Year 7 SQA Statistics: Core Knowledge Review | 七年级 SQA 统计：核心知识点梳理

📚 Year 7 SQA Statistics: Core Knowledge Review | 七年级 SQA 统计：核心知识点梳理

Statistics helps us make sense of the world by collecting, organising, displaying and interpreting data. In Year 7 SQA, you will build a strong foundation in statistical thinking — from telling a bar chart from a pie chart to calculating the mean and understanding what probability really means. This article walks you through every core idea, with clear examples and explanations in both English and Mandarin, so you can revise confidently.

统计学帮我们理解世界，通过收集、整理、展示和解读数据。在七年级 SQA 课程中，你会打下一个扎实的统计思维基础——从区分条形图和饼图，到计算平均数，再到理解概率的真正含义。这篇文章带你过一遍所有核心概念，配有清晰的中英文讲解和例子，让你自信备考。

1. What is Statistics? | 什么是统计学？

Statistics is the science of data. It involves asking a question, gathering information, summarising that information and then drawing conclusions. In school, we often start with a simple question like ‘What is the most common pet in our class?’ and use statistical methods to find an answer.

统计学是数据的科学。它包括提出问题、收集信息、总结信息，然后得出结论。在学校里，我们通常从一个简单的问题开始，比如 “我们班上最常见的宠物是什么？”，然后用统计方法找出答案。

Key stages in any statistical investigation are: posing a question, collecting data, analysing data and interpreting results. These steps ensure that our conclusions are based on evidence, not just guesses.

任何统计调查的关键阶段是：提出问题、收集数据、分析数据和解释结果。这些步骤确保我们的结论基于证据，而不仅仅是猜测。

2. Types of Data | 数据类型

Data can be split into two main types: qualitative and quantitative. Qualitative data describes qualities or categories, like eye colour or favourite food. Quantitative data is numerical and tells us about quantities, like height, age or test scores.

数据可以分为两大类：定性数据和定量数据。定性数据描述的是性质或类别，比如眼睛颜色或最喜欢的食物。定量数据是数值型的，告诉我们数量，比如身高、年龄或考试分数。

Quantitative data can be further divided into discrete and continuous data. Discrete data can only take certain values, usually whole numbers, like the number of siblings. Continuous data can take any value within a range, like height (you could be 142.5 cm). Recognising data types helps you choose the right chart and the right average.

定量数据又可以进一步分为离散数据和连续数据。离散数据只能取特定的值，通常是整数，比如兄弟姐妹的数量。连续数据可以取一个范围内的任意值，比如身高（你可能是 142.5 cm）。认识数据类型能帮你选择正确的图表和正确的平均数。

3. Collecting Data | 收集数据

Good statistics start with good data. We collect data using surveys, questionnaires, observations or experiments. When we design a questionnaire, we must be careful to ask clear, unbiased questions. A closed question, like ‘Do you walk to school? Yes/No’, is easier to analyse than an open question like ‘Tell me about your journey to school’.

好的统计始于好的数据。我们通过调查、问卷、观察或实验来收集数据。设计问卷时，必须注意提问清晰、不偏不倚。像 “你是否走路上学？是/否” 这样的封闭式问题，比 “说说你上学的路程” 这样的开放式问题更容易分析。

Sampling is another important idea. It is often impossible to ask everyone in a population, so we take a sample. A random sample gives every member of the population an equal chance of being chosen, which helps avoid bias.

抽样是另一个重要的概念。通常不可能问整个人群中的每一个人，所以我们抽取一个样本。随机样本让总体中的每个成员都有同等被选中的机会，这有助于避免偏差。

4. Organising Data: Frequency Tables | 数据整理：频数表

Once data is collected, it is messy. A frequency table organises data by listing each category or value and how many times it occurs. The tally column helps you count without losing track. The total frequency should match the number of data values collected.

数据收集好了往往是乱糟糟的。频数表通过列出每个类别或数值及其出现次数来整理数据。计数符号栏帮你一边数一边不丢失记录。总频数应与收集到的数据个数相符。

Here is an example of a frequency table showing favourite colours in a class:

这是一个展示班上最喜欢颜色的频数表示例：

Colour	Tally	Frequency
Red	||||	4
Blue	|||| ||	7
Green	|||	3
Other	|	1

5. Bar Charts and Pictograms | 条形图和象形图

A bar chart uses rectangular bars to represent frequencies. The height of each bar represents the frequency for that category. Bar charts must have a clear title, labelled axes and equal gaps between the bars. For discrete categorical data, bars should not touch.

条形图用矩形条来表示频数。每个条的高度对应该类别的频数。条形图必须有清晰的标题、标注了名称的坐标轴，并且条与条之间要有相等的间距。对于离散的分类数据，条形不应相互接触。

Pictograms use pictures or symbols to represent data. A key tells you how many items one symbol stands for. For example, one smiley face could represent 2 students. Pictograms are very visual and easy to read, but they can be less precise when representing larger numbers.

象形图用图片或符号来表示数据。图例会告诉你一个符号代表多少个物体。例如，一个笑脸可以代表 2 个学生。象形图非常直观易读，但在表示较大数字时可能不够精确。

Always check the scale on a bar chart. A clever choice of scale can make differences look bigger or smaller than they really are — be careful when interpreting charts drawn by others.

永远要检查条形图的比例尺。巧妙选择比例尺会让差异看起来比实际更大或更小——在解读别人画的图表时要当心。

6. Pie Charts | 饼图

A pie chart shows how a whole is divided into parts. The angle of each slice represents the proportion of that category. To draw a pie chart, you need to find the angle for each sector: multiply the fraction for that category by 360°. For example, if 10 out of 40 students chose cats as their favourite pet, the angle is (10/40) × 360° = 90°.

饼图展示的是一个整体如何被分成各个部分。每个扇区的角度代表该类别所占的比例。绘制饼图时，你需要算出每个扇区的角度：用该类别的分数乘以 360°。例如，如果 40 个学生中有 10 个选了猫作为最喜欢的动物，角度就是 (10/40) × 360° = 90°。

Pie charts are excellent for comparing parts to the whole at a glance. However, they are not good for showing changes over time or for data sets with many small categories. A pie chart should always have a key or labels so the reader knows what each slice represents.

饼图非常适合一眼比较各部分与整体。然而，它不适合展示随时间的变化，也不适合有很多细小类别的数据集。饼图一定要有图例或标签，让读者知道每块代表什么。

7. Line Graphs and Scatter Plots | 折线图和散点图

Line graphs are used to show how data changes over time. The horizontal axis usually represents time, while the vertical axis shows the quantity being measured. Points are joined with straight lines to highlight trends. Always use equally spaced intervals on the time axis.

折线图用来展示数据如何随时间变化。横轴通常代表时间，纵轴显示被测量的量。各点用直线连接起来以突出变化趋势。时间轴上一定要使用等距间隔。

Scatter plots (or scatter graphs) show the relationship between two sets of quantitative data. Each point on the graph represents a pair of values. If the points tend to go upwards from left to right, there is a positive correlation; if they go downwards, a negative correlation; if there is no clear pattern, there is no correlation. Scatter plots can help you decide if one variable affects another.

散点图显示两组定量数据之间的关系。图上的每个点代表一对数值。如果点的大致走向是从左到右上升的，就是正相关；如果下降，就是负相关；如果没有清晰模式，就是无相关。散点图可以帮助你判断一个变量是否影响另一个变量。

8. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：平均数、中位数、众数

An average is a single value that summarises a whole set of data. The three most common averages are the mean, median and mode.

平均数是一个能概括整组数据的单一数值。最常见的三种平均数是平均数（均值）、中位数和众数。

Mode: The mode is the value that appears most often. A data set can have no mode, one mode or more than one mode. The mode is the only average that works for qualitative data.

众数：众数是出现次数最多的值。一组数据可以没有众数、有一个众数或多个众数。众数是唯一适用于定性数据的平均数。

Median: The median is the middle value when the data is put in order. If there are two middle numbers, the median is the number halfway between them. The median is not affected by extreme values, so it is useful when data contains outliers.

中位数：中位数是将数据按顺序排列后处于中间位置的值。如果有两个中间数，中位数就是它们之间的那个数。中位数不受极端值的影响，因此当数据含有异常值时它很有用。

Mean: The mean is found by adding up all the values and dividing by the number of values. Formula:

平均数：平均数通过把所有数值加起来，再除以数值的个数得到。公式为：

Mean = (x₁ + x₂ + … + xₙ) ÷ n

The mean uses every piece of data, so it can be pulled up or down by extreme values. In Year 7, you are expected to calculate the mean from a small data set and solve simple problems like finding a missing value when you know the mean.

平均数用到了每一个数据，所以会被极端值拉高或拉低。在七年级，你需要从小数据集中计算平均数，并解决简单问题，例如已知平均数求缺失值。

9. Range | 极差

Range tells us how spread out the data is. It is the difference between the largest and smallest values. A small range means the data points are close together, while a large range means they are more spread out. Range is quick to calculate but can be heavily influenced by just one extreme value.

极差告诉我们数据的离散程度。它是最大值和最小值之间的差值。极差小意味着数据点比较集中，极差大意味着数据比较分散。极差计算起来很快，但很容易仅受一个极端值的影响。

For example, the test scores 12, 15, 18, 19, 20 have a range of 20 – 12 = 8. If one student scored 2 instead of 12, the range becomes 20 – 2 = 18, which tells a very different story about consistency.

例如，测验分数 12, 15, 18, 19, 20 的极差是 20 – 12 = 8。如果有一个学生考了 2 分而不是 12 分，极差就变成了 20 – 2 = 18，这关于稳定性讲述了一个完全不同的情况。

10. Introduction to Probability | 概率入门

Probability is the chance that something will happen. It is measured on a scale from 0 (impossible) to 1 (certain). The probability of an event E can be written as a fraction, decimal or percentage. The basic formula is:

概率是某事发生的可能性。它用 0（不可能）到 1（一定发生）之间的数值来衡量。事件 E 的概率可以写成分数、小数或百分比。基本公式为：

P(E) = Number of favourable outcomes ÷ Total number of possible outcomes

A fair coin has P(Heads) = 1/2, or 0.5, or 50%. If you roll a fair six‑sided die, the probability of rolling a 3 is 1/6. Probabilities can also be shown on a probability scale or a probability line.

一枚公平硬币的 P(正面) = 1/2，即 0.5 或 50%。掷一个公平的六面骰子，掷出 3 的概率是 1/6。概率也可以用概率刻度或概率线来表示。

In Year 7, you might also explore simple experiments, like tossing two coins and recording outcomes, and learn that the sum of probabilities of all possible outcomes is always 1.

在七年级，你可能还会探索简单的实验，比如掷两枚硬币并记录结果，并学到所有可能结果的概率之和总是 1。

11. Drawing Conclusions from Data | 从数据得出结论

The final step of any statistical enquiry is interpreting what the charts and numbers mean. A good conclusion uses the evidence from your data to answer the original question. It should mention the averages and spread, and point out any relationships or trends you have found.

任何统计调查的最后一步都是解读图表和数字意味着什么。一个好的结论要用你的数据证据来回答最初的问题。它应该提及平均数和离散程度，并指出你发现的任何关系或趋势。

Avoid making claims the data does not support. For example, if a bar chart shows that more girls than boys chose reading as a hobby in your small class survey, you cannot say all girls prefer reading. You can only say ‘In this survey, a higher proportion of girls chose reading.’

避免做出数据不支持的主张。例如，如果条形图显示在你小规模的全班调查中，选择阅读作为爱好的女生比男生多，你不能说所有女生都更喜欢阅读。你只能说 “在本次调查中，有更高比例的女生选择了阅读”。

Always check whether your results could be due to chance, especially when sample sizes are small. Statistics helps us make informed decisions, not to prove things absolutely.

始终检查你的结果是否可能出于偶然，尤其是在样本量小的时候。统计学帮我们做知情的决定，而不是绝对证明什么。

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Published by TutorHao | Statistics Revision Series | aleveler.com

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