📚 Year 9 Cambridge Statistics: Quick Guide to Key Vocabulary | Year 9 剑桥统计：词汇术语速记指南
Building a solid statistical vocabulary is the first step towards mastering data handling in Year 9 Cambridge Mathematics. This guide clusters key terms into memorable groups, helping you understand definitions, recognise when to use each concept, and avoid common mix-ups during exams.
建立扎实的统计词汇库是掌握 Year 9 剑桥数学数据处理的第一步。本指南将关键术语分成便于记忆的组群，帮助你理解定义、识别何时使用每个概念，并避免考试中常见的混淆。
1. Types of Data | 数据类型
Qualitative data (also called categorical data) describes qualities that cannot be measured numerically. Examples include favourite colour, type of pet or blood group. It is often displayed using bar charts or pie charts.
定性数据（也称分类数据）描述无法用数值测量的特质，例如最喜欢的颜色、宠物类型或血型。通常用条形图或饼图展示。
Quantitative data consists of numerical measurements or counts. It is subdivided into discrete data, which can only take specific separate values (like number of students in a class or shoe size), and continuous data, which can take any value within a range (like height, mass or time).
定量数据由数值测量或计数组成。它细分为离散数据——只能取特定的分立值（如班级人数或鞋码），以及连续数据——可以取某个范围内的任意值（如身高、质量或时间）。
A quick test: if it makes sense to say '2.3 children', the data is qualitative or discrete; if it can be measured with increasing precision, it is continuous.
一个快速检验：如果说“2.3 个孩子”有意义，数据是定性或离散的；如果数据可以被越来越精确地测量，它就是连续的。
2. Measures of Central Tendency | 集中趋势的度量
number of values. It uses every piece of data, so it can be affected by extreme outliers.
均值是算术平均数。对一组数据，均值 = 所有数值的总和 ÷ 数值的个数。它使用了每一个数据，所以容易受到极端离群值的影响。
The median is the middle value when the data is arranged in order. For an even number of values, the median is the mean of the two middle numbers. It is not distorted by outliers, making it a better measure of central tendency for skewed data.
中位数是将数据按顺序排列后处于中间位置的数值。当数值个数为偶数时，中位数是中间两个数的均值。它不受离群值扭曲，因此对偏态数据来说是更好的集中趋势度量。
The mode is the most frequently occurring value. A data set can have one mode (unimodal), more than one mode (bimodal or multimodal) or no mode at all. The mode is the only average that can be used with qualitative data.
众数是出现次数最多的数值。一组数据可以有一个众数（单峰），多于一个众数（双峰或多峰）或完全没有众数。众数是唯一可用于定性数据的平均数。
= 3, mode = 3. Notice how the median and mode remain at 3 even if the 7 is replaced by 70.
对于数据集 2, 3, 3, 5, 7：均值 = 4，中位数 = 3，众数 = 3。注意即使将 7 替换为 70，中位数和众数仍为 3。
3. Measures of Spread | 离散程度的度量
The range is the simplest measure of spread: range = maximum value – considers the two extremes, so it does not tell us about the distribution within the set.
极差是最简单的离散量数：极差 = 最大值 – 最小值。它只考虑两个极端，因此无法反映数据内部的分布情况。
Quartiles divide an ordered data set into four equal parts. The lower quartile (Q₁) is the median of the lower half, the upper quartile (Q₃) is the median of the upper half, and the second quartile (Q₂) is the median itself.
四分位数将有序数据集分成四等份。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，第二四分位数（Q₂）就是中位数。
The interquartile range (IQR) = Q₃ – Q₁. It measures the spread of the middle 50% of the data, making it a robust measure that is not influenced by outliers.
四分位距（IQR）= Q₃ – Q₁。它衡量中间 50% 数据的分散程度，是一种不受离群值影响的稳健量数。
, 18, n=7: median (Q₂)=9, lower half: 4,6,7 → Q₁=6; upper half: 12,15,18 → Q₃=15. IQR = 15 – 6 = 9.
对于有序列表 4, 6, 7, 9, 12, 15, 18，n=7：中位数(Q₂)=9，下半部分 4,6,7 → Q₁=6；上半部分 12,15,18 → Q₃=15。IQR = 15 – 6 = 9。
4. Frequency Tables and Cumulative Frequency | 频率表与累计频率
A frequency table organises raw data by listing each distinct value or class alongside its frequency (count). It is the foundation for drawing many statistical diagrams.
频率表通过列出每个不同数值或组别及其频数（计数）来整理原始数据。它是绘制许多统计图的基础。
'Cumulative frequency' is the running total of frequencies. The last cumulative frequency always equals the total number of data items. Cumulative frequency graphs (ogives) are used to estimate the median and quartiles for large grouped data sets.
“累计频率”是频数的累加总和。最后一个累计频率总是等于数据总个数。累计频率图（折线图）用于估算大型分组数据集的中位数和四分位数。
To find the median from a cumulative frequency graph, locate half the total frequency on the vertical axis, draw a horizontal line to the curve, then drop down to the horizontal axis. The same method gives Q₁ at one-quarter the total and Q₃ at three-quarters.
从累计频率图中找中位数时，在纵轴上定位至总频数的一半，画水平线与曲线相交，再向下画垂线至横轴。用相同方法在总频数的四分之一处得到 Q₁，在四分之三处得到 Q₃。
5. Statistical Diagrams | 统计图表
Bar charts represent categorical or discrete data with rectangular bars. The height of each bar shows the frequency, and gaps between bars emphasise that the categories are separate. Horizontal bar charts are also common.
条形图用矩形条表示分类数据或离散数据。每个条形的高度代表频数，条形之间的空隙强调类别是独立的。水平条形图也很常见。
0°. They are excellent for showing relative shares but cannot display exact values easily.
饼图展示整体中各部分的比例。每个扇形的角度按（频数 ÷ 总频数）× 360° 计算。它们适合展示相对份额，但难以精确显示具体数值。
A stem-and-leaf diagram preserves the original data while showing its shape. The 'stem' typically carries the higher place value digits and the 'leaf' the lower. A key is essential, e.g., '5 | 2 means 52'.
茎叶图在展示数据分布形态的同时保留了原始数据。“茎”通常承载较高位数的数值，“叶”承载较低位数的数值。必须提供图例，如“5 | 2 表示 52”。
g the five-number summary: minimum, Q₁, median, Q₃, maximum. The box spans the IQR and the 'whiskers' in extend to the min and max within 1.5 × IQR from the quartiles. Outliers are plotted as individual points.
盒形图（箱线图）利用五数概括法总结数据：最小值、Q₁、中位数、Q₃、最大值。盒子横跨 IQR，“触须”延伸至距四分位数 1.5 × IQR 范围内的最小和最大值。离群值单独绘制为点。
6. Scatter Graphs and Correlation | 散布图与相关性
A scatter graph (scatter plot) displays the relationship between two continuous variables. Each point on the graph represents a pair of values (x, y).
散布图（散点图）显示两个连续变量之间的关系。图上的每个点代表一对数值 (x, y)。
Correlation describes the direction and strength of the relationship. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one variable increases, the other tends to decrease. No correlation indicates no apparent linear pattern.
相关性描述关系的方向和强度。正相关意味一个变量增加时另一个也倾向增加。负相关意味一个变量增加时另一个倾向减少。零相关表示没有明显的线性模式。
A line of best fit is a straight line drawn through the data points to summarise the trend. It should have roughly equal numbers of points above and below it, and it can be used to make predictions (interpolation within the range, extrapolation outside). Tell students to be cautious with extrapolation as the trend may not continue.
最佳拟合线是一条穿过数据点的直线，用于总结趋势。该线上下方的点数应大致相等，并可用来进行预测（范围内的内插，范围外的外推）。提醒学生外推需谨慎，因为趋势可能不会持续。
Correlation does not imply causation. Just because ice cream sales and drowning incidents both rise in summer does not mean one causes the other – there is a lurking variable (hot weather).
相关不代表因果。冰淇淋销量和溺水事件都在夏季上升，并不意味着一方导致另一方——存在一个潜在变量（炎热天气）。
7. Introduction to Probability | 概率入门
Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 (impossible) and 1 (certain), or as a percentage between 0% and 100%.
概率是衡量事件发生可能性的度量。它用 0（不可能）到 1（确定）之间的数表示，或用 0% 到 100% 的百分数表示。
comes / total number of possible outcomes. For a fair six-sided die, P(rolling a 4) = 1/6.
理论概率基于等可能结果计算：P(事件) = 有利结果数 / 所有可能结果总数。对于一个公平的六面骰子，P(掷出 4) = 1/6。
umber of times the event occurs / total number of trials. As the number of trials increases, experimental probability tends to get closer to theoretical probability (the law of large numbers).
实验概率（相对频率）通过进行实验得出：相对频率 = 事件发生的次数 / 总试验次数。随着试验次数增加，实验概率会趋近于理论概率（大数定律）。
or B) = P(A) + P(B). Complementary events are two mutually exclusive events that cover all outcomes, so P(not A) = 1 – P(A).
互斥事件不能同时发生（例如一次抛硬币既得正面又得反面）。对于互斥事件 A 和 B，P(A 或 B) = P(A) + P(B)。互补事件是两个覆盖所有结果的互斥事件，因此 P(不是 A) = 1 – P(A)。
8. Sampling and Population | 抽样与总体
The population is the entire group we want information about. A sample is a subset of the population selected for study. A census collects data from every member of the population.
总体是我们想获取信息的整个组群。样本是从总体中选出来用于研究的子集。普查会收集总体中每个成员的数据。
A sample must be representative to produce reliable conclusions. Bias occurs when a sample systematically favours certain outcomes. For instance, surveying only people at a gym about exercise habits gives a biased view of the whole town's activity levels.
为了得出可靠结论，样本必须具有代表性。当样本系统性地偏向某些结果时，就产生了偏差。例如，仅在健身房调查运动习惯会给出该镇整体活动水平的有偏视角。
Simple random sampling gives every member of the population an equal chance of being chosen, for example by using a random number generator. Other methods include stratified sampling (dividing the population into groups and sampling proportionally from each) and systematic sampling (selecting every nth member).
简单随机抽样使总体中的每个成员都有相等的机会被选中，例如使用随机数生成器。其他方法包括分层抽样（将总体分组并从中按比例抽样）和系统抽样（每隔 n 个成员选取一个）。
The larger a random sample, the more accurate its results tend to be, but practical considerations like time and cost must be balanced.
随机样本越大，结果往往越准确，但必须权衡时间、成本等实际因素。
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