📚 Year 10 AQA Statistics: Key Terms Memorisation Guide | Year 10 AQA 统计：关键术语速记指南
Statistics is all about collecting, analysing, and interpreting data. In Year 10 AQA Statistics, mastering the key vocabulary is crucial for understanding concepts and solving problems. This guide provides a quick reference to essential terms, paired with their Chinese translations, to help you memorise them effectively and boost your exam confidence.
统计学是关于收集、分析和解释数据的学科。在 Year 10 AQA 统计课程中，掌握关键术语词汇对于理解概念和解决问题至关重要。本指南提供了核心术语的速查参考，并附有中文翻译，帮助你高效记忆术语，提升考试信心。
1. Types of Data | 数据类型
Categorical (Qualitative) Data: Data that can be grouped into categories based on qualities or characteristics, such as eye colour, gender, or type of car. These are non-numerical labels.
分类型（定性）数据： 可以根据品质或特征分组的数据，例如眼睛颜色、性别或汽车品牌。这类数据不是数值型的。
Numerical (Quantitative) Data: Data that represents counts or measurements and can be treated numerically, such as height, test scores, or number of siblings.
数值型（定量）数据： 表示计数或测量结果的数据，可以按数值处理，例如身高、考试分数或兄弟姐妹的数量。
Discrete Data: Numerical data that can only take specific, separate values, often whole numbers. Examples: number of students in a class, shoe size.
离散型数据： 只能取特定、分离值的数值型数据，通常是整数。例如：班级学生人数、鞋码。
Continuous Data: Numerical data that can take any value within a given range and is usually measured. Examples: height, weight, temperature, time.
连续型数据： 可以在给定范围内取任意值的数值型数据，通常通过测量得到。例如：身高、体重、温度、时间。
Primary Data: Data collected directly by the researcher for a specific purpose. It is original and first-hand, such as survey responses or measurements from an experiment.
一手数据： 研究人员为特定目的直接收集的数据。它是最原始的第一手资料，例如问卷调查的答复或实验测量结果。
Secondary Data: Data that has been collected by someone else for a different purpose but is used by the researcher. Examples include government statistics, historical records, or data from the internet.
二手数据： 由其他人为不同目的收集，但被研究人员再次使用的数据。例如政府统计资料、历史记录或互联网上的数据。
2. Population and Sample | 总体与样本
Population: The complete set of all individuals or items that are of interest in a statistical study. It can be very large, such as all students in England or all light bulbs made by a factory.
总体： 统计研究中感兴趣的全部个体或项目的集合。总体可以十分庞大，例如英格兰所有学生或某工厂生产的所有灯泡。
Sample: A subset of the population that is selected to be representative of the whole population. Studying a sample saves time and resources, and conclusions about the population are inferred from it.
样本： 从总体中选出的、能代表整个总体的一个子集。研究样本可以节省时间和资源，并由此推断关于总体的结论。
Census: A study that collects data from every member of the population. While a census gives the most accurate results, it is often impractical or too expensive to conduct.
普查： 从总体中每个成员收集数据的研究方式。普查能给出最准确的结果，但通常因不切实际或成本太高而难以实施。
Sampling Frame: A list of all the members of the population from which the sample is drawn. A good sampling frame should be accurate and up to date, e.g. a school register or electoral roll.
抽样框： 一份列出总体所有成员的清单，用于抽取样本。一个好的抽样框应当准确且及时更新，如学校花名册或选民登记册。
Parameter: A numerical value that describes a characteristic of the entire population, such as the population mean μ or population standard deviation σ. Parameters are usually unknown and estimated using statistics.
参数： 描述总体某特征的数值，例如总体均值 μ 或总体标准差 σ。参数通常未知，需要用统计量来估计。
Statistic: A numerical value calculated from a sample, used to estimate an unknown population parameter. Examples include the sample mean x̄, sample proportion, and sample standard deviation s.
统计量： 从样本中计算出的数值，用于估计未知的总体参数。例如样本均值 x̄、样本比例和样本标准差 s。
3. Measures of Central Tendency | 集中趋势度量
Mean (Arithmetic Average): The sum of all data values divided by the number of values. It is the most common measure of central location, but is sensitive to extreme values (outliers). For a data set x₁, x₂, ..., xₙ:
均值（算术平均数）： 所有数据值之和除以数值的个数。它是最常用的集中趋势度量，但对极端值（异常值）很敏感。对于数据集 x₁, x₂, ..., xₙ：
Mean x̄ = (Σxᵢ) / n
Median: The middle value when the data are arranged in order. If there is an even number of values, the median is the average of the two middle numbers. The median is not affected by outliers and is a better measure of central tendency for skewed distributions.
中位数： 将数据按顺序排列后位于中间的值。如果数据个数为偶数，中位数是中间两个数的平均值。中位数不受异常值影响，对于偏态分布是更好的集中趋势度量。
Mode: The data value that occurs most frequently. A data set can have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all. The mode is useful for categorical data.
众数： 出现频率最高的数据值。一个数据集可以有一个众数（单峰）、多个众数（双峰或多峰）或没有众数。众数对于分类型数据很有用。
Weighted Mean: An average where each data value is multiplied by a weight reflecting its importance. It is often used when combining means from groups of different sizes or when some observations are more significant.
加权平均数： 每个数据值乘以反映其重要性的权重后计算的平均值。常用于合并不同大小组的均值，或某些观测值较为重要的情形。
4. Measures of Spread | 离散程度度量
Range: The difference between the largest and smallest values in a data set. It is the simplest measure of spread but can be heavily influenced by a single extreme value.
极差（全距）： 数据集中最大值与最小值之差。它是最简单的离散度量，但极易受单个极端值的影响。
Quartiles: Values that divide an ordered data set into four equal parts. The lower quartile (Q₁) is the median of the lower half, the median (Q₂) is the overall median, and the upper quartile (Q₃) is the median of the upper half.
四分位数： 将有序数据集分成四个相等部分的值。下四分位数（Q₁）是下半部分的中位数，中位数（Q₂）是整体中位数，上四分位数（Q₃）是上半部分的中位数。
Interquartile Range (IQR): en the upper and lower quartiles: IQR = Q₃ − Q₁. It represents the spread of the middle 50% of the data and is resistant to outliers.
四分位距（IQR）： 上四分位数与下四分位数之差：IQR = Q₃ − Q₁。它表示中间 50% 数据的分散程度，且不受异常值影响。
Percentile: A value below which a given percentage of the data falls. The median is the 50th percentile, Q₁ is the 25th percentile, and Q₃ is the 75th percentile.
百分位数： 给定百分比的数据位于其下方的值。中位数是第 50 百分位数，Q₁ 是第 25 百分位数，Q₃ 是第 75 百分位数。
Variance and Standard Deviation: Variance measures the average squared deviation from the mean. The standard deviation is the square root of the variance, giving a measure of spread in the original units. For a population:
方差与标准差： 方差衡量数据与均值之差的平方的平均值。标准差是方差的平方根，以原始单位衡量离散程度。对于总体：
σ² = Σ(xᵢ − μ)² / N
σ = √[Σ(xᵢ − μ)² / N]
For a sample, the sample variance s² divides by (n − 1) to provide an unbiased estimate of the population variance.
对于样本，样本方差 s² 除以 (n − 1) 以便给出总体方差的无偏估计。
5. Graphical Representation | 数据图表呈现
Frequency Table: A table that lists categories or data values alongside the number of times each occurs (frequency). Tally marks are often used to construct one. Cumulative frequency tables add up frequencies as you move through the categories.
频数表： 列出类别或数据值及其出现次数（频数）的表格。常用划记法来制作。累积频数表则随着类目前进逐步累加频数。
Bar Chart: A graph used for categorical or discrete data where rectangular bars of equal width represent the frequency or value of each category. The bars are separated by gaps to show distinct categories.
条形图： 用于分类或离散型数据的图表，等宽的矩形条表示每个类别的频数或数值。条与条之间留有间隙，以区分不同的类别。
Histogram: may vary to represent different class intervals. Frequency density = frequency / class width.
直方图： 用于连续型数据的图表，每个条形的面积与频数成正比。与条形图不同，条形之间紧密相连，且宽度可能不同，以表示不同的组距。频数密度 = 频数 / 组距宽度。
Frequency Polygon: A line graph formed by joining the midpoints of the tops of the bars in a histogram (or by plotting midpoints against frequencies). It is useful for comparing two or more distributions.
频数折线图： 通过连接直方图中每个条形顶端中点而形成的折线图（或直接绘制中点与频数）。它便于比较两个或多个分布。
Stem-and-Leaf Diagram: A method of displaying data where each value is split into a 'stem' (the leading digit(s)) and a 'leaf' (the final digit). It retains the original data values and shows the distribution shape. A back-to-back stem-and-leaf plot compares two sets.
茎叶图： 一种数据展示方法，将每个数值拆分为“茎”（前面的数位）和“叶”（最后一位）。它保留了原始数据值并显示分布形态。背靠背茎叶图可以用来比较两组数据。
Box Plot (Box-and-Whisker Plot): A graphical summary of data based on the five-number summary: minimum, Q₁, median, Q₃, and maximum. The box spans the IQR, and whiskers extend to the extremes. Box plots clearly show outliers and skewness.
箱线图（盒须图）： 基于五数概览的图形化数据摘要：最小值、Q₁、中位数、Q₃ 和最大值。箱子覆盖 IQR，须线延伸到极值。箱线图能清晰地显示异常值和偏态。
Scatter Graph (Scatter Diagram): A plot of bivariate data where two variables are plotted on the horizontal (x) and vertical (y) axes. It reveals the relationship, or correlation, between the two variables.
散点图： 将双变量数据绘制在横轴（x）和纵轴（y）上的图表。它可以揭示两个变量之间的关系或相关性。
6. Correlation and Regression | 相关与回归
Correlation: A measure of the strength and direction of a linear relationship between two variables. Correlation can be positive (as x increases, y tends to increase), negative (as x increases, y tends to decrease), or zero (no linear relationship). It does not imply causation.
相关： 衡量两个变量之间线性关系强度和方向的度量。相关可以是正相关（x 增加时 y 也趋于增加）、负相关（x 增加时 y 趋于减少）或零相关（无线性关系）。相关并不能推出因果关系。
The Correlation Coefficient r (PMCC): tive correlation, r = -1 perfect negative correlation, and r ≈ 0 little or no correlation.
相关系数 r（积差相关系数）： 介于 -1 和 +1 之间的数值，用于量化线性相关程度。r = +1 表示完全正相关，r = -1 表示完全负相关，r ≈ 0 表示几乎没有线性相关。
r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √[Σ(xᵢ − x̄)² Σ(yᵢ − ȳ)²]
Line of Best Fit (Regression Line): ast squares method minimizes the sum of squared residuals to find the equation y = a + bx.
最佳拟合线（回归直线）： 通过散点图、最好地表示线性关系的一条直线。在回归分析中，最小二乘法通过最小化残差平方和来求得方程 y = a + bx。
Interpolation and Extrapolation: Interpolation uses the line of best fit to estimate values within the range of the given data. Extrapolation extends beyond the data range to make predictions, which can be unreliable as the relationship may not hold.
内插与外推： 内插是使用最佳拟合线估计给定数据范围内的值。外推则是将预测扩展到数据范围之外，这可能不太可靠，因为关系不一定在范围外依然成立。
7. Introduction to Probability | 概率基础
Random Experiment: A process for which the outcome cannot be predicted with certainty before it is performed, such as rolling a fair die or flipping a coin.
随机试验： 在实施前无法准确预测结果的过程，例如掷一枚公平的骰子或抛一枚硬币。
Outcome: A single possible result of a random experiment. For a rolled die, the outcomes are 1, 2, 3, 4, 5, 6.
结果： 随机试验
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