📚 Year 7 WJEC Statistics: Core Knowledge Review | 七年级 WJEC 统计：核心知识点梳理
In Year 7 WJEC Statistics, students build the foundation for handling data confidently. They learn how to collect, organise, present and interpret information, and begin to explore chance. This bilingual article summarises the essential knowledge areas, from types of data and charts to averages, range and basic probability, with paired English‑Chinese explanations to support learning and revision.
七年级 WJEC 统计课程帮助学生打下数据处理的基础。他们将学习如何收集、整理、展示和解读信息，并开始探索可能性。本篇双语文章梳理了核心知识点，涵盖数据类型、图表、平均数、极差和基础概率，每个要点都配有中英文对照讲解，便于学习和复习。
1. Data Collection and Questionnaire Design | 数据收集与问卷设计
Statistics begins with asking questions and collecting data. A well‑designed questionnaire uses clear, unbiased questions and provides appropriate response options such as yes/no, multiple choice or open‑ended boxes. Pilot testing helps spot confusing wording before the real survey.
统计从提出问题和收集数据开始。一份好的问卷应使用清晰、无偏见的问题，并提供合适的回答选项，比如是/否、选择题或开放式作答框。正式调查前先进行试测，可以发现表述上的问题。
When you design a questionnaire, avoid leading questions that push people towards a particular answer. Instead of asking ‘Don’t you think maths is the best subject?’, ask ‘Which is your favourite subject?’ to get honest responses.
设计问卷时，要避免引导性问题，这类问题会暗示某种答案。不要问“难道你不觉得数学是最好的科目吗？”，而要问“你最喜欢的科目是什么？”，这样才能得到真实的回答。
2. Types of Data: Qualitative, Quantitative, Discrete and Continuous | 数据类型：定性、定量、离散与连续
Data can be qualitative (describing qualities) or quantitative (describing quantities). Qualitative data is non‑numerical, like favourite colour or hair type. Quantitative data involves numbers and can be split into discrete data (counted, whole numbers) and continuous data (measured, can take any value in a range).
数据可以是定性（描述性质）或定量（描述数量）。定性数据是非数值的，比如最喜欢的颜色或头发类型。定量数据涉及数字，又可细分为离散数据（计数得到，取整数值）和连续数据（测量得到，在范围内可取任意值）。
| Type | Description | Example |
|---|---|---|
| Qualitative | Categories, words | Eye colour: blue, brown |
| Quantitative Discrete | Counted, whole numbers | Number of siblings: 0, 1, 2, … |
| Quantitative Continuous | Measured, any value in interval | Height: 142.5 cm, 158.3 cm |
Recognising data types helps you choose the right chart and calculation later. For instance, you would not calculate the mean of favourite colours, but you can calculate the mean height.
识别数据类型有助于后续选择合适的图表和计算方式。例如，你不能计算“最喜欢的颜色”的平均数，但可以计算身高的平均数。
3. Frequency Tables and Tally Charts | 频率表与计数表
A frequency table organises raw data by listing each value or category and counting how many times it appears. A tally chart uses strokes (|||| and the fifth mark crossing through) to record frequencies before they are totalled.
频率表通过列出每个数值或类别，并统计其出现的次数来整理原始数据。计数表使用笔画（先画竖线，第五画横线穿过前四画）来记录频数，然后再汇总。
When constructing a frequency table, always include a total row to check your counting is correct. The total frequency should equal the number of data items.
制作频率表时，一定要加上合计行，以核对计数是否正确。总频数应等于数据项的总个数。
4. Bar Charts and Dual Bar Charts | 条形图与双重条形图
A bar chart displays categorical or discrete data using bars of equal width but varying height, with gaps between the bars. The height of each bar represents the frequency. A dual bar chart compares two related sets of data side by side, using different colours or shading for each group.
条形图用等宽不等高的长条来展示分类或离散数据，条形之间留有间隙。每个条形的高度代表该类别出现的频数。双重条形图则将两组相关数据并排比较，每组使用不同的颜色或阴影区分。
Always label your axes clearly: the horizontal axis for categories, the vertical axis for frequency. Give your chart a title and include a key if a dual bar chart is used.
记得清楚标注坐标轴：横轴表示类别，纵轴表示频数。为图表加上标题，如果是双重条形图，还要附上图例。
5. Line Graphs and Time Series | 折线图与时间序列
A line graph plots points joined by straight line segments, making it ideal for showing how data changes over time. In a time series graph, time (e.g. days, months, years) is always plotted on the horizontal axis, and the quantity being measured goes on the vertical axis.
折线图通过绘制数据点并用直线段连接，特别适合展示数据随时间的变化。在时间序列图中，时间（如日、月、年）总是标在横轴上，而测量的量标在纵轴上。
When interpreting a line graph, look for trends – is the line going up, going down or staying level? Steep slopes indicate rapid change, while gentle slopes show slow change.
解读折线图时，要寻找趋势——折线是上升、下降还是平稳？陡峭的坡度表示变化迅速，平缓的坡度则表示变化缓慢。
6. Pie Charts and Interpreting Angles | 饼图与角度解读
A pie chart shows proportions of a whole. Each slice’s angle is calculated as (category frequency ÷ total frequency) × 360°. The size of each slice tells you how large a share each category has.
饼图展示整体的各个部分所占的比例。每个扇形的角度计算公式为：（类别频数 ÷ 总频数）× 360°。扇形的大小反映该类别所占份额的大小。
When you read a pie chart, remember that a quarter circle is 90°, half is 180°, and three‑quarters is 270°. This helps you quickly estimate proportions without measuring the angle every time.
阅读饼图时，记住四分之一圆对应 90°，半圆对应 180°，四分之三圆对应 270°。这能帮助你快速估计比例，而不必每次都去量角度。
7. Stem‑and‑Leaf Diagrams | 茎叶图
A stem‑and‑leaf diagram keeps all original data values while showing their distribution. You split each number into a stem (usually the tens digit) and a leaf (the units digit), then list them in order. A key explains how to read the values.
茎叶图既能显示数据的分布状态，又能保留原始数据值。把每个数拆分为“茎”（通常是十位数）和“叶”（个位数），然后按顺序排列。通过图例来说明如何解读数值。
For example, if the stem 2 has leaves 3, 5, 8, the values are 23, 25 and 28. Always put leaves in ascending order and include a key such as ‘2 | 3 means 23’.
例如，茎为 2，叶为 3、5、8，则表示 23、25 和 28。务必把叶片按从小到大的顺序排列，并附上图例，如“2 | 3 表示 23”。
8. Mean, Median, Mode and Range | 平均数、中位数、众数与极差
The mean is the arithmetic average. Add all the values together and divide by the number of values.
Mean = (sum of all values) ÷ (number of values)
平均数是算术平均值。将所有数值相加，再除以数值的个数。
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.
中位数是将数据按大小顺序排列后处于中间位置的值。如果数据的个数是偶数，则中位数为中间两个数的平均值。
The mode is the value that appears most often. A data set may have one mode, more than one mode (bimodal/multimodal), or no mode at all.
众数是出现次数最多的值。一组数据可能有一个众数、多个众数（双众数/多众数）或完全没有众数。
The range measures spread: it is the difference between the highest and lowest values.
Range = Largest value − Smallest value
极差衡量数据的分散程度，它是最大值与最小值之差。
9. Comparing Data Sets | 比较数据集
You can compare two data sets by looking at both their averages and their spread. Which group has the higher mean or median? Which is more consistent – a smaller range usually means less variation.
可以通过比较两个数据集的平均数和离散程度来加以对比。哪一组的平均数或中位数更高？哪一组更稳定——通常极差越小，波动越小。
For example, when comparing test scores of two classes, Class A may have a higher mean but also a larger range, meaning some students scored very low while others scored very high. Class B might have a slightly lower mean but a smaller range, showing more consistent performance.
例如，比较两个班的测验成绩时，A 班可能有较高的平均数，但极差也较大，意味着有的学生得分很低，有的得分很高。B 班平均数略低，但极差较小，说明成绩更均衡。
10. Introduction to Probability | 概率入门
Probability describes how likely an event is to happen. It is often placed on a scale from 0 (impossible) to 1 (certain). Key words include impossible, unlikely, even chance, likely and certain. The probability of an event can be written as a fraction, decimal or percentage.
概率描述某个事件发生的可能性大小。通常把它放在 0（不可能）到 1（一定发生）的尺度上。关键词包括：不可能、不太可能、相等机会、很可能和一定。事件的概率可以用分数、小数或百分比表示。
For a fair six‑sided dice, the probability of rolling a 4 is 1/6, because there is one favourable outcome out of six equally likely outcomes. The probability of rolling an even number is 3/6 = 1/2.
对于一个均匀的六面骰子，掷出 4 的概率是 1/6，因为在六个等可能的结果中，有一面是 4。掷出偶数的概率是 3/6，即 1/2。
Probabilities can be estimated from experiments. If you toss a coin 50 times and get 27 heads, the experimental probability of heads is 27/50. As you increase the number of trials, the experimental probability tends to get closer to the theoretical probability of 1/2.
概率也可以通过实验来估计。如果你抛一枚硬币 50 次，得到 27 次正面，那么正面的实验概率就是 27/50。随着试验次数的增加，实验概率会越来越接近理论概率 1/2。
Published by TutorHao | Statistics Revision Series | aleveler.com
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