均数、极差、概率以及调查技能。
To make the most of this summer, try to spot statistics in daily life – notice the graphs on news websites, look at weather probabilities in apps, and ask your own questions.
要想充分利用这个暑假，试着在生活中寻找统计——注意新闻网站上的图表，看看天气应用里的概率，并问出你自已的问题。
Keep a small ‘stats journal’ where you paste a graph you find and write one sentence in English and one in Chinese about what it shows.
准备一本小小的“统计日志”，贴上一张你找到的图表，并用英文和中文各写一句话说明它展示了什么。
Practise the key vocabulary: mode, median, mean, range, discrete, continuous, tally, frequency, probability, and sample. Say them aloud in both languages.
练习关键术语：众数、中位数、平均数、极差、离散、连续、计数、频率、概率和样本。试着双语大声朗读这些词汇。
Entering Year 7 with a solid foundation in statistics will give you a real advantage, not just in maths but in science, geography, and everyday decisions too.
带着扎实的统计基础进入 Year 7，不仅能让你在数学上占优势，在科学、地理和日常决策中也是如此。
We hope this bridging course has sparked your curiosity. Welcome to the fascinating world of data!
我们希望这个衔接课程点燃了你的好奇心。欢迎来到迷人的数据世界！
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