📚 Year 11 Edexcel Statistics: Core Concepts Review | Year 11 Edexcel 统计：核心知识点梳理
Success in Edexcel GCSE Statistics hinges on a confident grasp of the fundamental ideas that appear throughout the specification. This article brings together the core concepts you will encounter in Year 11, from data types and sampling to probability distributions and index numbers. Each section is presented as a concise explanation followed by its Chinese translation, helping you reinforce understanding in both languages.
要想在 Edexcel GCSE 统计考试中取得成功，关键在于透彻掌握考试大纲中反复出现的基础概念。本文汇集了 Year 11 需要面对的所有核心知识点，从数据类型和抽样方法到概率分布和指数，逐一进行梳理。每个要点都采用英文解释加中文对照的形式，帮助你在双语环境中巩固理解。
1. Types of Data | 数据类型
Data can be classified as qualitative or quantitative. Qualitative data describes categories or attributes, such as eye colour or vehicle type. Quantitative data is numerical and can be further divided into discrete and continuous types.
数据可以分为定性数据和定量数据。定性数据描述类别或属性，例如眼睛颜色或车辆类型。定量数据是数值型的，可以进一步分为离散型和连续型。
Discrete data can only take specific values, often counts like the number of siblings. Continuous data can take any value within a range, such as height or temperature.
离散数据只能取特定的值，通常是计数，例如兄弟姐妹的数量。连续数据可以取某个范围内的任意值，比如身高或温度。
Primary data is collected first-hand by the researcher, while secondary data has been gathered by someone else. Understanding the source helps assess reliability.
原始数据由研究者亲自收集，二手数据则来自他人的收集成果。了解数据的来源有助于评价其可靠性。
2. Sampling Methods | 抽样方法
A sample is a subset of a population used to draw conclusions about the whole group. Random sampling gives every member an equal chance of being selected, reducing bias.
样本是从总体中抽取的一部分，用于推断整体特征。随机抽样使每个个体被选中的机会均等，能减少偏差。
Stratified sampling divides the population into distinct groups (strata) and takes a proportional random sample from each. This ensures all subgroups are fairly represented.
分层抽样先将总体分成不同的层，再从每一层中按比例随机抽取样本，从而确保所有子群体都得到公平的代表。
Systematic sampling selects members at regular intervals from an ordered list, while convenience sampling simply picks the easiest individuals to reach – the latter often introduces bias.
系统抽样从有序名单中等间隔地选取个体，而便利抽样则只选择最容易接触到的对象，后者往往会引入偏差。
3. Charts and Graphs | 图表与图形
Bar charts display categorical data with gaps between the bars, whereas histograms are used for continuous data with no gaps and the area of each bar is proportional to frequency.
条形图用于展示分类数据，条形之间有间隔；直方图则用于连续数据，条形之间不留空隙，且每个条形的面积与频数成正比。
In a histogram, frequency density is calculated as frequency ÷ class width. This ensures the total area represents the total frequency.
在直方图中，频率密度等于频数除以组距，确保整个图形的总面积代表总频数。
Pie charts show proportions of a whole, with each sector’s angle = (frequency ÷ total) × 360°. Cumulative frequency polygons are useful for finding medians and quartiles.
饼图展示各部分占整体的比例，每个扇形的角度 = (频数 ÷ 总和) × 360°。累积频率折线图则方便寻找中位数和四分位数。
4. Averages: Mean, Median, Mode | 平均数：平均值、中位数、众数
The mean is the sum of all values divided by the number of values. For grouped data, use the midpoint of each class. The formula for ungrouped data is x̄ = Σx / n.
平均值是所有数值之和除以数值的个数。对于分组数据，要用每个组的中点来计算。未分组数据的公式为 x̄ = Σx / n。
The median is the middle value when data is ordered; for n values, its position is (n + 1)/2. The mode is the most frequent value.
中位数是排序后位于正中间的值；当有 n 个数据时，中位数的位置为 (n + 1)/2。众数是出现次数最多的值。
The choice of average depends on the data shape. The mean is sensitive to outliers, whereas the median and mode are more robust.
选择哪种平均数取决于数据分布的形状。平均值对极端值很敏感，而中位数和众数更加稳健。
5. Measures of Spread: Range, IQR, Standard Deviation | 离散程度的度量
The range is the difference between the largest and smallest values. It is simple but heavily influenced by outliers.
极差是最大值与最小值之差。它计算简单，但极易受异常值的影响。
The interquartile range (IQR) is Q₃ – Q₁, where Q₁ and Q₃ are the lower and upper quartiles. IQR focuses on the middle 50% and resists outliers.
四分位距 (IQR) 等于上四分位数 Q₃ 减去下四分位数 Q₁。IQR 关注中间50%的数据，不受异常值干扰。
Standard deviation measures how spread out the data are around the mean. For a population, σ = √[ Σ(x – μ)² / N ]. In GCSE Statistics, the formula using the mean of the sample is commonly applied as σ = √[ Σ(x – x̄)² / n ].
标准差衡量数据围绕平均值的离散程度。总体标准差公式为 σ = √[ Σ(x – μ)² / N ]。在 GCSE 统计中，常用样本均值计算的标准差公式为 σ = √[ Σ(x – x̄)² / n ]。
6. Cumulative Frequency and Box Plots | 累积频率与箱线图
A cumulative frequency table lists the running total of frequencies. Plotting these against the upper class boundaries gives a smooth curve used to estimate medians and quartiles.
累积频率表列出频数的逐项累加结果。将累积频率对组距上界描点，即可得到光滑曲线，用于估算中位数和四分位数。
A box plot (box-and-whisker) displays the minimum, Q₁, median, Q₃ and maximum. It is excellent for comparing distributions side by side.
箱线图（箱须图）展示最小值、下四分位数、中位数、上四分位数和最大值。它非常适合并排比较不同数据集的分布情况。
Outliers can be identified using the 1.5 × IQR rule: a value is an outlier if it lies more than 1.5 × IQR below Q₁ or above Q₃.
异常值可通过 1.5 × IQR 法则识别：如果一个值低于 Q₁ – 1.5×IQR 或高于 Q₃ + 1.5×IQR，就被视为异常值。
7. Probability and Tree Diagrams | 概率与树形图
Probability is a measure of how likely an event is, ranging from 0 to 1. The probability of an event not happening is 1 – P(event).
概率用于衡量事件发生的可能性，取值在 0 到 1 之间。事件不发生的概率等于 1 减去该事件发生的概率。
Tree diagrams help list all possible outcomes of two or more events. Multiply probabilities along the branches for combined events, and add probabilities of relevant paths for ‘or’ scenarios.
树形图可以列出两个或多个事件的所有可能结果。沿着分支相乘概率得到组合事件的概率，将相关路径的概率相加则得到“或”情形下的概率。
Conditional probability P(A|B) represents the probability of A given that B has occurred. In a tree diagram, this is shown by probabilities on the second set of branches.
条件概率 P(A|B) 表示在事件 B 已发生的前提下事件 A 发生的概率。在树形图中，这通过第二层分支上的概率体现。
8. Scatter Graphs and Correlation | 散点图与相关
A scatter graph displays the relationship between two variables. If points follow an upward trend, correlation is positive; a downward trend indicates negative correlation.
散点图展示两个变量之间的关系。如果点呈上升趋势，则为正相关；若呈下降趋势，则为负相关。
Correlation does not imply causation. The strength of linear correlation is measured by the correlation coefficient r, which lies between –1 and +1.
相关关系不意味着因果关系。线性相关的强度由相关系数 r 衡量，其取值在 –1 到 +1 之间。
A line of best fit can be drawn by eye or calculated as the least-squares regression line. The equation has the form y = a + bx, where b is the gradient.
最佳拟合线可以通过目测画出，也可以计算最小二乘回归线。回归方程的形式为 y = a + bx，其中 b 是斜率。
9. Time Series and Moving Averages | 时间序列与移动平均
A time series records data at regular intervals over time. It can show a long-term trend, seasonal variations, and random fluctuations.
时间序列按固定时间间隔记录数据，可以显示长期趋势、季节变动和随机波动。
Moving averages smooth out short-term fluctuations to reveal the underlying trend. For a 4-point moving average, average each consecutive block of four periods.
移动平均可以平滑短期波动，揭示潜在趋势。对于四点移动平均，需对每四个连续时段的数据取平均值。
Seasonal variation can be estimated by subtracting the trend from the actual data. This helps in making forecasts for future periods.
季节变动可以通过从实际数据中减去趋势值来估算。这有助于对未来时期进行预测。
10. Binomial Distribution | 二项分布
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success p.
二项分布描述在固定次数的独立试验中成功的次数，且每次试验的成功概率 p 相同。
The probability of exactly r successes in n trials is given by: P(X = r) = nCr × pr × (1–p)n–r, where nCr = n! / [r!(n–r)!].
在 n 次试验中恰好成功 r 次的概率公式为：P(X = r) = nCr × pr × (1–p)n–r，其中 nCr = n! / [r!(n–r)!]。
Conditions for a binomial distribution: fixed n, independent trials, two outcomes per trial (success/failure), and constant p. You can calculate expected number = np.
二项分布的条件为：试验次数 n 固定、各次试验独立、每次试验只有两个结果（成功或失败），且 p 保持不变。期望成功次数为 np。
11. Normal Distribution | 正态分布
The normal distribution is a continuous, bell-shaped curve symmetric about the mean μ. The total area under the curve equals 1.
正态分布是一种连续型、钟形对称曲线，对称轴为均值 μ。曲线下的总面积等于 1。
About 68% of data lie within 1 standard deviation of the mean, 95% within 2σ, and 99.7% within 3σ. This is the empirical rule.
大约 68% 的数据落在均值 ±1 个标准差的范围内，95% 落在 ±2σ 内，99.7% 落在 ±3σ 内，这就是经验法则。
To find probabilities, convert an x-value to the standard normal variable z using z = (x – μ) / σ, then use standard normal tables. This allows comparisons across different normal distributions.
计算概率时，先将 x 值转化为标准正态变量 z：z = (x – μ) / σ，然后查阅标准正态分布表。这样可以比较不同正态分布的数据。
12. Index Numbers | 指数
An index number measures the change in a variable over time relative to a base period. The base period is normally set to 100.
指数用于衡量一个变量相对于基期的变化程度。基期通常被设为 100。
A simple price index = (price in current period ÷ price in base period) × 100. Composite indices, such as the Retail Price Index, combine many items.
简单价格指数 = (现期价格 ÷ 基期价格) × 100。零售价格指数等综合指数则把多种商品组合在一起。
The weighted Laspeyres index uses base-period quantities: Σ(p₁×q₀) / Σ(p₀×q₀) × 100. The Paasche index uses current-period quantities and can reflect changes in spending patterns.
加权拉氏指数使用基期数量：Σ(p₁×q₀) / Σ(p₀×q₀) × 100。帕氏指数使用现期数量，能反映消费模式的变化。
Published by TutorHao | Statistics Revision Series | aleveler.com
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