📚 Quick Guide to Statistical Vocabulary for Year 8 SQA | Year 8 SQA 统计：词汇术语速记指南
Mastering statistics starts with knowing your words. In the SQA Year 8 course, you will meet many specific terms that describe data, how to collect it, and how to summarise it. This guide gives you clear definitions, crisp examples and memory hooks for every key term you need to command. Use it to read questions accurately and write answers that examiners love.
精通统计学从掌握术语开始。在 SQA 八年级课程中，你会遇到许多描述数据、如何收集数据以及如何概括数据的专有名词。这份指南为你提供清晰的定义、简洁的例子和记忆诀窍，覆盖你需要掌握的每一个关键术语。借助它，你可以准确读懂题目，并写出阅卷老师喜欢的答案。
1. Population, Sample and Census | 总体、样本与普查
A population is the entire set of people, objects or events that you want to investigate. For example, all S2 pupils in Scotland would be the population if you are exploring their reading habits.
总体是你想要调查的全部人、物体或事件的集合。例如，如果你在探究苏格兰所有中二学生的阅读习惯，那么全体苏格兰中二学生就是总体。
A sample is a smaller group chosen from the population. A good sample should be representative and randomly selected so that the results can be generalised back to the population.
样本是从总体中选出的较小群体。一个好的样本应具有代表性，并且是随机选取的，这样得出的结果才能推广回总体。
A census collects data from every single member of the population. It gives the most accurate picture, but is often expensive, time‑consuming or simply impossible.
普查是从总体中的每一个成员那里收集数据。它能提供最精确的全貌，但通常花费昂贵、耗时，或者根本不可能实现。
2. Types of Data | 数据的类型
Qualitative data (also called categorical data) describes qualities or groups. Colours, favourite subjects, or types of pet are all qualitative.
定性数据（也称分类数据）描述的是性质或组别。颜色、最喜欢的科目或宠物类型都属于定性数据。
Quantitative data measures quantities and is made of numbers. It can be further split into discrete and continuous data.
定量数据衡量数量，由数字组成。它可以进一步分为离散数据和连续数据。
Discrete data can only take certain separate values, usually whole numbers. The number of books in a bag or goals in a match are discrete.
离散数据只能取某些分开的数值，通常是整数。书包里的书本数量或比赛中的进球数就是离散数据。
Continuous data can take any value within a range. Height, weight and temperature are continuous because they can be measured to more and more decimal places.
连续数据可以在一个范围内取任何值。身高、体重和温度都是连续数据，因为它们可以测量到越来越多的小数位。
3. Frequency Tables and Tally Marks | 频数表与计数符号
A frequency table organises data by listing each data value (or group) alongside how many times it occurs. The count is called the frequency.
频数表通过列出每个数据值（或组）及其出现的次数来整理数据。这个计数值就称为频数。
Tally marks are short strokes drawn in bundles of five to help you count while collecting data. Each fifth stroke crosses the previous four, making totals quick to see.
计数符号是一捆五条画的短竖线，帮助你在收集数据时计数。每第五条线横穿前四条，让总数一目了然。
When constructing a frequency table, always include a total frequency row that shows the sum of all frequencies. This acts as a check.
在构建频数表时，务必包含一个总计频数行，显示所有频数的总和。这起到核查作用。
4. Measures of Central Tendency: Mean, Median and Mode | 集中趋势的度量：平均数、中位数和众数
The mean is the sum of all data values divided by the number of values. It is what most people call the 'average', but it can be affected by extreme outliers.
平均数是用所有数据值的总和除以数据个数。它是大多数人所说的“平均”，但可能受极端异常值的影响。
Mean = (∑ data values) ÷ (number of values)
平均数 = (∑ 数据值) ÷ (数据的个数)
The median is the middle value when data is arranged in order. If there are two middle numbers, take their mean. The median is resistant to outliers.
中位数是将数据按顺序排列后居中的那个值。如果有两个中间数，则取它们的平均数。中位数不受异常值影响。
The mode is the value that appears most often. There can be one mode, more than one mode, or no mode at all. It works for both numbers and categories.
众数是出现次数最多的那个值。可以有一个众数、多个众数，或者完全没有众数。它既适用于数字，也适用于分类。
5. Range as a Measure of Spread | 作为离差度量的极差
The range tells you how spread out the data values are. It is simply the difference between the largest and smallest values.
极差告诉你数据值的分散程度。它就是最大值与最小值之间的差。
Range = Maximum value − Minimum value
极差 = 最大值 − 最小值
Two sets of data can have the same mean but very different ranges. The one with the smaller range is more consistent.
两组数据可能有相同的平均数，但极差大不相同。极差较小的那一组数据更为一致。
Always subtract the smallest number from the largest; the range is never negative. A range of zero means all values are identical.
始终用最大的数减去最小的数；极差永远不会是负数。极差为零意味着所有值都相同。
6. Bar Charts, Pie Charts and Pictograms | 条形图、饼图和象形图
A bar chart uses rectangular bars to represent frequencies. The height or length of each bar shows the count for that category. Bars are separated by equal gaps because the data is categorical.
条形图用矩形条来表示频数。每个条形的高度或长度显示该分类的计数。因为数据是分类的，条形之间留有空隙。
A pie chart is a circular display where each 'slice' has an angle proportional to its frequency. The whole circle stands for the total frequency, 360°.
饼图是一个圆形图示，每一“份”的角度与其频数成比例。整个圆代表总频数，即 360°。
A pictogram uses small, identical pictures or symbols to represent a fixed number of items. A key must explain the value of one symbol, and you may use half or quarter symbols.
象形图用相同的小图片或符号来表示固定数量的项目。必须有一个图例说明每个符号代表的值，并且可以使用半符号或四分之一符号。
7. Stem‑and‑Leaf Diagrams | 茎叶图
A stem‑and‑leaf diagram shows data in order while keeping every original value visible. The stem is usually the tens digit, and the leaf is the units digit.
茎叶图有序地展示数据，同时保留每一个原始数值。茎通常是十位数，叶是个位数。
You must include a key, e.g. '3 | 5 means 35'. The leaves should be arranged in ascending order, and there should be no commas between leaves.
你必须包含一个图例，例如“3 | 5 表示 35”。叶子应从左往右按升序排列，且叶之间不要加逗号。
Stem‑and‑leaf diagrams make it easy to find the median, quartiles and range, because the data is already arranged from smallest to largest.
茎叶图让寻找中位数、四分位数和极差变得容易，因为数据已经从小到大排好了。
8. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph is used to display the relationship between two quantitative variables. Each point represents a pair of values (x, y).
散点图用来展示两个定量变量之间的关系。每一个点代表一对（x，y）值。
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 increases, the other tends to decrease.
相关性描述关系的方向和强度。正相关意味着当一个变量增加时，另一个变量也倾向于增加。负相关意味着当一个变量增加时，另一个变量倾向于减少。
No correlation means there is no clear pattern; the points are scattered randomly. A line of best fit can be drawn to model the trend, but it does not prove causation.
无相关意味着没有明显的模式，点随机散布。可以画一条最佳拟合线来模拟趋势，但这并不能证明因果关系。
9. Probability Basics: Language and Scale | 概率基础：语言与尺度
Probability measures how likely an event is to happen. It is given as a fraction, decimal or percentage between 0 (impossible) and 1 (certain).
概率衡量一个事件发生的可能性。它以分数、小数或百分数的形式给出，范围在 0（不可能）和 1（必然）之间。
An experiment is a repeatable action with a set of possible results, e.g. rolling a dice. An outcome is a single possible result, like rolling a 4. An event is a set of one or more outcomes, such as rolling an even number.
试验是一个可重复的动作，有一组可能的结果，例如掷骰子。结果是一个单一的可能结果，比如掷出 4。事件是一组一个或多个结果的集合，例如掷出偶数。
Use words like impossible, unlikely, even chance, likely and certain to describe probability in everyday language. Always back these with numerical values where possible.
在日常语言中，使用“不可能”、“不太可能”、“对半机会”、“很可能”和“必然”等词来描述概率。在可能的情况下，总是用数值来支撑它们。
10. Calculating the Mean from a Frequency Table | 从频数表计算平均数
When data is given in a frequency table, multiply each data value by its frequency, sum those products, then divide by the total frequency.
当数据以频数表的形式给出时，将每个数据值乘以其频数，求出这些乘积的总和，然后除以总频数。
Mean = ∑(value × frequency) ÷ ∑(frequency)
平均数 = ∑(数值 × 频数) ÷ ∑(频数)
Add extra columns to your frequency table labelled 'value × frequency' to show working clearly. Then total that column and divide by the sum of frequencies.
在频数表中添加额外一列，标为“数值 × 频数”，清晰地展示计算过程。然后将该列求和，并除以频数的总和。
This method is much faster than listing every single value, especially for large data sets, and it eliminates simple copying errors.
这种方法比逐一列出每个数值要快得多，尤其对于大数据集，并且能消除简单的抄写错误。
11. Memory Tricks for Key Terms | 关键术语的记忆技巧
Mean rhymes with 'bean', and to find it you add everything up and share equally, like sharing beans among friends.
Mean 与“bean”（豆子）押韵，求平均数就像把豆子全部倒在一起然后平分给朋友一样。
Median sounds like 'medium', the middle size. Always line data up in order and pick the middle one, just like finding the medium‑sized shoe.
中位数 Median 很像“中等”（medium），就是中间尺寸。始终把数据排好队，选中中间那个，就像找中等大小的鞋。
Mode starts with 'most'. It is the value that appears most often. Think of 'the most fashionable' item you spot most frequently.
众数 Mode 开头是“most”（最多）。它是出现次数最多的值。联想你“最常见到的最时尚”的东西。
Range reminds you of a mountain range, with a peak and a valley. Calculate range by taking the highest mountain (max) and subtracting the lowest valley (min).
极差 Range 让你想起山脉，有最高峰和最低谷。计算极差就用最高峰（最大值）减去最低谷（最小值）。
Frequency has the word 'frequent' inside it. How frequently does a value appear? Count it with tally marks – five makes a gate.
频数 Frequency 中间藏着“frequent”（频繁）。一个值有多频繁地出现？用计数符号来数——五个一组打成“闸门”。
12. Common Pitfalls and How to Avoid Them | 常见陷阱与如何避免
Forgetting to order the data before finding the median is the most common error. Always sort values from smallest to largest first, then pick the middle.
在求中位数之前忘记把数据排序是最常见的错误。始终先把数值从小到大排好，然后选取中间的位置。
Confusing the mean and the median when there are extreme outliers. An outlier keeps pulling the mean away from the centre, but the median stays steady.
当存在极端异常值时，混淆平均数和中位数。异常值会将平均数拉离中心，但中位数保持稳定。
Ignoring the frequency multipliers in a frequency‑table mean question. Count each value as many times as its frequency, never just average the distinct values.
在根据频数表求平均的题目中，忽略频数乘数。要把每个数值按其频数重复计算，绝不要只对不同的数值求平均。
Treating discrete data as continuous, or drawing bar charts with touching bars. Discrete categories need gaps; continuous data can use histograms with no gaps.
将离散数据处理成连续数据，或者把条形图的条形紧贴在一起。离散分类图需要留空隙；连续数据才用无空隙的直方图。
Claiming that correlation means causation just because a scatter graph shows a clear pattern. A hidden third factor could be responsible, so always say 'linked' or 'associated'.
仅因散点图显示出清晰的模式就声称相关性意味着因果关系。可能有一个隐藏的第三因素在起作用，所以始终说“相联系”或“相关”。
Published by TutorHao | Statistics Revision Series | aleveler.com
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