📚 Core Topics in Year 10 WJEC Statistics | Year 10 WJEC 统计：核心知识点梳理
Welcome to your go‑to revision guide for Year 10 WJEC Statistics. This article pulls together the most important concepts you will meet in the course, from planning a survey to interpreting probability diagrams. Each section pairs a clear explanation in English with a matching Chinese translation, so you can check your understanding quickly and build confidence for class tests and the final assessment.
欢迎来到 Year 10 WJEC 统计的复习指南。这篇文章梳理了课程中最核心的概念，从调查设计到概率图的解读，每个知识点都用英文和中文进行对照讲解，帮助你快速检查理解、增强对单元测验和期末考试的信心。
1. Planning a Statistical Investigation | 设计统计调查
A good investigation starts with a clear hypothesis – a statement you want to test, such as ‘Boys in Year 10 spend more time gaming than girls’. You then decide what data to collect, who to ask (the population or a sample), and how to record answers fairly. The plan must consider practicality, ethics, and possible bias in your questions.
一项好的调查始于一个明确的假设——你想要检验的陈述，例如‘Year 10 男生打游戏的时间多于女生’。接着你需要确定收集哪些数据、向谁收集（总体还是样本），以及如何公正地记录回答。调查计划必须考虑可行性、伦理和问题中可能存在的偏差。
- Hypothesis: a testable prediction about a population.
- 假设：关于总体的一个可检验的预测。
- Pilot study: a small trial to check your methods work.
- 先导研究：小范围试调查，检验方法是否可行。
2. Types of Data | 数据类型
Data can be split into qualitative (non‑numerical, e.g. favourite colour) and quantitative (numerical). Quantitative data divides further into discrete (counted, like number of pets) and continuous (measured, like height). Knowing the type of data helps you choose the right graph and statistical measure.
数据可以分为定性数据（非数值，如最喜欢的颜色）和定量数据（数值）。定量数据又分为离散型（计数，如宠物数量）和连续型（测量，如身高）。了解数据类型有助于你选择正确的图表和统计指标。
| Type | Example |
|---|---|
| Qualitative | Hair colour, Year group |
| Discrete quantitative | Shoe size, number of siblings |
| Continuous quantitative | Time taken to run 100 m, mass |
表格总结：定性、离散定量、连续定量及对应例子。
3. Sampling Methods | 抽样方法
To avoid bias, we select a sample using a recognised method. A simple random sample gives every member an equal chance. Stratified sampling preserves the proportions of different groups, while systematic sampling selects at regular intervals (e.g. every 10th person). A census asks the entire population but is often impractical.
为了避免偏差，我们使用公认的方法选取样本。简单随机抽样让每个成员被选中的机会相等。分层抽样保持不同群体的比例，而系统抽样按固定间隔选择（如每隔10人）。普查调查整个总体，但常常不切实际。
- Simple random sample – like drawing names from a hat.
- 简单随机样本——就像从帽子里抽名字。
- Stratified sample – divides the population into groups (strata) and samples proportionally from each.
- 分层样本——将总体分成不同组（层），按比例从每组抽样。
- Systematic sample – choose a starting point randomly, then pick every k‑th item.
- 系统样本——随机选择起点，然后每隔k个元素选取一个。
4. Frequency Tables and Grouping | 频数表与分组
tervals, e.g. 0 ≤ h < 10. When grouping, we must avoid gaps and overlaps so every piece of data fits exactly one interval.
原始数据杂乱无章，频数表可以将其整理好。对于离散数据，我们列出每个取值及其频数。对于连续数据，我们归入组距，如0 ≤ h < 10。分组时必须避免空隙和重叠，确保每个数据恰好落入一个组。
Class interval: 10 ≤ t < 20 means 10 is included, 20 is excluded.
组距：10 ≤ t < 20 表示包含下限10，不包含上限20。
5. Charts for Qualitative and Discrete Data | 定性与离散数据的图表
h. Pie charts show proportions: the angle for a category = (category frequency ÷ total frequency) × 360°. Always label clearly and give a title.
条形图用分开的柱形表示各类别或离散数值的频数。每根柱子的高度代表频数，柱子互不相连。饼图则展示比例：某一类的扇形角度 = (该类频数 ÷ 总频数) × 360°。务必清晰标注并写上标题。
- Bar chart – ideal for favourite sport, eye colour, or number of children.
- 条形图——适用于最喜爱的运动、眼睛颜色或小孩数目。
- Pie chart – shows how a whole is split; good for budget shares.
- 饼图——展示整体如何被划分；适合表示预算份额。
6. Histograms and Frequency Density | 直方图与频数密度
quency density = frequency ÷ class width. The area of each bar then represents the frequency, not the height alone. This stops wider intervals from appearing artificially more important.
对于分组连续数据，我们使用直方图。如果组距相等，纵轴可以直接用频数。组距不相等时，必须使用频数密度 = 频数 ÷ 组距。此时每一块矩形的面积代表频数，而不仅仅是高度。这防止较宽的组看起来过分重要。
Frequency density = Frequency ÷ Class width
频数密度 = 频数 ÷ 组距
7. Cumulative Frequency and Box Plots | 累计频数与箱线图
A cumulative frequency table adds frequencies as you go, and a cumulative frequency curve (ogive) lets you estimate medians and quartiles. From these we build a box plot – a diagram showing the minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃), and maximum. Box plots are ideal for comparing spreads of two or more data sets.
累计频数表逐步加总频数，累计频数曲线（折线图）可以帮助你估计中位数和四分位数。由此我们可以构建箱线图——展示最小值、下四分位数(Q₁)、中位数(Q₂)、上四分位数(Q₃)和最大值的图形。箱线图非常适合比较两个或多个数据集的离散程度。
- Lower quartile Q₁: 25% of data lies below it.
- 下四分位数 Q₁：25% 的数据低于此值。
- Median Q₂: 50% below, 50% above.
- 中位数 Q₂：50% 数据低于它，50% 高于它。
- Upper quartile Q₃: 75% below.
- 上四分位数 Q₃：75% 数据低于它。
8. Averages: Mean, Median and Mode | 平均数：均值、中位数与众数
The mode is the most frequent value. The median is the middle value when data are ordered. The mean uses every piece of data: sum all values and divide by the number of values. For grouped data, use the midpoint of each class. Which average is best depends on the data shape – the median resists outliers, while the mean is affected by extreme values.
众数是出现次数最多的值。中位数是排序后位于中间的值。均值使用每一个数据：将所有数值相加，再除以数据个数。对于分组数据，使用每组的组中值。采用哪种平均数取决于数据的分布形态——中位数不易受异常值影响，而均值会被极端值拉偏。
Mean = (Σx) ÷ n, or for grouped data Σ(f × midpoint) ÷ Σf
均值 = (Σx) ÷ n，或分组数据 Σ(f × 组中值) ÷ Σf
9. Measures of Spread: Range and Interquartile Range | 离散度量：极差与四分位距
asy but affected by outliers. The interquartile range (IQR) = Q₃ − Q₁ covers the middle 50% of data and is more robust. A smaller IQR indicates more consistent data.
离散度反映数据的一致性。极差 = 最大值 − 最小值计算简单，但易受异常值影响。四分位距 (IQR) = Q₃ − Q₁ 覆盖中间50%的数据，更加稳健。IQR 越小，数据越一致。
- Range = max − min (simple but sensitive).
- 极差 = 最大值 − 最小值（简单但敏感）。
- IQR = Q₃ − Q₁ (resistant to extreme values).
- IQR = Q₃ − Q₁（对极端值有抵抗力）。
10. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph plots paired data (e.g. revision hours and test score). Correlation describes the strength and direction of the relationship. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one increases, the other tends to decrease. No correlation means no obvious pattern. We can add a line of best fit to make predictions, but only within the range of the data (interpolation) – beware of extrapolation beyond the data.
散点图用于描绘成对数据（如复习时间与测验分数）。相关性描述关系的强弱与方向。正相关意味着一个变量增加，另一个也倾向于增加。负相关意味着一个变量增加，另一个倾向于减少。无相关则表示没有明显模式。我们可以添加最佳拟合线来进行预测，但只能在数据范围内（内插）——注意不要过度外推。
- Correlation does not imply causation – a link does not prove one thing causes another.
- 相关性不等于因果性——存在关联并不证明一个变量导致另一个变量变化。
11. Probability Basics and Tree Diagrams | 概率基础与树形图
able outcomes ÷ total number of outcomes. Tree diagrams are powerful tools for showing all possible outcomes of two or more events. Multiply along branches for combined events, and add the probabilities of different paths for ‘or’ situations.
概率衡量事件发生的可能性，范围从0（不可能）到1（必然）。对于等可能结果而言，P(事件) = 有利结果数 ÷ 总结果数。树形图是展示两个或多个事件所有可能结果的强大工具。沿着分支相乘得出组合事件的概率，对于“或”的情况则将不同路径的概率相加。
P(A and B) = P(A) × P(B) for independent events.
对于独立事件，P(A 且 B) = P(A) × P(B)。
P(A or B) = P(A) + P(B) when events are mutually exclusive.
当事件互斥时，P(A 或 B) = P(A) + P(B)。
12. Time Series and Moving Averages | 时间序列与移动平均
A time series plots data over time (e.g. monthly sales). It often shows trend, seasonal variation, and random fluctuations. A moving average smooths out short‑term fluctuations to reveal the underlying trend. To find a 3‑point moving average, average each group of three consecutive values; continue by moving one time period ahead. Plotting moving averages helps forecast future values.
时间序列图展示随时间变化的数据（如月度销售额）。它通常显示长期趋势、季节性变动和随机波动。移动平均可以平滑短期波动，揭示潜在趋势。计算3点移动平均时，对每连续三个值求平均，然后向前移动一个时期继续。绘制移动平均线有助于预测未来值。
- Trend: the long‑term direction of the data.
- 趋势：数据的长期走向。
- Seasonal variation: regular ups and downs within a fixed period (e.g. each year).
- 季节性变动：在固定周期内（如每年）有规律的起伏。
Published by TutorHao | Statistics Revision Series | aleveler.com
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