📚 Year 9 WJEC Statistics: Core Knowledge Overview | Year 9 WJEC 统计：核心知识点梳理
This article brings together the essential topics in the Year 9 WJEC Statistics curriculum. From types of data and collection methods to probability and expectation, mastering these fundamentals will build a strong foundation for future statistical work. Each section is paired in English and Chinese to support bilingual learning and revision.
本文梳理了 Year 9 WJEC 统计课程中的核心知识点，涵盖数据类型、收集方法、图表、概括统计量与概率初步等内容。每个小节均提供中英双语对照，帮助巩固基础概念，为后续的统计学习打好根基。
1. Types of Data | 数据类型
Data can be classified as qualitative or quantitative. Qualitative data (also called categorical data) describes qualities or categories, such as eye colour or favourite subject. Quantitative data records numerical measurements or counts, like height or number of siblings.
数据可分为定性数据和定量数据。定性数据（也称分类数据）描述的是特征或类别，例如眼睛的颜色、最喜欢的科目；定量数据则记录数值度量或计数，如身高或兄弟姐妹人数。
Quantitative data is further split into discrete and continuous. Discrete data can only take specific, separate values, usually whole numbers (e.g. number of cars in a household). Continuous data can take any value within a range and is measured (e.g. the weight of a bag of apples, time taken to run 100 m).
定量数据又分为离散型和连续型。离散数据只能取特定的、彼此分隔的值，通常是整数（如一个家庭拥有汽车的数量）。连续数据在一定范围内可以取任意值，且需要测量得到（如一袋苹果的重量、跑 100 米所用的时间）。
2. Data Collection Methods | 数据收集方法
Common methods for collecting primary data include surveys, questionnaires, interviews, observation and experiments. A well-designed question should be clear, unbiased and relevant to the purpose. For example, asking 'How often do you exercise per week?' is more precise than 'Do you exercise regularly?'.
收集原始数据（一手数据）的常见方法包括调查、问卷、访谈、观察和实验。一份设计良好的问题应当清晰、无偏见且紧扣调查目的。例如，问 "你每周运动几次？" 比 "你经常运动吗？" 更加精确。
Secondary data is information that has already been collected by someone else for a different purpose, such as census data, academic journals or online databases. It is important to check the reliability and date of secondary sources before using them.
二手数据是指他人已经为其他目的收集好的信息，例如人口普查数据、学术期刊或在线数据库。在使用二手数据前，一定要检查其来源的可靠性和时效性。
3. Sampling Techniques | 抽样方法
When it is impractical to survey an entire population, a sample is used. A simple random sample gives every member of the population an equal chance of being chosen, often using random number generators or a lottery method. This helps reduce bias.
当调查整个总体不切实际时，就需要抽取样本。简单随机抽样能让总体中每个成员被选中的机会均等，通常使用随机数生成器或抽签法。这有助于减少偏差。
Stratified sampling involves dividing the population into distinct groups (strata) based on a characteristic, such as year group or gender, and then randomly selecting from each stratum in proportion to its size. This method ensures that each group is fairly represented.
分层抽样是将总体按照某一特征（如年级或性别）划分为若干互不重叠的组（层），然后从每一层中按比例随机抽取样本。这种方法能确保每个群体都被公平地代表。
4. Organising Data: Frequency Tables | 数据整理：频数表
A frequency table records how often each value or category occurs. Tally marks are used during data collection to keep a running count. For grouped data, class intervals should be equal in width where possible, and we must define class boundaries precisely.
频数表记录每个数值或类别出现的次数。在收集数据时，可以使用划记符号（如 "正" 字）进行实时计数。对于分组数据，组距应尽量取等宽，并且需要明确定义每组的上下界限。
Cumulative frequency adds up the frequencies as you go down the table. It is useful for finding how many data points lie below a certain value and forms the basis for drawing cumulative frequency curves at a later stage.
累计频数将频数表中的频数依次累加，能够直观地显示有多少个数据点低于某一特定值。在后续学习中，累计频数是绘制累计频数曲线的基础。
5. Representing Data: Bar Charts and Pie Charts | 数据表示：条形图和饼图
Bar charts represent frequency or count using rectangular bars of equal width. The height of each bar corresponds to its frequency, and the bars are separated by gaps to show the categories are distinct. Bar charts are ideal for discrete and categorical data.
条形图用等宽的矩形条表示频数或计数。每个条形的高度对应该类别的频数，条形之间留有间隙，以表明各类别是相互独立的。条形图非常适合用来展示离散数据和分类数据。
Pie charts show proportions of a whole. Each sector' cy) x 360 degrees. Using a protractor and compass ensures an accurate diagram. Pie charts work best when there are relatively few categories.
饼图用于展示各部分占整体的比例。每个扇形的角度可通过 角度 = (频数 / 总频数) x 360° 计算得出。使用量角器和圆规绘图可以保证图的精确性。当类别不太多时，饼图的表现效果最佳。
6. Summary Statistics: Mean, Median, Mode | 概括统计量：均值、中位数、众数
eme values (outliers). For the data set 3, 5, 7, 8, 30, the mean is (3+5+7+8+30)/5 = 10.6.
均值（平均数）是将所有数据值相加再除以数据个数得到的。它很容易受到极端值（异常值）的影响。对于数据集 3, 5, 7, 8, 30，均值为 (3+5+7+8+30)/5 = 10.6。
The median is the middle value when the data is arranged in order. If there is an even number of values, the median is the mean of the two central numbers. The median resists the influence of outliers. For the data set above, the ordered values are 3,5,7,8,30, so the median is 7.
中位数是将数据按大小排序后位于中间位置的数值。如果数据个数为偶数，则取中间两个数的均值作为中位数。中位数不受异常值影响。对于上述数据集，排序后为 3,5,7,8,30，因此中位数是 7。
The mode is the value or category that occurs most often. A data set may have one mode, more than one mode (bimodal or multimodal) or no mode at all. For categorical data, the mode is the only average that can be used meaningfully.
众数是出现次数最多的数值或类别。一个数据集可能有一个众数、多个众数（双众数或多众数），也可能没有众数。对于分类数据，众数是唯一有意义的平均数。
7. Measures of Spread: Range | 离散度量：极差
a quick idea of how spread out the data is, but it only uses two values and can be heavily distorted by outliers.
极差是最简单的离散度量，等于最大值减去最小值：极差 = 最大值 - 最小值。它能快速反映数据的散布程度，但只用到两个数值，因此极易被异常值扭曲。
ing picture of the overall spread. For this reason, the range is often paired with the interquartile range at higher levels.
例如，数据集 4, 8, 15, 21, 23 的极差为 23 - 4 = 19。若加入一个异常值 102，极差立即变为 102 - 4 = 98，这可能无法真实反映整体散布情况。因此，在更高阶段的学习中通常会将极差与四分位距结合使用。
8. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph (scatter plot) shows the relationship between two sets of quantitative data. Each point represents a pair of values (x, y). By looking at the pattern of points, we can describe the correlation as positive, negative or none.
散点图用于展示两组定量数据之间的关系。每一个点代表一对数据 (x, y)。观察点的分布形态，我们可以判断两变量之间是正相关、负相关还是无相关。
Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one variable increases, the other tends to decrease. If the points show no clear pattern, there is no correlation. A line of best fit can be drawn to model the trend and make predictions.
正相关指当一个变量增大时，另一个变量也倾向于增大；负相关则指一个变量增大时，另一个倾向于减小。如果点的分布没有明显规律，则为无相关。我们可以通过画一条最佳拟合线来近似描述趋势并进行预测。
9. Introduction to Probability | 概率初步
Probability measures 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. It can also be written as a fraction, decimal or percentage.
概率用于度量事件发生的可能性，用一个介于 0 和 1 之间的数表示，0 代表不可能发生，1 代表必然发生。概率还可以写成分数、小数或百分数。
ilities of all mutually exclusive outcomes is 1. For a fair six-sided die, P(rolling a 4) = 1/6.
当所有结果等可能时，事件发生的概率 = 有利结果的数量 / 所有可能结果的总数。所有互斥结果的概率之和为 1。对于一枚均匀的六面骰子，P(掷出 4) = 1/6。
10. Experimental Probability and Expectation | 实验概率与期望
Experimental probability (or relative frequency) is based on actually carrying out trials or collecting data. It is calculated as frequency of the event / total number of trials. As the number of trials increases, the experimental probability tends to get closer to the theoretical probability.
实验概率（或称相对频率）是通过实际进行试验或收集数据得到的，等于事件发生的次数 / 总试验次数。随着试验次数的增加，实验概率会越来越接近理论概率。
rials. For example, if the probability of rain tomorrow is 0.3, out of 20 similar days we would expect rain on 0.3 x 20 = 6 days.
一个事件的出现期望次数可以通过概率乘以试验次数得到：期望次数 = P(事件) x 试验次数。例如，若明天下雨的概率为 0.3，那么在 20 个类似的日子中，我们预计会有 0.3 x 20 = 6 天下雨。
Published by TutorHao | Statistics Revision Series | aleveler.com
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