📚 Statistical Vocabulary Quick Memorisation Guide | 统计学术词汇速记指南
Statistics is the science of collecting, analysing and interpreting data. For Year 10 CCEA students, mastering statistical vocabulary is the first and most important step. A solid understanding of terms such as 'mean', 'median', 'range' and 'probability' will not only help you solve numerical problems but also enable you to write clear, accurate explanations in exams. This guide breaks down the essential terminology into manageable sections, with each concept presented in both English and Chinese to strengthen your bilingual recall.
统计学是收集、分析、解释数据的科学。对 CCEA 十年级学生来说，掌握统计术语是首要且至关重要的一步。透彻理解‘平均数’、‘中位数’、‘极差’和‘概率’等术语，不仅能帮助你解决计算问题，还能让你在考试中写出清晰、准确的解释。本指南将核心术语拆分为易于掌握的章节，每个概念都配有中英双语讲解，以强化你的双语记忆。
1. Population, Sample and Variables | 总体、样本与变量
In statistics, a population is the entire set of individuals, items or data points that we are interested in studying. Because populations are often too large or costly to examine completely, we select a sample — a smaller, manageable subset that is chosen to represent the population. The process of drawing conclusions about the population from a sample is called inference.
在统计学中，总体是我们感兴趣研究的全体个体、项目或数据点的集合。由于总体往往太大或研究成本太高，我们会选取一个样本——一个较小的、易于管理的子集，用来代表总体。从样本推断总体结论的过程称为统计推断。
A variable is any characteristic that can vary from one member of the population to another. Variables can be quantitative (measuring 'how much' or 'how many') or qualitative (describing a quality or category). Being able to identify the type of variable correctly is essential for choosing the right graph and summary statistic.
变量是指总体中不同个体之间可能变化的任何特征。变量可以是定量的（测量‘多少’或‘几个’）或定性的（描述品质或类别）。能够正确识别变量类型对于选择合适的图表和汇总统计量至关重要。
2. Types of Data | 数据类型
Data fall into two broad numerical categories: discrete and continuous. Discrete data can only take particular, separate values — usually whole numbers, such as the number of goals scored in a match or the shoe sizes available in a shop. Continuous data can take any value within a given range and are obtained by measuring; temperature, length and mass are typical examples.
数据分为两大类数值类型：离散型和连续型。离散型数据只能取特定的、分开的值——通常是整数，比如一场比赛的进球数或商店可供的鞋码。连续型数据可以取给定区间内的任何值，通过测量获得；温度、长度和质量都是典型的例子。
We also work with categorical data (such as eye colour or type of transport) and ordinal data, which has a natural order but no consistent numerical difference between ranks — for example, survey ratings like 'poor, satisfactory, good, excellent'. Recognising data type determines whether a bar chart, histogram, or pie chart is the most suitable display.
我们还会遇到类别型数据（如眼睛颜色或交通方式）和顺序型数据，后者有自然顺序但各等级之间没有一致的数值差异——例如，‘差、满意、好、极好’这样的调查评分。识别数据类型决定了条形图、直方图还是饼图是最合适的展示方式。
3. Measures of Central Tendency | 集中趋势度量
The three principal averages are the mean, median and mode. They summarise the centre of a data set in different ways and each has its own strengths.
三种主要的平均数是平均数、中位数和众数。它们以不同的方式概括数据集的中心，且各有优势。
The mean (often written as x̄) is calculated by summing all the observations and dividing by the number of observations. For values x₁, x₂, ..., xₙ, the formula is:
平均数（常写作 x̄）由所有观测值之和除以观测值的个数算出。对于数值 x₁, x₂, ..., xₙ，其公式为：
x̄ = (x₁ + x₂ + ... + xₙ) ÷ n
The mean uses every value and is therefore influenced by extreme values (outliers).
平均数用到了每一个值，因此会受极端值（异常值）的影响。
The median is the middle number when the data are arranged in ascending order. If the list has an even count, the median is the mean of the two central numbers. The median is often preferred when outliers are present because it remains stable.
中位数是数据按升序排列后位于中间的数。如果数据个数为偶数，中位数则是中间两个数的平均数。存在异常值时，中位数往往是更受青睐的平均数，因为它能保持稳定。
The mode is simply the value that occurs most frequently. A data set may be unimodal, bimodal or have no mode at all. The mode is the only average that can be used with categorical data.
众数就是出现频率最高的值。一个数据集可以是单峰的、双峰的或者根本没有众数。众数是唯一可用于类别型数据的平均数。
4. Measures of Spread | 离散程度度量
While a central value describes location, a measure of spread tells us how much the data vary. The simplest is the range:
集中量数描述的是位置，而离散程度度量告诉我们数据的变化有多大。最简单的度量是极差：
Range = Maximum – Minimum
Although quick to find, the range depends only on the two extreme values and can be misleading if there are outliers.
极差虽然求取快捷，但仅仅依赖于两个极端值，一旦存在异常值就可能产生误导。
The interquartile range (IQR) ower half and the upper quartile Q₃ is the median of the upper half. Then IQR = Q₃ − Q₁. The IQR ignores extreme values and is used to construct box plots.
四分位距 (IQR) 通过关注中间一半的数据克服了这个问题。将排序后的数据分成四等份，下四分位数 Q₁ 是下半部分的中位数，上四分位数 Q₃ 是上半部分的中位数。于是 IQR = Q₃ − Q₁。四分位距不受极端值影响，并用于构建箱线图。
Variance and standard deviation quantify spread by measuring the average squared distance from the mean. The standard deviation (denoted s for a sample, σ for a population) is the positive square root of the variance. A small standard deviation means the data cluster tightly around the mean; a large one indicates widespread dispersion.
方差和标准差通过度量与平均值的平均平方距离来量化离散程度。标准差（样本记为 s，总体记为 σ）是方差的正平方根。标准差小表示数据紧密聚集在平均值周围；标准差大则表示分布广泛。
5. Frequency and Cumulative Frequency | 频数与累积频数
Frequency is a simple count of how often a value or group of values occurs. A frequency table organises raw figures into classes, revealing the distribution's shape. Where class intervals are used, you must be consistent — for example, 0‒9, 10‒19, and so on.
频数就是对某个值或某组值出现次数的简单计数。频数表将原始数据分组整理，揭示分布的形状。当使用组距时，必须保持一致——例如 0‒9, 10‒19 等。
Relative frequency Total frequency. This is incredibly useful when comparing groups of unequal size or when estimating probabilities from experimental data.
相对频数将频数置于整体背景中，表示占总数比例：相对频数 =
Published by TutorHao | Year 10 统计 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图