📚 Year 9 SQA Statistics: Core Knowledge Review | Year 9 SQA 统计：核心知识点梳理
In Year 9, the SQA Statistics syllabus builds on earlier data handling skills, introducing formal methods for collecting, displaying and interpreting data. Students explore measures of central tendency and spread, learn to construct various statistical diagrams, and begin to understand probability as a measure of chance. This revision guide covers the core knowledge needed to succeed in assessments and to build a strong foundation for National 5 Mathematics.
在 Year 9 阶段，SQA 统计课程在早期数据处理技能的基础上，引入了收集、展示和解读数据的正式方法。学生将探究集中趋势和离散程度的度量，学习绘制各种统计图表，并开始将概率理解为可能性的度量。本复习指南涵盖了评估所需的核心知识，为 National 5 数学打下坚实基础。
1. Types of Data | 数据类型
Data can be classified as qualitative or quantitative. Qualitative data describes qualities or categories, such as eye colour or favourite subject. Quantitative data can be counted or measured, and is further divided into discrete and continuous types. Discrete data takes only specific separate values (e.g. number of students), while continuous data can take any value within a range (e.g. height, temperature). Understanding data type is essential for choosing appropriate diagrams and calculations.
数据可分为定性数据和定量数据。定性数据描述特征或类别，例如眼睛颜色或最喜欢的学科。定量数据可以计数或测量，并进一步分为离散型和连续型。离散数据只取特定的、分离的值（例如学生人数），而连续数据可以取某个范围内的任何值（例如身高、温度）。理解数据类型对于选择合适的图表和计算方法至关重要。
| Category | Sub-type | Description | Example |
|---|---|---|---|
| Qualitative | – | Categorical, non-numeric | Hair colour, type of pet |
| Quantitative | Discrete | Countable, separate values | Number of goals |
| Quantitative | Continuous | Measurable, any value in range | Mass of an apple |
数据类型可如上表所示：定性数据是非数值的类别数据，如头发颜色；定量数据中的离散数据是可数的独立值，如进球数；连续数据是可测量且在区间内取任意值的，如苹果的质量。
Quantitative data can also be identified as discrete or continuous by asking ‘Can it be measured in fractions or decimals?’ If yes, it is continuous; if only whole numbers make sense, it is discrete. For example, shoe size is discrete (UK sizes allow half sizes but are treated as discrete), but weight is continuous.
定量数据也可以通过“它是否可以用分数或小数测量？”来判断是离散还是连续。如果可以，则是连续的；如果只有整数有意义，则是离散的。例如，鞋码是离散的（英国尺码允许半码，但仍视为离散），而体重是连续的。
2. Frequency Tables and Tally Charts | 频率表和计数表
A frequency table organises raw data by counting how often each value occurs. Tally marks ( |||| ) are used to record counts, and the total frequency is the sum of all tallies. Grouped frequency tables are used for large datasets or continuous data, where values are grouped into class intervals. The class boundaries must be clearly defined to avoid gaps.
频率表通过统计每个值出现的次数来整理原始数据。计数符号（正字）用于记录次数，总频率是所有计数的总和。对于大型数据集或连续数据，使用分组频率表，其中数值被分组到组距中。组界必须明确界定以避免空隙。
When creating grouped frequency tables, intervals should be equal in width where possible, and we often use symbols like 0 ≤ x < 10 to show that 0 is included and 10 is excluded. The midpoint of each interval can be used for further calculations.
创建分组频率表时，区间宽度应尽可能相等，我们通常使用 0 ≤ x < 10 这样的符号表示包括 0 而不包括 10。每个区间的中点可用于后续计算。
3. Bar Charts and Pie Charts | 条形图与饼图
Bar charts display discrete or categorical data using rectangular bars of equal width, with gaps between bars. The height or length of each bar represents the frequency. A bar chart can be vertical or horizontal. Pie charts show proportions of a whole, where the angle of each sector is calculated using: Sector angle = (Frequency / Total frequency) × 360°.
条形图使用等宽且带有间隙的矩形条来显示离散或分类数据。每个条形的高度或长度代表频率。条形图可以是垂直或水平的。饼图展示整体的各个部分，每个扇区的角度通过公式计算：扇区角度 = (频率 / 总频率) × 360°。
Bar charts make it easy to compare frequencies visually, while pie charts effectively highlight the relative size of each category within the whole. However, pie charts are less precise for exact comparisons and are best suited when there are few categories.
条形图便于在视觉上比较频率，而饼图则有效地突出每个类别在整体中的相对大小。然而，饼图在精确比较方面较不精确，最适合类别较少的情况。
4. Stem-and-Leaf Diagrams | 茎叶图
A stem-and-leaf diagram preserves the original data values while showing the distribution shape. The ‘stem’ is the leading digit(s) and the ‘leaf’ is the final digit. A key must always be provided, e.g. 3 | 2 means 32. Ordered stem-and-leaf diagrams arrange leaves in ascending order, making it easy to find the median, quartiles and range.
茎叶图在展示分布形状的同时保留了原始数据值。“茎”是前导数字，“叶”是最后一位数字。必须提供图例，例如 3 | 2 表示 32。有序茎叶图将叶子按升序排列，便于找到中位数、四分位数和极差。
To compare two datasets, back-to-back stem-and-leaf diagrams use a common stem with leaves extending left and right. This allows direct comparison of distributions.
为了比较两个数据集，背靠背茎叶图使用共同的茎，叶子向左和向右延伸。这样可以直观地比较分布。
5. Mean, Median, Mode and Range | 平均数、中位数
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