📚 Year 9 WJEC Statistics: Quick Vocabulary Memorisation Guide | 九年级 WJEC 统计：词汇术语速记指南
Statistics is full of special words that can easily be mixed up. This guide helps Year 9 WJEC students master the key terms through simple explanations, clever memory hooks, and side‑by‑side Chinese translations. Once you can speak the language of data, reading questions and writing answers become much easier.
统计学中有很多容易混淆的专业词汇。这份速记指南通过简单的解释、巧妙的记忆法和中英对照，帮助九年级WJEC学生掌握关键术语。当你学会了数据的语言，读题和答题都会变得轻松很多。
1. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：平均数、中位数、众数
Mean is the average you get by adding up all the values and dividing by the number of values (Σx / n). Think of 'mean' as 'fair share' – if everyone got the same amount, what would it be? Memory trick: the word mean contains an 'a', just like average.
平均数是把所有数值相加再除以数值个数的结果。把平均数想象成“公平分配”——如果每个人拿到的数量都一样，会是多少？记忆诀窍：英文 mean 里有一个 'a'，和 average（平均）共享这个字母。
Median is the middle value when the data is ordered from smallest to largest. If there are two middle numbers, take their mean. Remember: median sounds like medium – the size in the centre, or think of the strip of grass in the middle of a road called the median strip.
中位数是将数据从小到大排列后位于正中间的值。如果有两个中间数，就取它们的平均数。记忆方法：median 听起来像 medium（中等），就是中心位置；也可以想象马路中间的隔离带叫 median strip。
Mode is the value that appears most often. It is the 'most popular' number. A dataset can have one mode, more than one mode (bimodal or multimodal), or no mode at all. Link mode with most – both start with 'mo'.
众数是出现次数最多的值，也就是“最受欢迎”的数字。一组数据可能有一个众数、多个众数（双众数或多众数），或者完全没有。把 mode 和 most 联系起来——它们都以 'mo' 开头。
2. Measures of Spread: Range and Interquartile Range | 离散程度度量：极差与四分位距
Range is the difference between the largest and smallest values. Range = Maximum – ta are very spread out; a small range means they are bunched up. Think of the range as the 'wingspan' of the data.
极差是最大值与最小值之差。极差 = 最大值 – 最小值。它告诉你整个数据集的分散程度。极差大说明数据很分散；极差小说明数据比较集中。把极差想象成数据的“翼展”。
Interquartile Range (IQR) is the range of the middle 50% of the data. IQR = Upper Quartile (Q3) – gnores extreme values, giving a better picture of spread for skewed data. Memory hook: the 'I' in IQR stands for the 'inner' half of the data, like the inner core.
四分位距 (IQR) 是中间 50% 数据的范围。IQR = 上四分位数 (Q3) – 下四分位数 (Q1)。它剔除了极端值，对于偏斜数据的离散情况描述得更好。记忆窍门：IQR 中的 'I' 可以看作 'inner'（内部的），代表数据的内部核心一半。
Quartiles split the ordered data into four equal parts. Q1 is the median of the lower half, Q2 is the overall median, and Q3 is the median of the upper half. Imagine cutting a cucumber into four equal pieces – each cut is a quartile.
四分位数把有序数据分成四个相等的部分。Q1 是下半部分的中位数，Q2 是整体的中位数，Q3 是上半部分的中位数。想象把一根黄瓜切成四等份——每一刀就是一个四分位数。
3. Types of Data | 数据类型
Qualitative data are non‑numerical, describing qualities or categories, such as eye colour, favourite food, or car brand. They can be nominal (no order) or ordinal (can be ordered, e.g., small/medium/large). Remember: Qualitative – qualities.
定性数据是非数值型的，描述性质或类别，例如眼睛颜色、最喜欢的食物或汽车品牌。它们可以是名义型的（无序）或顺序型的（可以排序，如小/中/大）。记忆：Qualitative——品质（quality）。
Quantitative data are numerical and tell you 'how many' or 'how much'. They split into discrete (counted, e.g., number of students – you cannot have 2.3 students) and continuous (measured, e.g., height, time, weight – can take any value in a range). Think 'discrete' like individual steps; 'continuous' like a smooth stream.
定量数据是数值型的，告诉你“有多少”或“多少量”。它们分为离散型（计数获得，如学生人数——不可能有 2.3 个学生）和连续型（测量获得，如身高、时间、质量——在一定范围内可以取任意值）。把离散想象成一级一级的台阶；连续就像不间断的水流。
4. Graphs and Charts | 图表类型
Bar chart – uses separate bars to show frequencies of categorical data. Bars do not touch. Stick a 'bar' in front of you: it is a separate piece – so bars are separate.
条形图——用分离的条形表示分类数据的频率。条形之间不接触。把 bar（棒）拿在手里，每一根是独立的——所以条形也是分开的。
Histogram – looks like a bar chart but is used for continuous data grouped into intervals. Bars touch because the data flows continuously. The area of the bar represents frequency. Key visual: a histogram has no gaps, just like continuous data have no breaks.
直方图——看起来像条形图，但用于分组连续数据。条形紧挨在一起，因为数据是连续流动的。条形的面积代表频率。关键图像：直方图没有间隙，就像连续数据没有断裂一样。
Pie chart – e is a whole; you cut slices to share. The angle of each slice = (frequency/total) × 360°.
饼图——用圆形并按比例分割成扇区，表示各部分占整体的比例。每个扇区的大小表示占总体的份额。记忆：一整个派 (pie) 是一整个；你切块分享。每块的圆心角 = (频数/总数) × 360°。
Line graph – points connected by lines, often used to show changes over time. The horizontal axis usually shows time. Think of a line of footprints tracking a journey – the line goes up and down as you progress.
折线图——用点连接成线，常用于显示随时间变化的趋势。横轴通常是时间。想象一串脚印追踪一段旅程——随着前行，线条会上下起伏。
Scatter graph – plots pairs of data on two axes to look for a relationship between two variables. Each point represents one item. No line is drawn through the points unless there is a correlation and a line of best fit is added. See Section 8 for more.
散点图——在两个数轴上绘制成对的数据，来观察两个变量之间的关系。每个点代表一个个体。除非存在相关性并需要添加最佳拟合线，否则不会在点之间画线。详见第8节。
5. Frequency and Cumulative Frequency | 频率与累积频率
Frequency is simply the number of times something occurs. A frequency table organises data by listing values or groups alongside how often they appear. Tally charts are a quick way to build frequency tables – every fifth tally crosses the previous four, like a gate.
频率就是某事发生的次数。频率表通过列出数值或区间以及相应的出现次数来整理数据。画记表是建立频率表的快捷方法——每第五个画记会画一条斜线穿过前四画，像一扇门。
Cumulative frequency is the running total of frequencies as you move through the dataset. It answers 'how many up to this point?'. A cumulative frequency diagram plots the running total against the upper boundary of each group, producing an S‑shaped curve (ogive). Memory tip: 'cumulative' comes from 'accumulate', so you keep adding up.
累积频率是随着你浏览数据集时频率的累计总和。它回答“到目前为止一共有多少？”累积频率图将累计总数与每一组的上限相对应，绘制出一条 S 形曲线（累积曲线）。记忆技巧：'cumulative' 源于 'accumulate'（积累），所以不断往上加。
From the curve you can estimate the median and quartiles. The median is the value where cumulative frequency reaches half the total; Q1 is at one quarter, Q3 at three quarters.
从累积曲线可以估算中位数和四分位数。中位数是累积频率到达总数一半时的数值；Q1 在四分之一处，Q3 在四分之三处。
6. Probability Terminology | 概率基础术语
Experiment – a repeatable process that produces outcomes, e.g., rolling a dice. Outcome – a single possible result, like rolling a 4. Event – a set of outcomes, e.g., rolling an even number. Sample space – the list of all possible outcomes, often shown in a table or diagram.
试验——可重复的、产生结果的过程，比如掷骰子。结果——一个可能的单一结果，比如掷出 4。事件——一组结果的集合，比如掷出偶数。样本空间——所有可能结果的列表，常用表格或图形表示。
The probability of an event is a number between 0 and 1 (or 0% and 100% le outcomes) / (total number of outcomes). A probability of 0 means impossible; 1 means certain. Imagine a probability scale as a ladder from 0 to 1 – unlikely is near the bottom, likely is near the top.
事件的概率是一个介于 0 和 1（或 0% 到 100%）之间的数。概率 =（有利结果数）/（全部可能结果数）。概率为 0 表示不可能；1 表示必然。把概率标尺想象成从 0 到 1 的梯子——不太可能的靠近底部，很可能的靠近顶部。
Fair means each outcome has the same probability. A fair dice gives each number a 1/6 chance. Bias means some outcomes are more likely than others – watch out for loaded dice!
公平意味着每个结果有相同的概率。一个公平的骰子每个数字出现概率是 1/6。偏差（偏倚）指某些结果比其他结果更可能出现——小心灌铅骰子！
7. Sampling Methods | 抽样方法
Population is the entire group you want information about. A sample is a smaller group selected from the population to represent it. Sampling saves time and money, but the sample must be chosen carefully to avoid bias.
总体是你想了解的全部对象。样本是从总体中选出的、用来代表总体的较小群体。抽样省时省钱，但必须谨慎选择样本以避免偏差。
Random sample – every member of the population has an equal chance of being selected. Methods include drawing names from a hat or using a random number generator. Think of a lottery: every ticket has the same chance.
随机样本——总体中每个成员被选中的机会均等。方法包括抽签或用随机数生成器。想象彩票：每一张彩票中奖机会相等。
Bias occurs when the sample does not fairly represent the population, leading to unreliable conclusions. For example, asking only football fans about sport preferences. Remember: bias can be avoided by using random sampling or stratified sampling (where the population is divided into groups and random samples are taken from each group proportionally).
偏差发生在样本不能公正代表总体时，导致结论不可靠。例如，只问足球迷关于运动偏好的问题。记住：通过随机抽样或分层抽样（将总体分成几个组，然后从每组按比例随机抽取样本）可以避免偏差。
8. Correlation and Scatter Graphs | 相关性与散点图
When two variables are plotted on a scatter graph, the pattern of points may show correlation. Positive correlation: as one variable increases, the other tends to increase (points slope upwards to the right, like climbing a hill). Negative correlation: as one variable increases, the other tends to decrease (points slope downwards, like going downhill). No correlation: no clear pattern – points form a cloud.
当两个变量的数据绘制在散点图上时，点的分布可能显示出相关性。正相关：一个变量增大时，另一个也倾向于增大（点向右上倾斜，像爬坡）。负相关：一个变量增大时，另一个倾向于减小（点向右下倾斜，像下坡）。无相关：没有明显模式——点形成一团。
Correlation does not imply causation – just because two things change together does not mean one causes the other. Memory: 'corr‑' is about going together, not causing.
相关性并不意味着因果关系——两个事物一起变化不代表一个导致了另一个。记忆：corr‑ 表示“一起走”，不是“导致”。
A line of best fit is a straight line drawn through the points to represent the trend. It should have roughly equal numbers of points above and below. This line can be used to estimate values (interpolation – within the data range; extrapolation – outside the data range, which is less reliable).
最佳拟合线是一条穿过点群来代表趋势的直线。它应该使线上方和线下方的点数大致相等。这条线可用来估计数值（内推——在数据范围内；外推——超出数据范围，可靠性较低）。
9. Statistical Enquiry Cycle (PPDAC) | 统计探究循环
Statistics is not just about calculations; it is a problem‑solving process. WJEC follows the PPDAC cycle:
统计不仅是计算，更是一个解决问题的过程。WJEC 使用 PPDAC 循环：
- P – Problem: Clarify the question you want to answer. What are you investigating? | 问题：明确你想回答的问题。你在调查什么？
- P – Plan: Decide what data to collect, how to collect it, and from whom. This includes sampling method and data type. | 计划：决定收集哪些数据、如何收集以及从谁那里收集。这包括抽样方法和数据类型。
- D – Data: Collect the data carefully, recording it accurately in tables or spreadsheets. | 数据：仔细收集数据，准确记录在表格或电子表格中。
- A – Analysis: Process data – draw graphs, find averages, spread, and look for patterns. | 分析：处理数据——绘制图形、求平均数和离散程度、寻找模式。
- C – Conclusion (and Discussion): Answer the problem question, state what you found, and discuss limitations (possible bias, sample size, reliability). | 结论（与讨论）：回答问题，陈述你发现了什么，并讨论局限性（可能的偏差、样本大小、可靠性）。
Memorise PPDAC as 'Please Plan Data And Conclude' or 'Penguins Playing Disco Always Cool'. The cycle is iterative – you may go back and refine your problem or plan based on findings.
把 PPDAC 记作“Please Plan Data And Conclude”或“Problem-Plan-Data-Analysis-Conclusion 五步走”。这个循环是可迭代的——你可能需要根据发现回头调整问题或计划。
10. Comparing Data Sets and Drawing Conclusions | 比较数据集与得出结论
When asked to compare two or more sets of data, always comment on both a measure of central tendency (mean/median) and a measure of spread (range/IQR). For example: 'Class A has a higher median score than Class B, so on average they performed better. However, Class B has a smaller IQR, so their scores are more consistent.'
当需要比较多组数据时，一定要同时提及集中趋势度量（平均数/中位数）和离散程度度量（极差/IQR）。例如：“A 班的中位数分数比 B 班高，所以平均上看他们表现更好。然而，B 班的 IQR 更小，因此他们的分数更集中稳定。”
Always refer back to the context of the problem. A conclusion should answer the original question, be supported by numbers from your analysis, and mention any uncertainty. Phrases like 'on average', 'tends to', and 'in general' are useful because statistics deal with trends, not certainties.
始终要回到问题背景上。结论应回答原始问题，用你分析得出的数据支持，并提及任何不确定性。像“平均地看”、“倾向于”、“总体而言”这样的短语很有用，因为统计学处理的是趋势，而不是确定性。
Reliability depends on sample size and sampling method. A larger random sample usually gives more reliable results. If the data are very spread out or the sample is biased, conclusions are less trustworthy.
可靠性取决于样本大小和抽样方法。较大的随机样本通常给出更可靠的结果。如果数据非常分散或样本有偏差，结论的可信度就会降低。
Published by TutorHao | Statistics Revision Series | aleveler.com
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