📚 OCR Year 10 Statistics: Key Vocabulary Quick Guide | OCR 十年级统计：词汇术语速记指南
In OCR Year 10 Statistics, mastering the language of data is the first step to exam success. This guide breaks down essential statistical terms into clear, memorable definitions, each with a practical example. Whether you are calculating averages, interpreting charts, or discussing probability, a strong vocabulary will help you explain your reasoning accurately and earn full marks.
在 OCR 十年级统计课程中，掌握数据的语言是考试成功的第一步。本指南将核心统计术语拆解为清晰易记的定义，每个术语都配有实例。无论你在计算平均数、解读图表还是讨论概率，扎实的词汇基础都能帮助你准确表达推理过程，从而拿到满分。
1. Averages: Mean, Median, Mode | 平均数：均值、中位数、众数
The mean is found by adding all data values together and dividing by the number of values. It is the most common measure of central tendency but can be heavily influenced by extreme values.
均值是将所有数据值相加后再除以数据个数得到的。它是最常用的集中趋势度量，但容易受到极端值的影响。
The median is the middle value when the data is ordered from smallest to largest. If there are two middle values, the median is the mean of those two. It is not affected by outliers, making it a better average for skewed data.
中位数是将数据从小到大排序后位于中间位置的数值。如果有两个中间值，则中位数为这两个值的平均数。中位数不受异常值影响，因此在偏斜数据中是更好的平均数。
The mode is the value that occurs most frequently in a data set. There can be more than one mode, or no mode at all if all values appear with the same frequency.
众数是数据集中出现频率最高的值。可能有多个众数，也可能一个都没有（如果所有值出现频率相同）。
2. Measures of Spread: Range, Quartiles and IQR | 离散程度：极差、四分位数和四分位距
The range is the difference between the largest and smallest values. It is simple to calculate but only uses two data points, so it ignores the distribution of the rest of the data.
极差是最大值与最小值的差。计算很简单，但只用了两个数据点，因此忽略了其余数据的分布情况。
he upper quartile (Q₃) is the median of the upper half. The interquartile range (IQR) = Q₃ – Q₁, which measures the spread of the middle 50% of the data and is resistant to outliers.
下四分位数（Q₁）是数据下半部分的中位数，上四分位数（Q₃）是数据上半部分的中位数。四分位距（IQR）= Q₃ – Q₁，它衡量的是中间50%数据的离散程度，且不受异常值影响。
3. Standard Deviation and Variance | 标准差与方差
Variance is the average of the squared differences from the mean. It shows how data points are spread out, but its unit is squared, which can be difficult to interpret directly.
方差是各数据点与均值之差的平方的平均数。它反映数据点的分散程度，但单位是原单位的平方，直接解读起来不太方便。
Standard deviation is the square root of the variance. It is measured in the same units as the original data, making it a widely used measure of spread. A small standard deviation means data points cluster closely around the mean.
标准差是方差的平方根。它的单位与原始数据一致，因此成为广泛使用的离散程度度量。标准差小意味着数据点紧密聚集在均值周围。
4. Data Types: Qualitative, Quantitative, Discrete, Continuous | 数据类型：定性、定量、离散、连续
Qualitative data describes qualities or categories and cannot be measured numerically, such as eye colour or favourite sport. Quantitative data is numerical and can be measured, like height or number of pets.
定性数据描述质量或类别，无法用数字度量，例如眼睛颜色或最喜爱的运动。定量数据是数值型的，可以进行测量，如身高或宠物数量。
Quantitative data splits further into discrete and continuous. Discrete data can only take certain values, usually whole numbers (e.g., number of students in a class). Continuous data can take any value within a range (e.g., time taken to run 100 m).
定量数据又分为离散数据和连续数据。离散数据只能取某些特定值，通常是整数（例如班上的学生人数）。连续数据可以取某一范围内的任何值（例如跑100米所用的时间）。
5. Graphs and Charts: Histogram, Bar Chart, Frequency Polygon | 图表：直方图、条形图、频数多边形
A bar chart uses separate bars of equal width to represent categorical data. The gaps between bars emphasise that the categories are distinct and not on a continuous scale.
条形图用等宽的独立条形表示分类数据。条形之间的空隙强调了类别是独立的，并不在连续尺度上。
data grouped into class intervals, where the frequency density = frequency ÷ class width.
直方图也使用条形，但条形紧挨在一起，且每个条形的面积与频数成正比。直方图用于已分成组距的连续数据，其中频率密度 = 频数 ÷ 组距宽度。
A frequency polygon is created by plotting the frequencies against the midpoints of class intervals and joining the points with straight lines. It is useful for comparing distributions.
频数多边形是将频数对应组距中点描点后，用直线连接而成的。它对比较分布很有用。
6. Probability Fundamentals | 概率基础
Experimental probability is calculated from the results of an experiment or trial: it is the number of times an event occurs divided by the total number of trials. It can also be called relative frequency.
实验概率是根据实验或试验结果计算得出的：事件发生的次数除以总试验次数。它也可称为相对频率。
Theoretical probability is what we expect to happen based on equally likely outcomes: it is the number of favourable outcomes divided by the total number of possible outcomes. As the number of trials increases, experimental probability tends to approach theoretical probability.
理论概率是基于等可能结果我们期望发生的情况：有利结果数除以所有可能结果总数。随着试验次数增加，实验概率会趋近于理论概率。
A sample space is the set of all possible outcomes of an experiment, often shown as a list, table or tree diagram. The sum of probabilities of all outcomes in a sample space is always 1.
样本空间是试验所有可能结果的集合，通常用列表、表格或树状图表示。样本空间中所有结果的概率总和总是1。
7. Data Collection and Sampling | 数据收集与抽样
Primary data is collected directly by the researcher for a specific purpose, such as a questionnaire or experiment. It is usually up to date and relevant but can be time-consuming to gather.
原始数据是研究人员为特定目的直接收集的数据，例如问卷调查或实验。它通常最新且相关性强，但收集起来可能耗时。
Secondary data is data that already exists, collected by someone else for a different purpose, such as government statistics or internet sources. It is often quick and cheap to obtain but may not perfectly match the current investigation.
二手数据是已经存在的、由他人为其他目的收集的数据，例如政府统计数据或互联网资料。获取通常快捷且成本低，但可能与当前调查不能完全匹配。
A census collects data from every member of a population. A sample collects data from a subset. While a census gives accurate results, a sample is more practical and less expensive if chosen without bias.
普查是从总体中的每个成员收集数据。抽样是从一个子集收集数据。虽然普查结果准确，但如果能无偏选取样本，抽样则更实际、成本更低。
8. Sampling Methods and Bias | 抽样方法与偏差
A random sample gives every member of the population an equal chance of being selected. This method reduces selection bias but may not fully represent subgroups by chance.
随机抽样让总体中的每个成员都有均等的机会被选中。这种方法能减少选择偏差，但可能偶然未能充分代表某些子群体。
Stratified sampling divides the population into groups (strata) and selects a random sample from each group in proportion to its size. It provides better representation of different characteristics.
分层抽样将总体分成若干组（层），然后按各层规模比例从每层中随机抽样。它能更好地代表不同特征。
Bias is any systematic error that makes a sample unrepresentative of the population. Leading questions, convenience sampling, or voluntary response can all introduce bias and should be avoided.
偏差是任何使样本不能代表总体的系统性误差。诱导性问题、便利抽样或自愿回应都可能引入偏差，应当避免。
9. Correlation and Relationships | 相关与关系
Correlation describes the strength and direction of a linear relationship between two variables. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one variable increases, the other tends to decrease.
相关描述了两个变量之间线性关系的强度和方向。正相关意味着当一个变量增大时，另一个也倾向于增大。负相关意味着当一个变量增大时，另一个倾向于减小。
No correlation occurs when there is no obvious pattern between the variables. It is important to remember that correlation does not imply causation – a hidden third factor might be responsible.
无相关是指变量之间没有明显规律。要记住：相关并不意味着因果关系——可能存在一个隐藏的第三因素在起作用。
A line of best fit is drawn on a scatter graph to model the relationship and make predictions. Interpolation is estimating within the range of the data, which is reliable; extrapolation is estimating outside the data range, which can be unreliable.
最佳拟合线画在散点图上，以模型化关系并进行预测。内插法是在数据范围内进行估计，较为可靠；外推法是在数据范围之外进行估计，可能不可靠。
10. Describing Distributions | 描述分布
A symmetric distribution has data that is evenly spread around the centre, with the mean and median roughly equal. A skewed distribution has a longer tail on one side: in a right-skewed distribution, the mean is greater than the median; in a left-skewed distribution, the mean is smaller.
对称分布的数据围绕中心均匀散布，均值和中位数大致相等。偏斜分布一侧有较长的尾巴：右偏分布中，均值大于中位数；左偏分布中，均值小于中位数。
from the main body of data. They can be identified using the IQR rule: any value below Q₁ – R is considered an outlier. Outliers should be investigated but not automatically removed.
异常值是远离数据主体的数据点。可以通过IQR规则识别：任何低于 Q₁ – 1.5×IQR 或高于 Q₃ + 1.5×IQR 的值都被视为异常值。异常值需要调查，但不能自动删除。
11. Presenting and Comparing Data | 呈现和比较数据
When comparing two or more data sets, comment on a measure of central tendency (mean or median) and a measure of spread (range or IQR). Always use the actual statistics in your comparison, not just words like 'higher' or 'lower'.
在比较两个或更多数据集时，需要评论某个集中趋势度量（均值或中位数）和离散程度度量（极差或四分位距）。比较时务必使用实际统计值，而不是仅仅用“更高”或“更低”这样的词。
A box plot (box-and-whisker diagram) visually displays the minimum, Q₁, median, Q₃ and maximum. It clearly shows the centre, spread and skewness, making it excellent for comparing distributions side by side.
箱线图（箱须图）直观地展示了最小值、Q₁、中位数、Q₃和最大值。它清晰地展现了中心、离散程度和偏度，非常适合并列比较分布。
12. Key Formulas and Symbols | 关键公式与符号
For OCR Year 10, you should be familiar with basic statistical notation: Σ means 'sum of'. So Σx is the sum of all data values, and mean (x̄) = Σx ÷ n.
在OCR十年级课程中，你应当熟悉基本统计符号：Σ 表示“求和”。因此 Σx 是所有数据值的总和，均值 (x̄) = Σx ÷ n。
Variance formula for a population: σ² = Σ(x – μ)² ÷ N. Standard deviation: σ = √[Σ(x – μ)² ÷ N]. For a sample, divide by n – 1 instead of N to get an unbiased estimate.
总体方差公式：σ² = Σ(x – μ)² ÷ N。标准差：σ = √[Σ(x – μ)² ÷ N]。对于样本，除以 n – 1 而不是 N，这样才能得到无偏估计。
The probability of event A not occurring is P(A') = 1 – clusive events, P(A or B) = P(A) + P(B). For independent events, P(A and B) = P(A) × P(B).
事件A不发生的概率为 P(A') = 1 – P(A)。对于互斥事件，P(A 或 B) = P(A) + P(B)。对于独立事件，P(A 且 B) = P(A) × P(B)。
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