Year 9 Edexcel Statistics: Core Knowledge Review | Year 9 Edexcel 统计：核心知识点梳理

📚 Year 9 Edexcel Statistics: Core Knowledge Review | Year 9 Edexcel 统计：核心知识点梳理

Welcome to your essential revision guide for Year 9 Edexcel Statistics. This article breaks down the core topics you need to master, from handling data and calculating averages to understanding probability and drawing correct conclusions. Let us strengthen your statistical skills step by step.

欢迎阅读 Year 9 Edexcel 统计核心复习指南。本文将梳理你需要掌握的关键知识点，从数据处理、平均数计算，到理解概率和得出正确结论。让我们一起逐步强化你的统计技能。

1. Types of Data | 数据类型

In statistics, we first identify the type of data we are working with. Data can be categorical (qualitative) or numerical (quantitative).

在统计中，我们首先要确定所处理数据的类型。数据可以是分类（定性）数据或数值（定量）数据。

Categorical data describe qualities or groups, such as eye colour, favourite food or the brand of a smartphone. They cannot be measured on a numerical scale but can be counted.

分类数据描述性质或类别，例如眼睛颜色、最喜欢的食物或智能手机的品牌。它们不能用数字尺度测量，但可以计数。

Numerical data represent quantities and are split into two subtypes: discrete data and continuous data. Discrete data can only take specific, separate values – often whole numbers or counts, like the number of students in a class or the score on a dice. Continuous data can take any value within a given range, measured to a suitable degree of accuracy, such as height, mass or time.

数值数据表示数量，分为两个子类型：离散数据和连续数据。离散数据只能取特定的、分离的值——通常是整数或计数，比如班级学生人数或骰子点数。连续数据可以在给定范围内取任意值，并测量到合适的精度，例如身高、体重或时间。

Knowing the data type helps you choose the right chart and the most suitable average to use.

了解数据类型有助于你选择合适的图表和最恰当的平均数。

---

2. Collecting Data | 数据收集

Data may come from primary sources (collected by you for a specific purpose) or from secondary sources (already collected by someone else, such as government statistics or news articles). Primary data are often more reliable for your investigation, while secondary data can save time but need careful checking for bias.

数据可以来自一手来源（由你为特定目的收集）或二手来源（由他人事先收集，例如政府统计数据或新闻文章）。一手数据通常对你的调查更可靠，而二手数据可以节省时间，但需要仔细检查是否存在偏见。

When designing a questionnaire to gather data, questions must be clear, unbiased and easy to answer. Avoid leading questions, overlapping response boxes or vague language. For example, ‘How often do you exercise?’ should provide precise options like ‘0–1 times per week’, ‘2–3 times per week’, rather than ‘often’ or ‘sometimes’.

设计问卷收集数据时，问题必须清晰、无偏见且易于回答。避免诱导性问题、选项重叠或模糊用语。例如，“你多久锻炼一次？”应提供精确选项，如“每周0–1次”、“每周2–3次”，而不是“经常”或“有时”。

A sample is a smaller group selected from a population. To avoid bias, it should be representative. A random sample gives every member an equal chance of being chosen. Poor sampling can lead to misleading conclusions.

样本是从总体中选出的小组。为了避免偏见，样本应具有代表性。随机抽样给予每个成员同等的被选机会。不恰当的抽样会导致误导性结论。

---

3. Frequency Tables | 频率表

A frequency table organises raw data into a clear summary. You first list each data category or value, then use tallies to count how many times it occurs. The frequency is the total count for each category.

频率表将原始数据整理成清晰的摘要。你首先列出每个数据类别或数值，然后用画记法计数出现的次数。频率就是每个类别的总计数。

For grouped data, we create class intervals to handle continuous data or a wide range of values. You must ensure intervals do not overlap and are of equal width when possible. For example, 0 ≤ h < 10, 10 ≤ h < 20, and so on.

对于分组数据，我们创建组距来处理连续数据或较宽的数值范围。必须确保区间不重叠，并尽可能保持等宽。例如，0 ≤ h < 10，10 ≤ h < 20，以此类推。

Frequency tables make it easier to calculate totals and later to find the mode, median and mean.

频率表使计算总数以及接下来寻找众数、中位数和平均数变得更加容易。

---

4. Charts for Data Representation | 数据表示图表

The bar chart is used for categorical or discrete data. Each bar’s height represents frequency. Gaps between bars show that the categories are separate. A dual bar chart can compare two sets of data side by side.

条形图用于分类或离散数据。每个条形的高度代表频数。条形之间的间隙表明类别是分离的。复式条形图可以并排比较两组数据。

Pie charts show proportions of a whole. Each sector’s angle is calculated by (frequency ÷ total) × 360°. They are excellent for displaying percentages and comparing parts to the whole.

饼图展示整体的比例。每个扇区的角度通过（频数÷总数）×360°计算。它们在显示百分比和将部分与整体进行比较方面非常出色。

Vertical line charts (or bar-line charts) are often used for discrete numerical data. A thin vertical line is drawn for each value, making it easy to read the frequency and identify the mode.

垂直线图（或条形线图）常用于离散数值数据。为每个数值绘制一条细垂直线，使得读取频数和识别众数变得容易。

Always label axes, give a title and keep the scale consistent so your charts are accurate and easy to interpret.

务必标注坐标轴、给出标题，并保持刻度一致，这样你的图表才能准确且易于理解。

---

5. Mean, Median, Mode and Range | 平均数、中位数、众数和范围

The mean is the arithmetic average. It is calculated by adding all the values and dividing by the number of values.

平均数（均值）是算术平均值，通过将所有值相加再除以值的个数来计算。

Mean, x̄ = (Σx) / n

平均数 x̄ = (Σx) / n

The median is the middle value when the data are ordered. If there are two middle numbers, the median is their mean.

中位数是将数据排序后位于中间的值。如果有两个中间数，中位数就是它们的平均值。

The mode (or modal value) is the most frequently occurring data item. A dataset can have one mode, more than one mode (bimodal or multimodal) or no mode at all.

众数是出现最频繁的数据项。一个数据集可以有一个众数、多个众数（双众数或多众数），或者根本没有众数。

The range is a measure of spread. It is the difference between the largest and smallest values: Range = maximum – minimum. A larger range shows more variability.

范围是衡量离散程度的指标，是最大值与最小值的差：范围 = 最大值 − 最小值。范围越大表示变异性越大。

The choice of average depends on the data type and the presence of outliers. The mean is affected by extreme values, while the median is more robust.

选择哪种平均数取决于数据类型和是否存在异常值。平均数受极端值影响，而中位数更稳健。

---

6. Stem and Leaf Diagrams | 茎叶图

A stem and leaf diagram is a way of displaying raw data while keeping each original value visible. The ‘stem’ contains the leading digit(s) and the ‘leaf’ contains the final digit. Each leaf corresponds to one data item.

茎叶图是一种展示原始数据的方式，同时保留每个原始值可见。“茎”包含前一位或多位数字，“叶”包含最后一位数字。每一片叶对应一个数据项。

Always include a key, for example ‘4 | 2 means 42’, so anyone can read the values. The leaves must be ordered from smallest to largest for easy comparison and to find the median.

始终包含一个图例，例如“4 | 2 表示 42”，这样每个人都能读懂数值。叶子必须从小到大排列，以便于比较和寻找中位数。

Stem and leaf diagrams can also be used back-to-back to compare two distributions. From the ordered diagram you can quickly state the mode, median and range.

茎叶图也可以背靠背使用，以比较两个分布。从有序的图中，你可以快速说出众数、中位数和范围。

---

7. Scatter Graphs and Correlation | 散点图与相关性

A scatter graph (or scatter plot) displays the relationship between two numerical variables. Each point represents a pair of values (x, y). Plotting points helps you see whether a correlation exists.

散点图显示两个数值变量之间的关系。每个点代表一对数值 (x, y)。描点有助于观察是否存在相关性。

Positive correlation occurs when y tends to increase as x increases. Negative correlation means y tends to decrease as x increases. If no clear pattern is visible, there is no correlation or zero correlation.

当 y 随着 x 增加而增加时，存在正相关。负相关意味着 y 随着 x 增加而减少。如果没有明显的模式，则为无相关或零相关。

You can draw a line of best fit through the points to model the relationship. This line should go through the ‘middle’ of the points, with roughly equal numbers above and below it. Use the line to estimate unknown values (interpolation).

你可以通过点画出最佳拟合线来模拟这种关系。该线应该穿过点的“中间”，上下点数大致相等。利用这条线可以估计未知值（内插法）。

Remember: correlation does not imply causation. Just because two variables are related does not mean one causes the other. An external factor might explain the link.

记住：相关性并不意味着因果关系。两个变量相关并不表示一个导致了另一个，外部因素可能解释这种联系。

---

8. Introduction to Probability | 概率入门

Probability measures how likely an event is to happen. It is always given on a scale from 0 (impossible) to 1 (certain). You can write probabilities as fractions, decimals or percentages.

概率衡量一个事件发生的可能性大小，总在0（不可能）到1（必然）的尺度上。你可以将概率写成分数、小数或百分比。

If all outcomes are equally likely, theoretical probability is:

如果所有结果等可能发生，理论概率为：

P(Event) = Number of favourable outcomes / Total number of possible outcomes

P(事件) = 有利结果的数量 / 所有可能结果的总数

The probability of an event not happening is the complement: P(not A) = 1 − P(A). The sum of probabilities of all mutually exclusive outcomes in a sample space is 1.

一个事件不发生的概率是其补集：P(非A) = 1 − P(A)。样本空间中所有互斥结果的概率之和为1。

You must express probabilities in their simplest form and clearly show the steps when solving problems.

在解决问题时，你必须将概率表示为最简形式，并清楚地展示步骤。

---

9. Experimental Probability | 实验概率

Experimental probability, or relative frequency, is based on actual trials or observations. It is calculated as:

实验概率，或相对频率，基于实际试验或观察。其计算公式为：

Experimental Probability = Number of times the event occurred / Total number of trials

实验概率 = 事件发生的次数 / 试验的总次数

When a fair coin is tossed many times, the experimental probability of heads tends to get closer to the theoretical probability of 0.5. This is called the law of large numbers. However, small numbers of trials can give results very different from the theoretical expectation.

抛一枚公平硬币很多次时，正面的实验概率会趋近于理论概率0.5。这叫做大数定律。然而，少量试验的结果可能与理论期望相差很大。

Comparing experimental and theoretical probabilities helps you assess whether a game or situation is fair. If the experimental probability diverges significantly, there may be bias or a faulty assumption of equally likely outcomes.

比较实验概率和理论概率可以帮助你评估某个游戏或情况是否公平。如果实验概率显著偏离，可能存在偏见或等可能结果的假设有误。

---

10. Sample Spaces and Tree Diagrams | 样本空间与树状图

A sample space is a list of all possible outcomes of an experiment. For example, when rolling a fair six-sided dice and tossing a coin, the sample space can be shown as a table: (1,H), (1,T), (2,H), (2,T), etc., giving 12 equally likely outcomes.

样本空间是实验所有可能结果的列表。例如，掷一个公平的六面骰子并抛一枚硬币时，样本空间可以用表格表示为 (1,H), (1,T), (2,H), (2,T) 等，共12个等可能结果。

Tree diagrams are a powerful tool to map out sequential events. Each branch represents a possible outcome, and its probability is written along the branch. The end of each path shows the combined event.

树状图是描绘连续事件的有力工具。每个分支代表一个可能的结果，其概率写在分支旁边。每条路径的末端显示组合事件。

To find the probability of two independent events both happening, multiply the probabilities along their branches. For example, P(Heads and a 6) = 1/2 × 1/6 = 1/12. Always check that the probabilities from a single point sum to 1.

要求出两个独立事件同时发生的概率，将沿途分支的概率相乘。例如，P(正面和6) = 1/2 × 1/6 = 1/12。始终检查从一个点发出的所有分支概率之和是否为1。

Tree diagrams can also handle events where objects are not replaced (conditional probabilities), but in Year 9 the focus is on independent events with replacement.

树状图也可以处理不放回事件（条件概率），但 Year 9 的重点是放回的独立事件。

---

Published by TutorHao | Statistics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）