📚 Year 7 CIE Statistics: Core Knowledge Points Summary | Year 7 CIE 统计：核心知识点梳理
Statistics is an essential part of the Year 7 CIE mathematics curriculum. It equips you with the skills to collect, organise, represent and interpret data in a meaningful way.
统计是七年级 CIE 数学课程的重要组成部分。它使你掌握以有意义的方式收集、整理、表示和解读数据的技能。
1. What is Statistics? | 什么是统计？
Statistics is the branch of mathematics that deals with data. It involves collecting information, organising it into tables or graphs, and then drawing conclusions from it.
统计学是数学中处理数据的分支。它包括收集信息、将其整理成表格或图表，然后从中得出结论。
In your daily life, you encounter statistics in weather forecasts, sports scores and opinion polls. Understanding the basics helps you make sense of the world around you.
在日常生活中，你会在天气预报、体育比分和民意调查中遇到统计数据。了解基础知识有助于你理解周围的世界。
2. Types of Data | 数据类型
Data can be classified into qualitative data and quantitative data. Qualitative data describes qualities or categories, such as eye colour or favourite food. Quantitative data involves numbers and can be measured or counted.
数据可以分为定性数据和定量数据。定性数据描述性质或类别，例如眼睛颜色或最喜欢的食物。定量数据涉及数字，可以测量或计数。
Quantitative data is further split into discrete data and continuous data. 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., height or time).
定量数据进一步分为离散数据和连续数据。离散数据只能取特定值，通常是整数（例如，班级的学生人数）。连续数据可以取某个范围内的任何值（例如，身高或时间）。
3. Collecting Data | 收集数据
There are two main ways to gather data: primary data and secondary data. Primary data is information you collect yourself through surveys, interviews or experiments. Secondary data is information that someone else has already gathered, such as data from books or websites.
收集数据主要有两种方式：一手数据和二手数据。一手数据是你通过调查、访谈或实验自己收集的信息。二手数据是其他人已经收集好的信息，例如来自书籍或网站的数据。
When designing a survey, questions should be clear and unbiased. A tally chart is often used to record responses quickly and accurately.
设计调查问卷时，问题应该清晰且无偏见。通常用划线记数表来快速、准确地记录回答。
4. Frequency Tables | 频率表
A frequency table shows how often each value or category occurs. It usually includes a tally column and a frequency column.
频率表显示每个值或类别出现的频率。它通常包括一栏划线记数（或直接用数字）和一栏频数。
| Colour | Tally | Frequency |
|---|---|---|
| Red | |||| || | 7 |
| Blue | |||| | 5 |
| Green | ||| | 3 |
Once the frequency table is complete, we can easily see which category is most popular and which is least popular.
一旦频率表完成，我们就可以轻松看出哪个类别最受欢迎，哪个最不受欢迎。
5. Pictograms and Bar Charts | 象形图与条形图
A pictogram uses pictures or symbols to represent data. Each symbol stands for a certain number of items. It is important to include a key to show what each symbol represents.
象形图用图片或符号来表示数据。每个符号代表一定数量的项目。重要的是要包含一个图例，说明每个符号代表什么。
A bar chart displays data using rectangular bars. The height (or length) of each bar shows the frequency. Bars should be of equal width and separated by gaps, because the categories are distinct.
条形图使用矩形条来显示数据。每个条形的高度（或长度）表示频数。条形应等宽，并且之间留有间隙，因为各类别是互相独立的。
When drawing a bar chart, always label the axes, give the chart a title, and choose a suitable scale.
绘制条形图时，务必给坐标轴加标签，给图表加上标题，并选择合适的刻度。
6. Pie Charts | 饼图
A pie chart is a circular graph divided into sectors. Each sector represents a category, and its angle is proportional to the frequency.
饼图是一个圆形图，被划分成多个扇形。每个扇形代表一个类别，其角度与频数成比例。
The formula to calculate the angle for each sector is:
计算每个扇形的角度的公式是：
Angle = (Frequency ÷ Total Frequency) × 360°
For example, if 10 out of 30 students like apples, the sector angle for apples is (10 ÷ 30) × 360° = 120°.
例如，如果30个学生中有10个喜欢苹果，那么苹果对应的扇形角度为 (10 ÷ 30) × 360° = 120°。
Pie charts are excellent for showing proportions at a glance, but they are less effective when there are many small categories.
饼图非常适合一眼看出比例关系，但当有许多小类别时，效果就较差。
7. Line Graphs | 折线图
A line graph is used to show how a quantity changes over time. Data points are plotted on a grid and joined with straight line segments.
折线图用于显示数量如何随时间变化。数据点绘制在网格上，并用直线段连接起来。
In a line graph, the independent variable (e.g., time) is placed on the horizontal axis, and the dependent variable (e.g., temperature) on the vertical axis.
在折线图中，自变量（例如时间）放在横轴上，因变量（例如温度）放在纵轴上。
Line graphs make trends easy to spot, such as increasing or decreasing values.
折线图使趋势易于识别，比如数值在上升或下降。
8. Mean (Average) | 均值（平均数）
The mean is a measure of central tendency. It is found by adding up all the values and then dividing by the number of values.
均值是一种集中趋势量数。它的求法是将所有数值加起来，再除以数值的个数。
Mean = ∑x ÷ n
Here, ∑x represents the sum of all data values, and n is the count of values.
其中，∑x 表示所有数据值的总和，n 是数值的个数。
Example: The marks of five students are 4, 6, 7, 8 and 10. The mean mark is (4 + 6 + 7 + 8 + 10) ÷ 5 = 35 ÷ 5 = 7.
例子：五名学生的分数为 4、6、7、8 和 10。平均分是 (4 + 6 + 7 + 8 + 10) ÷ 5 = 35 ÷ 5 = 7。
The mean is very useful, but it can be affected by extremely high or low values (outliers).
均值非常有用，但可能受极高或极低值（异常值）的影响。
9. Median and Mode | 中位数与众数
The median is the middle value when the data is arranged in order. If there is an even number of values, the median is the mean of the two middle numbers.
中位数是将数据按顺序排列后的中间值。如果有偶数个数值，中位数是中间两个数的均值。
For the ordered list 3, 5, 7, 9, 12, the median is 7. For 3, 5, 7, 9, the median is (5 + 7) ÷ 2 = 6.
对于有序列表 3, 5, 7, 9, 12，中位数是 7。对于 3, 5, 7, 9，中位数是 (5 + 7) ÷ 2 = 6。
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.
众数是出现最频繁的值。一个数据集可以有一个众数、多个众数，或者没有众数。
Example: In the set 2, 4, 4, 5, 6, 6, 6, 8, the mode is 6 because it occurs three times.
例子：在集合 2, 4, 4, 5, 6, 6, 6, 8 中，众数是 6，因为它出现了三次。
10. Range | 极差
The range is a measure of spread. It tells us how spread out the data values are.
极差是一种离散程度量数。它告诉我们数据值分布得有多广。
Range = Largest Value – Smallest Value
For the data set 1, 3, 7, 12, the range is 12 – 1 = 11.
对于数据集 1, 3, 7, 12，极差是 12 – 1 = 11。
A small range suggests the data is closely grouped, while a large range suggests more variation.
极差小说明数据较为集中，极差大说明变化较大。
11. Interpreting Data and Graphs | 解读数据和图表
Once you have created a graph or found averages, you must be able to interpret what the data tells you. Look for trends, compare categories, and explain the findings in words.
一旦你创建了图表或求出了平均数，你必须能够解读数据告诉你什么。寻找趋势，比较类别，并用文字解释发现。
Beware of misleading graphs. If the vertical scale does not start at zero, or if the intervals are inconsistent, a graph can exaggerate differences.
当心误导性的图表。如果纵轴不从零开始，或者刻度间隔不一致，图表就可能夸大差异。
Always check labels, scales, and titles before drawing conclusions.
在得出结论之前，务必检查标签、刻度和标题。
12. Exam Tips and Common Mistakes | 考试技巧与常见错误
When tackling statistics problems, read the question carefully. Underline key words such as “mean”, “median”, “total frequency”, or “angle for pie chart”.
解答统计题目时，要仔细读题。在关键词下划线，如“均值”、“中位数”、“总频数”或“饼图角度”。
Common mistakes include forgetting to order the data before finding the median, using the wrong formula for the pie chart angle, and misreading the scale on a bar chart.
常见错误包括在求中位数前忘记对数据排序、饼图角度公式用错、以及读错条形图的刻度。
Show your working step by step. This helps you get method marks even if the final answer is slightly off.
一步一步地展示计算过程。这样，即使最终答案略有偏差，你也能获得步骤分。
Practise drawing neat, labelled graphs and double-check your calculations.
练习绘制整洁、带标签的图表，并仔细检查计算。
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