📚 Year 9 WJEC Statistics: Summer Prep and Bridging Course | 9年级WJEC统计：暑期预习与衔接课程
Welcome to the Year 9 WJEC Statistics summer preparation and bridging course. This article is designed to introduce you to key statistical concepts you will encounter in your upcoming WJEC course, helping you build confidence before the new school year. We’ll explore data, graphs, averages, probability, and more in a clear, step-by-step manner.
欢迎来到9年级WJEC统计暑期预习与衔接课程。本文旨在为你介绍即将在WJEC课程中遇到的关键统计概念，帮助你在新学年之前建立信心。我们将以清晰、循序渐进的方式探索数据、图表、平均数、概率等内容。
1. What is Statistics? | 什么是统计？
Statistics is the science of collecting, organising, presenting, analysing, and interpreting data. It helps us make informed decisions based on evidence. In everyday life, statistics are used in weather forecasts, sports performance, medical trials, and understanding trends in business. The WJEC Year 9 course will build your skills in handling data and thinking critically about numerical information.
统计学是收集、整理、展示、分析和解释数据的科学。它帮助我们在证据基础上做出明智决策。在日常生活中，统计数据用于天气预报、运动表现、医学试验以及理解商业趋势。WJEC九年级课程将培养你处理数据以及批判性思考数字信息的能力。
2. Methods of Data Collection | 数据收集方法
Before any analysis, we need data. Data can be primary, which means you collect it yourself for a specific purpose, for example through a questionnaire or an experiment. It can also be secondary, meaning someone else has already gathered it, such as data from official websites, books, or published reports. When designing a survey, it’s important to ask clear, unbiased questions and to consider the sample size to ensure the data is representative.
在分析之前，我们需要数据。数据可以是初级数据，即你为了特定目的亲自收集的，例如通过问卷或实验。它也可以是次级数据，即他人已经收集好的，比如来自官方网站、书籍或已发表报告的数据。设计调查时，重要的是提出清晰、无偏的问题并考虑样本量，以确保数据具有代表性。
3. Organising Data: Frequency Tables | 整理数据：频数表
Raw data often looks messy. A frequency table organises data by showing how many times each value or category appears. Tally marks are a useful tool for counting data on the fly. For continuous data that takes many different values, we group data into class intervals (e.g., 0-9, 10-19) and record the frequency for each group. This makes it much easier to see patterns and compare groups.
原始数据往往杂乱无章。频数表通过显示每个数值或类别出现的次数来整理数据。计数符号是一种随时记录数据的有用工具。对于取值众多的连续数据，我们将数据分组到组距（例如0-9、10-19），并记录各组的频数。这让我们更容易看清模式和进行比较。
4. Graphical Displays: Bar Charts and Pie Charts | 数据的图形展示：条形图和饼图
Bar charts use rectangular bars to represent frequencies for categorical data. The height of each bar corresponds to its frequency, and bars are separated to show distinct categories. They are perfect for comparing counts across different groups. Pie charts display proportions of a whole: each slice represents a category, and its angle is proportional to the frequency. Always include a title and label axes or sectors clearly.
条形图使用矩形条来表示分类数据的频数。每个条形的高度对应其频数，条形之间分开以显示不同类别。条形图非常适合比较不同组别的数量。饼图展示整体的比例：每个扇形代表一个类别，其角度与频数成正比。务必添加标题并清楚地标记坐标轴或扇区。
5. More Graphs: Line Graphs and Scatter Plots | 更多图表：折线图与散点图
Line graphs are ideal for displaying data that changes over time, such as temperatures over a week. Points are plotted and connected with lines to reveal trends and fluctuations. A scatter graph plots two related numerical variables, e.g., height and shoe size. By looking at the pattern of points, we can describe correlation as positive, negative, or none. A line of best fit can be drawn to estimate values and make predictions.
折线图非常适合展示随时间变化的数据，例如一周的温度。点上绘制点并用线连接，以揭示趋势和波动。散点图绘制两个相关的数值变量，例如身高和鞋码。通过观察点的分布模式，我们可以描述相关性为正、负或无相关。可以绘制最佳拟合线来估计数值并进行预测。
6. Stem and Leaf Diagrams | 茎叶图
A stem and leaf diagram keeps original data values while showing their distribution. The ‘stem’ is formed by all digits except the last, and the ‘leaf’ is the final digit. For the data 23, 25, 31, 31, 42, 45, the stems are 2, 3, 4; leaves for stem 2 are 3 and 5. An ordered diagram makes it easy to find the median and range. Stem and leaf diagrams work best for small sets of numerical data.
茎叶图在保留原始数据值的同时展示其分布。’茎’由除最后一位外的所有数字组成，’叶’是最后一位数字。对于数据23、25、31、31、42、45，茎为2、3、4；茎2的叶为3和5。排序后的图表使找到中位数和极差变得容易。茎叶图最适合小型数值数据集。
7. Measures of Central Tendency: Mean, Median, Mode | 集中趋势的度量：平均数、中位数、众数
An average is a single value that describes the centre of a dataset. The mode is the value that occurs most often. The median is the middle value when data is ordered from smallest to largest; if there are two middle values, the median is their midpoint. The mean is calculated by adding all the values together and dividing by how many values there are.
平均数是描述数据集中心的单一数值。众数是出现最频繁的值。中位数是将数据从小到大排序后位于中间的值；如果有两个中间值，则中位数是它们的中间点。平均数通过将所有数值相加然后除以数值个数来计算。
Mean = (Sum of all data values) ÷ Number of values
每种平均数在不同的场合有用。众数适合分类数据；中位数不受极端值影响，适合有离群值的数据集；平均数则利用了所有数据信息，但可能被极端值拉偏。
8. Measure of Spread: Range | 离散程度的度量：极差
The range tells us how spread out the data are. It is the difference between the largest and smallest values. A small range means the data are closely packed, while a large range indicates wide variation. The range is easy to compute but is sensitive to outliers.
极差告诉我们数据的分散程度。它是最大值与最小值之间的差值。极差小说明数据紧密集中，极差大则表明差异很大。极差计算简单，但容易受离群值影响。
Range = Largest value – Smallest value
For a fuller picture, always report both an average and a measure of spread, such as the median and range, or the mean and range.
为了获得更全面的信息，要同时报告平均数和离散程度度量，如中位数和极差，或者平均数和极差。
9. Introduction to Probability | 基本概率
Probability measures the chance of an event happening and is expressed on a scale from 0 (impossible) to 1 (certain). When all outcomes are equally likely, we calculate the theoretical probability using the formula:
概率衡量事件发生的可能性，用从0（不可能）到1（必然）的尺度表示。当所有结果等可能时，我们用以下公式计算理论概率：
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
Probabilities can be written as fractions, decimals, or percentages. For example, the probability of rolling a 3 on a fair dice is 1/6, which is about 0.167 or 16.7%.
概率可以写成分数、小数或百分比。例如，掷一个公平骰子得到3的概率是1/6，约为0.167或16.7%。
10. Probability Experiments and Relative Frequency | 概率实验与相对频率
When we cannot assume equally likely outcomes, we can estimate probability by performing an experiment or using historical data. The relative frequency of an event is found by dividing the number of times the event occurs by the total number of trials.
当我们不能假设结果等可能时，可以通过进行实验或使用历史数据来估计概率。事件的相对频率通过事件发生次数除以试验总次数求得。
Relative frequency = Frequency of event ÷ Total number of trials
As the number of trials increases, the relative frequency tends to stabilise and get closer to the true probability. This is called the law of large numbers.
随着试验次数增加，相对频率趋于稳定并接近真实概率。这被称为大数定律。
11. Statistical Project: From Question to Conclusion | 统计项目：从问题到结论
A complete statistical investigation follows these steps: pose a question or hypothesis, plan how to collect data, gather the data, organise it using tables, present it graphically, analyse using averages and spread, and finally draw conclusions. For instance, you might investigate “Do students who eat breakfast perform better in tests?” You would write a report summarising your findings and reflecting on any limitations, such as small sample size or biased sampling.
完整的统计调查遵循以下步骤：提出问题或假设，规划如何收集数据，收集数据，用表格整理数据，用图形展示，使用平均数和离散程度进行分析，最后得出结论。例如，你可以调查“吃早餐的学生考试是否表现更好？”然后撰写报告总结发现，并反思局限性，如样本量小或抽样有偏。
12. Summer Bridging Tips | 暑期衔接建议
To get a head start, practise calculating averages and the range from small data sets you find at home, such as daily screen time or exercise minutes. Create frequency tables and draw simple bar charts. Watch a weather forecast and note how temperatures are graphed. Try simple probability experiments with coins or dice and record relative frequencies. These activities will make the transition to Year 9 WJEC Statistics much smoother.
为了领先一步，练习从家里的数据（如每日屏幕时间或运动分钟数）计算平均数和极差。创建频数表并绘制简单的条形图。看天气预报并注意温度是如何用图表表示的。用硬币或骰子尝试简单的概率实验并记录相对频率。这些活动将使你更顺利地过渡到九年级WJEC统计课程。
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