📚 Year 8 WJEC Statistics: Formula & Theorem Quick Reference Handbook | Year 8 WJEC 统计：公式定理速查手册
This quick reference handbook covers the essential formulas, definitions and concepts for Year 8 WJEC Statistics. Each section presents a key topic with the core rules explained in both English and Chinese, perfect for revision and quick checks. Keep this guide handy to boost your confidence in handling data, charts and probability.
本速查手册涵盖了 Year 8 WJEC 统计课程的核心公式、定义与概念。每个小节都围绕一个关键主题，用中英双语解释核心规则，非常适合复习和快速查阅。随身携带这份指南，可以让你在处理数据、图表和概率时更加自信。
1. Types of Data | 数据类型
Data comes in different types. Categorical data describes qualities or groups, while numerical data is made up of numbers. Numerical data can be discrete (countable, like number of students) or continuous (measurable, like height). Understanding the data type helps you choose the right chart and calculation.
数据有不同的类型。分类数据描述的是属性或组别，而数值数据则由数字组成。数值数据可以是离散的（可数的，如学生人数）或连续的（可测量的，如身高）。理解数据类型有助于选择正确的图表和计算方式。
Quantitative discrete data takes only certain values, often whole numbers. Quantitative continuous data can take any value within a range. Qualitative data is non-numerical, for example eye colour or favourite subject.
定量离散数据只能取某些特定的值，通常是整数。定量连续数据可以在一个范围内取任意值。定性数据是非数值的，例如眼睛的颜色或最喜欢的科目。
2. Mean, Median and Mode | 均值、中位数与众数
These three averages summarise a set of data with a single typical value. The mean uses all data values, the median is the middle value, and the mode is the most frequent value. Always arrange data in order before finding the median.
这三种平均数用一个典型的数值来概括一组数据。均值用到了所有的数据值，中位数是居中的数值，而众数是出现次数最多的值。在寻找中位数之前，务必先对数据进行排序。
Mean = (Sum of all values) ÷ (Number of values)
均值 = 所有数值之和 ÷ 数值个数
To find the median for an odd number of values, pick the middle one. For an even number, find the mean of the two middle values. The mode is simply the value that appears most often; there can be more than one mode or no mode at all.
当数据个数为奇数时，中位数就是正中间的那个数。当个数为偶数时，需要计算中间两个数的均值。众数就是出现频率最高的值；可能有一个以上的众数，也可能根本没有众数。
3. Range | 极差
The range is a measure of spread. It tells you how far apart the smallest and largest values are. A larger range means more variation in the data set.
极差是衡量数据离散程度的一个指标。它告诉你最小值和最大值之间相距多远。极差越大，意味着数据集的变异性越大。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
Always subtract the minimum from the maximum. The range is quick to calculate but can be affected by extreme outliers. It is useful for comparing consistency between two sets of data.
永远用最大值减去最小值。极差计算起来很快，但会受到极端异常值的影响。它在比较两组数据的一致性时非常有用。
4. Frequency Tables | 频率表
A frequency table organises raw data by listing each value alongside how many times it occurs. It makes large data sets easier to read and allows you to calculate averages without listing every single value.
频率表通过列出每个数值及其出现的次数来整理原始数据。它使得大型数据集更易于阅读，也让你无需逐一列出所有数值就能计算平均数。
To find the total number of data values, sum the frequencies. To find the mean from a frequency table, multiply each value by its frequency, add all those products, then divide by the total frequency.
要计算数据的总个数，只需将所有频率相加。要从频率表求均值，先用每个数值乘以其频率，再把所有乘积相加，最后除以总频率。
Mean from frequency table = Σ(value × frequency) ÷ Σ frequency
频率表均值 = Σ(数值 × 频率) ÷ 总频率
5. Bar Charts and Pictograms | 条形图和象形图
Bar charts display categorical data using rectangular bars. The height or length of each bar represents the frequency. Bars should be of equal width and separated by gaps, as each category is distinct.
条形图用矩形长条来展示分类数据。每个长条的高度或长度代表频率。所有长条应该等宽，并且彼此之间留有间隔，因为每个类别都是各自独立的。
Pictograms use small pictures or icons to represent a number of items. A key is essential to show what one picture stands for. When a value is not a whole multiple, you may need to show a fraction of the picture.
象形图用小图片或图标来表示物品的数量。必须配有图例，说明每个图片代表多少。当某个数值不是整数倍时，可能需要画出图片的一部分。
Always label the axes of a bar chart: the horizontal axis for categories, the vertical axis for frequency. Choose a sensible scale that fits on the grid and uses equal intervals.
条形图的坐标轴一定要标注：横轴表示类别，纵轴表示频率。选择合理的刻度，使其适应网格，并且使用相等的间隔。
6. Pie Charts: Calculating Angles | 饼图：角度计算
A pie chart shows proportions as sectors of a circle. The whole circle (360°) represents the total frequency. The angle for each sector is proportional to the frequency of that category.
饼图以圆形扇区的形式展示各部分的比例。整个圆（360°）代表总频率。每个扇区的角度与该类别的频率成正比。
Sector angle = (Frequency of category ÷ Total frequency) × 360°
扇区角度 = (类别频率 ÷ 总频率) × 360°
After calculating each angle, use a protractor to draw the sectors accurately. Check that the angles add up to 360°. Label each sector or provide a colour-coded key.
计算完每个角度后，使用量角器精确绘制扇区。检查所有角度之和是否为 360°。为每个扇区添加标签，或提供带颜色标识的图例。
7. Line Graphs and Time Series | 折线图与时间序列
A line graph plots data points joined by straight lines. It is especially useful for showing trends over time, where the horizontal axis represents time periods and the vertical axis represents the measured variable.
折线图将数据点用直线连接起来。它在展示随时间变化的趋势时特别有用，横轴代表时间段，纵轴代表测量的变量。
When drawing a line graph, plot each point carefully, then connect them in time order. Use a ruler for straight lines. The main purpose is to reveal patterns such as upward or downward trends, or seasonal peaks and troughs.
绘制折线图时，要仔细标出每个点，然后按时间顺序将它们连接起来。作图时用直尺画直线。折线图的主要目的是揭示规律，例如上升或下降的趋势，或者季节性的波峰和波谷。
A time series is simply a sequence of data collected at regular time intervals. The line graph is the standard way to visualise a time series.
时间序列就是按固定时间间隔收集的一系列数据。折线图是可视化时间序列的标准方法。
8. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph displays paired numerical data on two axes. Each point represents a pair of values. It helps to see whether there is a relationship, or correlation, between the two variables.
散点图在两根坐标轴上展示成对的数值数据。每个点代表一对数值。它有助于观察两个变量之间是否存在关联，也就是相关性。
Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one increases, the other tends to decrease. No correlation means there is no clear pattern.
正相关意味着当一个变量增大时，另一个变量也趋于增大。负相关意味着当一个变量增大时，另一个变量趋于减小。无相关则意味着没有明显的规律。
You might be asked to draw a line of best fit. This is a straight line that goes through the middle of the points, with roughly equal numbers of points above and below it. It can be used to estimate unknown values within the data range.
考试中可能会要求你画一条最佳拟合线。这是一条穿过点群中央的直线，使其上方和下方的点数大致相等。它可以用来估计数据范围内的未知值。
9. Introduction to Probability | 概率入门
Probability measures how likely an event is to happen. It is given as a number between 0 and 1, or as a fraction, decimal or percentage. A probability of 0 means impossible, and 1 means certain.
概率衡量的是某个事件发生的可能性大小。它是一个介于 0 和 1 之间的数，可以用分数、小数或百分数表示。概率为 0 意味着不可能发生，概率为 1 意味着必然发生。
Probability of an event = Number of favourable outcomes ÷ Total number of possible outcomes
事件的概率 = 有利结果的数量 ÷ 所有可能结果的总数
All outcomes must be equally likely for this formula to apply. The probability scale from 0 to 1 helps describe likelihoods: unlikely outcomes are close to 0, even chance is 0.5, likely outcomes are close to 1.
只有当所有结果等可能发生时，这个公式才适用。从 0 到 1 的概率尺度有助于描述可能性：不大可能发生的结果靠近 0，机会均等是 0.5，很可能发生的结果靠近 1。
The probability of an event not happening is 1 minus the probability that it does happen. For example, if the chance of rain is 0.3, the chance of no rain is 0.7.
某个事件不发生的概率等于 1 减去它发生的概率。例如，如果下雨的概率是 0.3，那么不下雨的概率就是 0.7。
10. Collecting Data: Questionnaires and Sampling | 数据收集：问卷与抽样
Good data collection is fair and unbiased. A questionnaire should use clear questions that do not lead people towards a particular answer. Avoid vague words and give appropriate response options.
好的数据收集应该是公平且无偏的。问卷应该使用清晰的问题，不要引导人们给出某个特定的答案。避免使用模糊的词语，并给出恰当的回答选项。
A sample is a smaller group selected from a larger population. A random sample gives everyone an equal chance of being chosen, which helps to avoid bias. A biased sample may over-represent some groups and produce misleading conclusions.
样本是从一个较大的总体中选出的小组。随机抽样让每个人有同等机会被选中，这有助于避免偏差。有偏的样本可能会过度代表某些群体，从而得出误导性的结论。
Always plan how to collect data fairly: decide on your sample size, the method of selection, and how to record responses systematically. A data collection sheet or tally chart can help keep the recording accurate.
始终要规划好如何公平地收集数据：确定样本大小、选择方法，以及如何系统地记录答案。数据收集表或划记表有助于保持记录的准确性。
Published by TutorHao | Statistics Revision Series | aleveler.com
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