📚 WJEC Year 11 Statistics: Quick Guide to Key Vocabulary | WJEC 11 年级统计：关键术语速记指南
Having the right words at your fingertips turns a statistics question from a guessing game into a confident response. This guide takes every essential WJEC GCSE Statistics term and pairs it with a crystal-clear definition, a memory hook, and exam-savvy advice – all in bilingual paragraphs to double your understanding.
当统计术语烂熟于心时，答题便不再是猜谜，而是笃定的发挥。本指南将 WJEC GCSE 统计学每一个核心词汇与清晰定义、记忆挂钩和应试诀窍配对，采用中英对照段落，让你的理解翻倍。
1. Data Types | 数据类型
Data falls into qualitative (words or labels, like ‘red’ or ‘Welsh’) and quantitative (numbers). Quantitative data splits further into discrete (counted, e.g. number of goals) and continuous (measured, e.g. 1.82 m). Think of discrete as dots on a number line and continuous as a smooth flowing curve.
数据分为定性（文字或标签，如“红色”或“威尔士人”）和定量（数字）。定量数据又分离散型（可数，如进球数）和连续型（可测量，如 1.82 米）。把离散数据想象成数轴上的点，连续数据则是一条平滑曲线。
In WJEC exams, choosing a histogram, bar chart or line graph depends on getting this right. Mix up qualitative and continuous and you will lose marks. A quick mental check: ‘Can I measure it to an infinite number of decimal places?’ If yes, it is continuous.
在 WJEC 考试中，选择直方图、条形图还是折线图全看这一步。一旦混淆定性与连续，就会丢分。一个快速心法：“我能用无限位小数测量它吗？”如果可以，就是连续型。
2. Sampling Methods | 抽样方法
A population is the whole set; a sample is the part you actually study. Random sampling gives every member an equal chance of selection, often using a random number generator. Stratified sampling keeps the proportions of subgroups (strata) identical to the population, making it fair for mixed groups.
总体是完整的集合；样本是你实际研究的部分。随机抽样让每个成员被选中的概率相同，通常借助随机数生成器。分层抽样让子群（层）的比例与总体保持一致，适合混合群体，十分公平。
Systematic sampling picks every kth item after a random start – simple, but watch out for hidden patterns. Cluster sampling grabs entire pre-existing groups, such as one class from each year. Quota sampling relies on interviewers filling pre-set numbers and is non-random, often used in street surveys. Memory trick: ‘SRSCQ’ – Stratified keeps Ratio, Random is Raffle, Systematic Steps, Cluster Chunks, Quota Quick-fill.
系统抽样随机起点后每隔 k 个取一个——简单，但要当心隐藏的规律。整群抽样直接选取已有的整个小组，比如每年级抽一个班。配额抽样依赖调查员填满预设数量，是非随机的，常用于街头访问。记忆口诀：“分层看比例，随机似抽奖，系统等步走，整群整团抓，配额凑人头”。
3. Charts and Graphs | 图表与图形
Bar charts represent discrete or categorical data with gaps between bars. Histograms are for continuous data; the area of each bar is proportional to frequency, and bars touch. Always check: ‘Are the bars joined?’ If not, it is likely wrong for grouped continuous data.
条形图呈现离散或分类数据，柱子间有空隙。直方图用于连续数据，每一条的面积代表频率，柱子彼此相连。始终自问：“柱子连在一起吗？”如果不连，对于分组连续数据很可能就是错的。
A cumulative frequency curve shows the running total. Reading the median and quartiles from it is a core exam skill. Box plots (box-and-whisker) visualise the five-number summary: minimum, lower quartile Q1, median Q2, upper quartile Q3, maximum. The box spans the interquartile range (IQR). Scatter graphs reveal relationships between two variables, which we explore later.
累积频率曲线展示递加总数，从中读取中位数和四分位数是核心考试技能。箱线图（盒须图）可视化五数综合：最小值、下四分位数 Q1、中位数 Q2、上四分位数 Q3、最大值。箱子覆盖了四分位距 (IQR)。散点图则揭示两个变量的关系，稍后会细讲。
4. Averages and Measures of Central Tendency | 平均数与集中趋势度量
Mean, median and mode are the three averages. The mean uses every value (sum divided by count) and suits symmetric data. The median is the middle value when ordered, resistant to outliers. The mode is the most frequent value, useful for qualitative data. For grouped data, find the modal class and estimate the mean with midpoints.
平均数、中位数和众数是三大集中趋势。平均数用到每个数值（总和除以个数），适合对称数据。中位数是排序后居中那一个，抗极端值。众数是出现最频的值，对定性数据有用。分组数据需找众数组并用中点估计平均数。
Formula for estimated mean from a frequency table:
Estimated mean = Σfx ÷ Σf
where f is frequency and x is the midpoint. In WJEC, you often need to add a column for fx. The median from a cumulative frequency diagram is read at the ½Σf position.
由频数表求估计平均数的公式：
估计平均数 = Σfx ÷ Σf
其中 f 是频数，x 是组中点。在 WJEC 考试中常需额外计算一列 fx。从累积频率图中读中位数，则是在 ½Σf 的位置读取。
5. Measures of Spread | 离散程度度量
Range (maximum – minimum) is the simplest spread measure but is affected by outliers. The interquartile range (IQR = Q3 – Q1) cuts off the extreme 25% at each end and is the preferred measure for skewed data. A smaller IQR means more consistent data.
极差（最大值–最小值）是最简单的离散度量，但受极端值影响。四分位距（IQR = Q3 – Q1）切除两端各 25% 的数据，是偏态分布中更可取的度量。IQR 越小，数据越集中。
Variance and standard deviation give the average squared distance from the mean. For a population:
σ² = Σ(x – μ)² ÷ N, s² = Σ(x – x̄)² ÷ (n–1) for a sample
The standard deviation is the square root: σ = √[Σ(x – μ)² ÷ N]. In WJEC, you may calculate it from a table or use a calculator. Remember: ‘IQR for skewed, SD for symmetric’.
方差和标准差给出数值到平均数距离平方的平均。总体：
σ² = Σ(x – μ)² ÷ N，样本：s² = Σ(x – x̄)² ÷ (n–1)
标准差是其平方根：σ = √[Σ(x – μ)² ÷ N]。WJEC 考试中可能让你根据表格计算或使用计算器。记住：“偏态用 IQR，对称用标准差”。
6. Probability Terminology | 概率术语
The probability scale runs from 0 (impossible) to 1 (certain). An experiment produces outcomes; the set of all outcomes is the sample space. Mutually exclusive events cannot happen together: P(A or B) = P(A) + P(B). Independent events have no influence on each other: P(A and B) = P(A) × P(B).
概率取值 0（不可能）到 1（必然）。一次试验产生结果，所有结果的集合称作样本空间。互斥事件不能同时发生：P(A 或 B) = P(A) + P(B)。独立事件互不影响：P(A 且 B) = P(A) × P(B)。
Conditional probability is the chance of A given B has occurred, written P(A|B) = P(A and B)/P(B). Tree diagrams are a must in WJEC: multiply along branches for ‘and’, add across branches for ‘or’. Always check if probabilities after an event sum to 1.
条件概率是已知 B 发生后 A 的概率，记作 P(A|B) = P(A 且 B)/P(B)。树形图是 WJEC 必用工具：沿分支相乘表示“且”，分支间相加表示“或”。务必检查事件后的概率是否总和为 1。
7. The Normal Distribution | 正态分布
The normal distribution is a bell-shaped, symmetric curve where the mean, median and mode all coincide at the peak. Real-world examples include heights, weights and test scores. Spread is controlled by the standard deviation: a larger SD flattens the curve.
正态分布是一条钟形对称曲线，平均数、中位数和众数均重合在顶峰。身高、体重、考试成绩等现实数据常呈正态分布。分布形状受标准差控制：标准差越大，曲线越扁平。
WJEC exams rely on the empirical (68-95-99.7) rule: roughly 68% of data lie within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. Draw a quick sketch and label the percentages to answer ‘what percentage lie above…’ questions.
WJEC 考试依据经验法则（68-95-99.7）：大约 68% 的数据落在均值左右 1 个标准差内，95% 在 2 个标准差内，99.7% 在 3 个标准差内。快速画出示意图并标上百分比，就足以应对“有多少百分比高于……”之类的问题。
8. Scatter Graphs and Correlation | 散点图与相关性
Correlation describes the strength and direction of a linear relationship between two variables. Positive correlation: as one variable rises, so does the other. Negative: one rises while the other falls. No correlation means there is no clear pattern. Correlation does not imply causation – a classic exam trap.
相关性描述两个变量间线性关系的强度和方向。正相关：一个变量上升另一个也上升。负相关：一个上升另一个下降。零相关表示无明显模式。相关≠因果——这是经典考试陷阱。
A line of best fit (drawn by eye or through means) allows predictions. Interpolation predicts inside the data range and is generally reliable. Extrapolation predicts beyond the data range and is risky. Remember: ‘Inter = inside, Extra = outside, risky guess’.
最佳拟合线（凭眼力或通过平均值画）可用来预测。内插法在数据范围内预测，通常可靠。外推法延伸到数据范围之外，风险较大。记住：“Inter 向内，Extra 向外，向外瞎猜不靠谱”。
9. Time Series and Index Numbers | 时间序列与指数
A time series graph plots values against time, revealing a trend (overall direction) and seasonal variation (regular ups and downs). Moving averages smooth out the bumps to make the trend clearer. In WJEC, you often calculate a 4-point or 12-point moving average and plot it.
时间序列图将数值对时间绘制，揭示趋势（总方向）和季节变动（规律起伏）。移动平均可以抹平波动，让趋势更清晰。WJEC 考试常要求计算 4 点或 12 点移动平均值并描点。
Index numbers compare a value to a base year where the index = 100. The formula:
Index number = (Value in current year ÷ Value in base year) × 100
They make percentage changes easy to compare over time. Typical WJEC tasks ask you to interpret an index of 112: it means a 12% increase from the base period.
指数用于将某时期数值与基期（指数=100）对比。公式：
指数 = (当年数值 ÷ 基年数值) × 100
指数让跨期百分比变化一目了然。WJEC 常见考点：解释指数 112，即比基期上涨 12%。
10. Exam Tips for Key Terms | 考试关键术语提醒
Command words shape your answer. ‘State’ means give a brief fact. ‘Describe’ asks for characteristics or trends. ‘Compare’ requires using words like higher, lower, more consistent, referring to a measure like mean or IQR. ‘Interpret’ means explain what the statistic means in context.
指令词决定了你的答题方式。“说出”要求给出简短事实。“描述”要写出特征或趋势。“比较”需用更高、更低、更稳定等词，并引用平均数或 IQR 等度量。“解读”则是结合情境解释统计量的实际意义。
Common pitfalls: using ‘discrete’ for height (continuous), measuring centre with range, forgetting to order data before finding median, and using a bar chart for grouped continuous data. Always link spread comments to IQR or SD, not just the range. Practise writing full sentences that embed the term: ‘The median time is 24 minutes, meaning half the pupils took less time.’
常见误区：把身高（连续）说成离散，用极差描述集中趋势，找中位数前忘记排序，对分组连续数据使用条形图。讨论离散程度时要联系 IQR 或标准差，不能只提极差。练习写出嵌入术语的完整句子：“中位数时间为 24 分钟，意味着半数学生用时更少”。
Before you finish, quickly match each chart to its data type, double-check probability branches sum to 1, and always label axes. These small habits will lift your marks significantly.
收尾前，快速把图表与数据类型匹配一次，检查概率树分支总和是否为 1，并且永远标注坐标轴。这些小习惯能让分数明显提升。
Published by TutorHao | Statistics Revision Series | aleveler.com
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