📚 Year 10 Edexcel Statistics: Key Concepts Summary | Year 10 Edexcel 统计：核心知识点梳理
Statistics is a powerful tool for understanding the world through data. In the Year 10 Edexcel course, you will learn how to collect, represent, analyse, and interpret data, as well as how to quantify uncertainty using probability. This article brings together the essential knowledge you need, covering everything from basic data types and sampling methods to cumulative frequency graphs, box plots, and probability rules. Use it as a checklist and a revision guide to strengthen your understanding and prepare confidently for assessments.
统计学是通过数据理解世界的强大工具。在 Year 10 Edexcel 课程中，你将学习如何收集、表示、分析和解释数据，以及如何用概率量化不确定性。本文汇总了所有你必须掌握的核心知识，涵盖从基本的数据类型和抽样方法，到累积频率图、箱线图和概率法则。你可以把它当作一份查漏补缺的清单和复习指南，帮助你巩固理解，自信地迎接考试。
1. Types of Data | 数据类型
Data can be classified as qualitative or quantitative. Qualitative data describes qualities or categories, such as hair colour, car brand, or types of fruit. Quantitative data deals with numbers and can be further split into discrete and continuous data. Discrete data can only take certain values – often whole numbers, like the number of students in a class. Continuous data can take any value within a range, such as height, weight, or time, and is usually measured rather than counted.
数据可分为定性数据和定量数据。定性数据描述性质或类别，例如头发颜色、汽车品牌或水果种类。定量数据涉及数字，可进一步分为离散数据和连续数据。离散数据只能取特定值——通常是整数，例如班级学生人数。连续数据可以在一个范围内取任何值，如身高、体重或时间，通常是测量得到的而非计数得到的。
Knowing the data type is crucial because it determines which diagrams and calculations are appropriate. For example, you would use a pie chart for categorical (qualitative) data, but a histogram for continuous grouped data. The distinction also affects your choice of averages: the mode is suitable for qualitative data, while the mean requires quantitative data.
了解数据类型至关重要，因为它决定了哪些图表和计算是合适的。例如，对类别（定性）数据你会使用饼图，而对连续的分组数据则使用直方图。这种区分还影响到你选择的平均数：众数适用于定性数据，而平均数则需要定量数据。
2. Sampling Techniques | 抽样方法
A population is the entire set of individuals or items you are interested in, while a sample is a subset selected to represent the population. Sampling is often necessary because it is impractical or too costly to collect data from everyone. A good sample must be representative and large enough to minimise bias.
总体是你关注的全部个体或项目的集合，而样本是从中选出的一个子集，用以代表总体。抽样往往是必要的，因为从每个人那里收集数据不切实际或成本太高。一个好的样本必须具有代表性，并且足够大，以尽量减少偏差。
Common sampling methods include random sampling, where every member of the population has an equal chance of being chosen; stratified sampling, where the population is divided into groups (strata) and a proportional number is randomly selected from each group; systematic sampling, where you select every nth item from a list; and opportunity (convenience) sampling, which uses people who are easily available. Each method has advantages and drawbacks. Stratified sampling is particularly useful for ensuring all subgroups are represented fairly.
常见的抽样方法包括随机抽样，即总体中每个成员被选中的机会均等；分层抽样，将总体分成若干层（组），按比例从每一层随机抽取；系统抽样，从名单中每隔 n 个选取一个；以及机会抽样（便利抽样），即使用容易接触到的人。每种方法都有优缺点。分层抽样在确保所有子群体都被公平代表方面特别有用。
3. Mean, Median, Mode, and Range | 平均数、中位数、众数与范围
The three main averages are the mode, median, and mean. The mode is the most frequently occurring value. The median is the middle value when data are arranged in order. The mean is the sum of all values divided by the number of values. Each average summarises the data differently: the mode is easiest to find, the median is not affected by extreme outliers, and the mean uses all data but can be distorted by outliers.
三种主要的平均数是众数、中位数和平均数。众数是出现频率最高的值。中位数是将数据按顺序排列后位于中间的值。平均数是用所有数值之和除以数值的个数。每种平均数对数据的概括方式不同：众数最容易找到，中位数不受极端异常值影响，而平均数使用了所有数据但会被异常值扭曲。
The range is a measure of spread and is calculated as the largest value minus the smallest value. It gives a quick sense of how spread out the data are, but it ignores the distribution between the extremes. When comparing two sets of data, it is often useful to compare both an average and the range.
范围是衡量数据离散程度的一个指标，计算方法是用最大值减去最小值。它能让你快速了解数据的分散程度，但忽略了极端值之间的分布情况。当比较两组数据时，通常比较平均数（或中位数）和范围是很有帮助的。
4. Quartiles and Interquartile Range | 四分位数与四分位距
Quartiles split an ordered data set into four equal parts. The lower quartile (Q₁) is the median of the lower half of the data, the upper quartile (Q₃) is the median of the upper half, and the median itself is Q₂. To find quartiles for a raw data list, you can use the position formulas: Q₁ at (n+1)/4, Q₂ at (n+1)/2, Q₃ at 3(n+1)/4, then pick the corresponding values.
四分位数将有序数据集分成四个相等的部分。下四分位数 (Q₁) 是数据下半部分的中位数，上四分位数 (Q₃) 是上半部分的中位数，而中位数本身就是 Q₂。对于原始数据列表，可以使用位置公式来查找四分位数：Q₁ 位于 (n+1)/4 的位置，Q₂ 位于 (n+1)/2，Q₃ 位于 3(n+1)/4，然后取出相应位置的值。
The interquartile range (IQR) is Q₃ − Q₁. It measures the spread of the middle 50% constructing box plots and identifying mild and extreme outliers using the 1.5 × IQR rule.
四分位距 (IQR) 等于 Q₃ − Q₁。它衡量的是中间 50% 数据的离散程度，比范围更稳健，因为它不受极端异常值的影响。IQR 对绘制箱线图和运用 1.5 × IQR 法则识别温和和极端异常值至关重要。
5. Frequency Tables and Averages from Grouped Data | 频率表与分组数据求平均数
When raw data are organised into a frequency table, the mean is calculated using the formula:
Mean = (Σ f × x) / Σ f
where f is the frequency and x is the data value. For grouped data, you use the midpoint of each class interval as an estimate of x. Remember that this gives an estimated mean because you assume all values in a class are at the midpoint.
当原始数据被整理成频率表时，平均数用以下公式计算：
平均数 = (Σ f × x) / Σ f
其中 f 是频率，x 是数据值。对于分组数据，你需要用每个组距的中点作为 x 的估计值。记住，这样得到的是估算的平均数，因为你假设该组内所有值都落在中点处。
The modal class for grouped data is the class interval with the highest frequency. The class containing the median can be found by using cumulative frequencies to locate the position (Σ f + 1) / 2, then identifying the class where this position falls. You can also estimate the median more precisely by linear interpolation, though at Year 10 a simple identification of the median class is often sufficient.
分组数据的众数类是频率最高的组距。可以通过累积频率来找到包含中位数的组：先计算中位数的位置 (Σ f + 1) / 2，然后找出这个位置落在哪个组。虽然可以通过线性插值更精确地估算中位数，但在 Year 10 阶段，通常只需要找出中位数所在的组即可。
6. Bar Charts, Pie Charts, and Pictograms | 条形图、饼图和象形图
ual gaps and all bars should have the same width. You can also create composite or stacked bar charts to show sub-categories. Pie charts show proportions of a whole: each slice angle is calculated as (category frequency / total frequency) × 360°.
条形图用于显示类别数据或离散数据。条形的高度表示频率或数值。条形之间应有相等的间隔，并且所有条形的宽度应相同。你也可以绘制复合或堆叠条形图来显示子类别。饼图则展示整体中的比例：每个扇形的角度等于（该类别频数 / 总频数）× 360°。
Pictograms use pictures or symbols to represent frequency; a key must be provided to explain the value of each symbol. They are visually appealing but less precise. When constructing any of these charts, always label axes, provide a title, and use a consistent scale. Comparisons become misleading if the scale is truncated or pictogram symbols are not drawn correctly.
象形图使用图片或符号来表示频率；必须提供图例说明每个符号代表的值。它们具有视觉吸引力但不够精确。在绘制任何这类图表时，务必标注坐标轴、提供标题，并使用一致的比例。如果比例被截断或象形图的符号没有正确绘制，比较就会变得具有误导性。
7. Histograms and Frequency Density | 直方图与频率密度
A histogram is used for continuous data grouped into intervals of unequal width. Unlike bar charts, the area of each bar represents frequency. When class widths are different, you must use frequency density:
Frequency Density = Frequency / Class Width
is Then the height of each bar is the frequency density. It is the area (frequency density × class width) that gives the frequency for that interval.
直方图用于按不等宽组距分组的连续数据。与条形图不同，每个条形的面积代表频率。当组距宽度不同时，你必须使用频率密度：
频率密度 = 频率 / 组距宽度
那么条形的纵坐标高度就是频率密度。正是面积（频率密度 × 组距宽度）给出了该区间的频率。
hould be continuous. You may be asked to complete a partially drawn histogram or to calculate frequencies from a given histogram by working backwards from frequency density × class width.
在解读或绘制直方图时，务必仔细检查组边界，确保条形之间没有间隙。横轴应该是连续的。考试中你可能需要补全一个部分绘制的直方图，或者根据给定的直方图，从频率密度 × 组距宽度反推频率。
8. Cumulative Frequency Graphs | 累积频率图
A cumulative frequency diagram shows the running total of frequencies. To construct it, add a cumulative frequency column to the frequency table, then plot the cumulative frequency against the upper class boundary of each interval. Join the points with a smooth curve.
累积频率图显示的是频率的累计总数。绘制时，先给频率表加上累积频率列，然后以每个区间的组上界为横坐标，对应的累积频率为纵坐标描点。用一条平滑的曲线将这些点连接起来。
You can use the graph to estimate the median (at the 50% cumulative frequency point), the quartiles (at 25% and 75%), and the interquartile range. The graph is also useful for finding what proportion of data lies below (or above) a particular value. For instance, to estimate how many students scored less than 60 marks, read up from 60 on the horizontal axis to the curve, then across to the cumulative frequency axis.
你可以用累积频率图来估算中位数（在 50% 累积频率处）、四分位数（在 25% 和 75% 处）和四分位距。该图也可用于找出有多少比例的数据低于（或高于）某个特定值。例如，要估计有多少名学生得分低于 60 分，从横轴上的 60 向上对着曲线读取，再水平移至纵轴上的累积频率值即可。
9. Box Plots | 箱线图
A box plot (or box-and-whisker diagram) gives a visual summary of a data set using five key numbers: the minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃), and maximum. The box is drawn from Q₁ to Q₃ with a line at the median, and whiskers extend to the smallest and largest values that are not outliers.
箱线图（或称箱须图）用五个关键数值直观地概括一个数据集：最小值、下四分位数 (Q₁)、中位数 (Q₂)、上四分位数 (Q₃) 和最大值。箱体从 Q₁ 画到 Q₃，中间用一条线标出中位数，胡须延伸到非异常值的最小值和最大值。
ed an outlier and plotted individually. Box plots are excellent for comparing distributions side by side, showing clearly differences in centre, spread, and skewness. A larger box indicates greater variability in the middle 50% of the data.
异常值可以用 1.5 × IQR 法则识别：任何低于 Q₁ − 1.5 × IQR 或高于 Q₃ + 1.5 × IQR 的值都被视为异常值，并单独标出。箱线图非常适合并排比较几个分布，能够清晰地显示中心位置、离散度和偏态的差异。箱体越大说明中间 50% 数据的变异性越大。
10. Scatter Diagrams and Correlation | 散点图与相关性
A scatter diagram is used to investigate the relationship between two continuous variables. Each point represents a pair of values (x, y). The pattern of points can indicate positive correlation (as one variable increases, the other tends to increase), negative correlation (as one increases, the other decreases), or no correlation.
散点图用于研究两个连续变量之间的关系。每个点代表一对数值 (x, y)。点的分布形态可以指示正相关（一个变量增大，另一个也倾向于增大）、负相关（一个增大，另一个减小）或无相关性。
The strength of correlation is described as strong, moderate, or weak, depending on how closely the points follow a straight line. A line of best fit (trend line) can be drawn by eye, passing through the mean point of the data. This line can be used to estimate one value given the other, a process called interpolation (within the data range) or extrapolation (outside the range). Extrapolation can be unreliable. Correlation does not imply causation: just because two variables are linked does not mean one causes the other to change.
相关性的强弱根据点围绕一条直线的紧密程度可分为强、中、弱。可以通过目测画一条最佳拟合线（趋势线），使它经过数据的均值点。这条线可以用来根据一个变量估计另一个变量，这个过程称为内插法（在数据范围内）或外推法（超出数据范围）。外推可能不可靠。相关并不意味着因果：两个变量有关联并不代表一个导致了另一个的变化。
11. Basic Probability Rules | 基础概率法则
he probability of an event not happening is 1 minus the probability that it does happen: P(not A) = 1 − P(A).
概率衡量一个事件发生的可能性，范围从 0（不可能）到 1（必定发生）。它可以用分数、小数或百分数表示。一个事件不发生的概率等于 1 减去它发生的概率：P(非 A) = 1 − P(A)。
her happening is P(A or B) = P(A) + P(B). For independent events, the probability of both happening is P(A and B) = P(A) × P(B). Sample space diagrams and Venn diagrams are useful tools for listing all possible outcomes and combining events.
对于互斥事件（不可能同时发生的事件），它们的概率之和等于 1。发生某一件或另一件的概率用 P(A 或 B) = P(A) + P(B) 计算。对于独立事件，两者都发生的概率是 P(A 且 B) = P(A) × P(B)。样本空间图和文氏图是列举所有可能结果及组合事件的有用工具。
12. Relative Frequency and Expected Outcomes | 相对频率与期望结果
Relative frequency is the estimated probability from an experiment or survey. It is calculated as the number of times an event occurs divided by the total number of trials. As the number of trials increases, the relative frequency stabilises and approaches the theoretical probability, providing empirical evidence for the law of large numbers.
相对频率是从实验或调查中得到的估计概率。它用事件发生的次数除以试验总次数来计算。随着试验次数的增加，相对频率会趋于稳定并接近理论概率，这为大数定律提供了经验证据。
xample, if the probability of rain on any given day is 0.3, you would expect rain on 30 out of 100 days. This links probability directly to predictions about real-world frequencies and is a key concept when evaluating risks or making forecasts.
要计算期望频率，只需用事件发生的概率乘以试验次数：期望频率 = P(事件) × 试验次数。例如，若某天下雨的概率是 0.3，那么在 100 天中你预计会下雨的天数为 30 天。这把概率直接与现实世界中的频率预测联系起来，是评估风险或进行预测时的关键概念。
Published by TutorHao | Statistics Revision Series | aleveler.com
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