📚 Year 7 CAIE Statistics: Core Concepts Summary | 核心知识点梳理
Welcome to your comprehensive revision guide for Year 7 CAIE Statistics. This article brings together every key concept you need to master, from collecting and organising data to interpreting graphs, calculating averages and understanding basic probability.
欢迎阅读 Year 7 CAIE 统计学综合复习指南。本文整理了所有你需要掌握的核心概念，涵盖数据收集与整理、图表解读、平均数计算及概率基础。
1. Types of Data | 数据类型
In Year 7 statistics, data is classified as either categorical or numerical. Categorical data describes qualities or groups, such as favourite colour or pet type. Numerical data represents quantities and can be discrete (countable, like the number of siblings) or continuous (measured, like height or time).
在七年级统计中，数据分为分类数据和数值数据。分类数据描述品质或组别，如最喜欢的颜色或宠物种类。数值数据表示数量，可以是离散型（可数，如兄弟姐妹个数）或连续型（测量得出，如身高或时间）。
Understanding the data type helps you choose the best graph and the appropriate average.
了解数据类型有助于你选择最合适的图表及恰当的平均数。
2. Collecting Data | 数据收集
Data can be collected through surveys, questionnaires, or observations. A common method is to use a tally chart, where each data value is recorded with tally marks. A group of five is shown by four vertical strokes and one diagonal crossing stroke.
数据可通过调查、问卷或观察来收集。常用方法是使用计数符号表，每个数据值用计数字号记录。五个一组表示为四条竖线加一条斜线。
Clear data collection helps you avoid mistakes before you even start making tables or graphs.
清晰的数据收集能让你在绘制表格或图表之前就避免错误。
3. Frequency Tables | 频数表
A frequency table organises data by listing each value alongside how many times it occurs (its frequency). Tally marks are often converted into numerical frequencies to make the table neat and ready for graphing.
频数表将数据按数值列出，并对应其出现的次数（频数）。计数符号通常转换为数字频数，使表格整洁且便于绘制图表。
Always check that the sum of the frequencies equals the total number of data points.
务必检查频数总和等于数据点的总数。
4. Bar Charts | 条形图
Bar charts display categorical or discrete data using rectangular bars. The height (or length) of each bar represents the frequency. Bars are drawn with equal widths and equal gaps between them. Always label both axes and give the chart a title.
条形图用矩形条展示分类或离散数据。每个条的高度（或长度）代表频数。条形等宽，条间等距。必须标注两轴并给出图表标题。
Bar charts make it easy to compare how common different categories are at a glance.
条形图让不同类别的常见程度一目了然。
5. Pictograms | 象形图
A pictogram uses pictures or symbols to represent data. A key tells you how many units one symbol stands for. For example, one smiley face might represent two people. Half symbols are used when the number is not a whole multiple of the key value.
象形图用图片或符号表示数据。图例说明一个符号代表多少个单位。例如，一个笑脸可能代表两个人。当数据不是图例值的整数倍时，使用半个符号。
Pictograms are visually attractive but must be drawn carefully so the key is accurate.
象形图视觉吸引力强，但绘制时必须确保图例准确无误。
6. Line Graphs | 折线图
Line graphs are used to show changes over time or continuous sequences. Points are plotted and connected by straight line segments. The horizontal axis usually shows time or order, and the vertical axis shows the measured quantity.
折线图用于展示随时间或连续序列的变化。先描点，再用直线段连接。横轴通常表示时间或顺序，纵轴表示测量的数量。
Look for trends, such as increasing, decreasing or staying constant.
观察趋势，如上升、下降或保持不变。
7. Pie Charts | 饼图
A pie chart shows how a whole is divided into parts. Each sector represents a category, and its angle is proportional to the frequency. The formula for the angle is:
饼图展示一个整体如何被分成若干部分。每个扇区代表一个类别，其角度与频数成正比。计算角度的公式为：
Angle = (Category frequency ÷ Total frequency) × 360°
角度 = (类别频数 ÷ 总频数) × 360°
Always use a protractor to draw the angles and label each sector or add a key.
始终用量角器绘制角度，并标注每个扇区或添加图例。
8. Mean, Median and Mode | 平均数、中位数和众数
Averages help summarise a data set with a single typical value. The three main averages are the mean, median and mode.
平均数用一个典型值概括一组数据。三种主要平均数是平均数、中位数和众数。
The mean is calculated by adding all values and dividing by the number of values.
平均数的计算方法是把所有数值相加再除以数值个数。
Mean = Sum of all values ÷ Number of values
平均数 = 所有数值之和 ÷ 数值总数
The median is the middle value when the data is arranged in order. If there are two middle numbers, the median is their average.
中位数是将数据排序后中间的那个值。如果有两个中间数，中位数是这两个数的平均数。
The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode at all.
众数是出现次数最多的数值。一个数据集可以有一个众数、多个众数或没有众数。
9. Range | 极差
The range measures how spread out the data is. It is the difference between the largest and the smallest values.
极差衡量数据的分散程度，它是最大值与最小值之差。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
A small range means the data points are close together; a large range means they are more spread out.
极差小表示数据点比较集中；极差大表示数据分布更分散。
10. Comparing Data Sets | 数据组比较
To compare two sets of data, you can use an average (mean, median or mode) and the range. The average tells you which set is generally higher or lower, while the range tells you which set is more varied.
要比较两组数据，你可以使用一个平均数（平均数、中位数或众数）和极差。平均数告诉你哪一组整体上偏高或偏低，而极差告诉你哪一组变化更大。
For example, if Class A has a higher mean score but a smaller range than Class B, Class A performed better on average and more consistently.
例如，如果A班的平均分数较高但极差较小，那么A班平均表现更好且更稳定。
11. Basic Probability | 概率基础
Probability describes how likely an event is to happen. It can be written as a fraction, decimal or percentage on a scale from 0 (impossible) to 1 (certain).
概率描述一个事件发生的可能性。它可以用分数、小数或百分数表示，尺度从0（不可能）到1（确定）。
For equally likely outcomes, the probability of an event is:
对于等可能结果，事件的概率为：
Probability = Number of favourable outcomes ÷ Total number of possible outcomes
概率 = 有利结果数 ÷ 所有可能结果总数
Probability helps you predict what might happen in experiments like rolling a fair dice or flipping a coin.
概率帮助你预测在抛硬币或掷骰子等实验中可能发生的结果。
Published by TutorHao | Statistics Revision Series | aleveler.com
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