📚 UK University Entry Requirements Comparison | 英国大学申请要求对照
Statistics helps us make sense of information in the real world. In this article, we will use basic statistical tools taught in Year 7 CAIE Mathematics to compare the entry requirements for different UK universities. You will learn how to collect data, organise it into a table, create a bar chart, and calculate the mean, median, mode and range. By the end, you will see how statistics can help you understand what grades you might need for your dream course.
统计学帮助我们理解现实世界中的信息。在这篇文章中，我们将使用 Year 7 CAIE 数学课程中教授的基本统计工具，比较不同英国大学的入学要求。你将学习如何收集数据、整理成表格、绘制条形图，并计算平均数、中位数、众数和极差。到最后，你会看到统计学如何帮助你理解申请梦想课程可能需要什么样的成绩。
1. Introduction to the Project | 项目介绍
Imagine you are a Year 7 student curious about university. You want to know which UK universities ask for the highest grades in a subject like Mathematics. To answer this question, you decide to investigate five to seven popular universities and record their typical A-Level entry requirements. This is a statistics project: you will gather numerical data, present it clearly, and draw conclusions.
假设你是一名对大学感到好奇的 Year 7 学生。你想知道哪些英国大学在数学这类专业上要求最高的成绩。为了回答这个问题，你决定调查五到七所受欢迎大学，并记录它们典型的 A-Level 入学要求。这是一个统计项目：你将收集数值型数据，清晰地展示出来，并得出结论。
The data we collect is quantitative (based on numbers) and discrete, because UCAS tariff points are whole numbers. The investigation will teach you how to handle data in a structured way, just like a real statistician.
我们收集的数据是定量的（基于数字）且是离散的，因为 UCAS 分数都是整数。这次调查将教你像真正的统计学家一样，有条理地处理数据。
2. What Are University Entry Requirements? | 什么是大学入学要求？
When you apply to a UK university, each course lists the minimum grades you need. These are usually expressed as A-Level grades, such as A*A*A, A*AA or ABB. Some universities also state an equivalent UCAS Tariff points total. Entry requirements vary by university, by subject, and sometimes even by the popularity of the course.
当你申请英国大学时，每个专业都会列出所需的最低成绩。这些通常表示为 A-Level 成绩，比如 A*A*A、A*AA 或 ABB。有些大学还会说明对应的 UCAS Tariff 总分。入学要求因大学、专业，有时甚至因课程的热门程度而异。
For A-Levels taken in England, each grade carries tariff points: A* = 56, A = 48, B = 40, C = 32, D = 24, E = 16. By adding the points from three A-Levels, we get a total UCAS score that makes it easier to compare offers, especially when different grade combinations are possible.
对于英格兰的 A-Level，每个等级对应一定的分数：A* = 56，A = 48，B = 40，C = 32，D = 24，E = 16。将三门 A-Level 的分数相加，就得到 UCAS 总分，这使得比较不同条件变得更容易，尤其是存在不同等级组合的时候。
3. The UCAS Tariff System | UCAS 分数系统
The UCAS Tariff is a numerical scale that translates grades and qualifications into points. Universities may specify a tariff score instead of, or in addition to, letter grades. For example, a course might ask for 144 UCAS points, which could be achieved with AAA (48+48+48) or A*A*C (56+56+32) and so on. This system allows comparison across different qualifications.
UCAS 分数体系是一个将成绩和资格证书转换成点数的数值标尺。大学可能会指定一个分数来代替字母等级，或作为附加条件。例如，某课程可能要求 144 个 UCAS 点，这可以通过 AAA（48+48+48）或 A*A*C（56+56+32）等组合来实现。这一体系使得不同资格证书之间的比较成为可能。
For our investigation, we will stick to standard three-subject A-Level combinations and assume students take three full A-Levels. The tariff points we calculate will let us put all offers on a single number line, making analysis much simpler.
在我们的调查中，我们将采用标准的三科 A-Level 组合，并假设学生都修读了三门完整的 A-Level。我们计算出的 tariff 分数将把所有录取条件放在同一条数轴上，使分析变得简单得多。
4. Collecting Our Data | 收集我们的数据
As a statistician, your first job is to decide which data to collect. You choose seven UK universities and look up the typical A-Level offer for their Mathematics courses on official websites. You record the grade requirement exactly as stated and then convert it to UCAS tariff points. This is secondary data because someone else has already published the information.
作为一名统计人员，你的第一项任务是决定收集哪些数据。你选择七所英国大学，在官网上查找其数学专业典型的 A-Level 录取条件。你按照上述方法准确记录成绩要求，然后将其转换为 UCAS 分数。这是二手数据，因为信息已经由他人发布。
Here is the set of data you gathered for BSc Mathematics (or equivalent) for 2024 entry. You made sure to include a range of universities: Russell Group members and a couple of others to see variation.
以下是你为 2024 年入学的数学理学士（或同等学力）收集的数据集。你确保涵盖了不同类型的大学：包括罗素集团成员和其他几所，以便观察差异。
- University of Oxford: A*A*A → 56+56+48 = 160 points
- University of Cambridge: A*A*A → 160 points
- Imperial College London: A*A*A → 160 points
- University College London (UCL): A*A*A → 160 points
- London School of Economics (LSE): A*AA (Maths and Economics) → 56+48+48 = 152 points
- University of Manchester: A*AA → 152 points
- Keele University: ABB → 48+40+40 = 128 points
中文对应：
- 牛津大学: A*A*A → 160 分
- 剑桥大学: A*A*A → 160 分
- 帝国理工学院: A*A*A → 160 分
- 伦敦大学学院: A*A*A → 160 分
- 伦敦政治经济学院: A*AA → 152 分
- 曼彻斯特大学: A*AA → 152 分
- 基尔大学: ABB → 128 分
5. Data Table: Entry Requirements for Mathematics | 数据表：数学专业入学要求
Organising data into a frequency table or a simple data table makes it easier to read and use. We will place our seven universities in a table, along with their typical A-Level offer and the corresponding UCAS tariff points. This table will be the foundation for our graphs and calculations.
将数据整理成频数表或简单的数据表，会更容易阅读和使用。我们将把七所大学放进一个表格，同时列出典型的 A-Level 录取条件和对应的 UCAS 分数。这个表格将成为我们绘图和计算的基础。
| University / 大学 | Typical A-Level Offer / 典型录取条件 | UCAS Tariff Points / UCAS 分数 |
|---|---|---|
| Oxford | A*A*A | 160 |
| Cambridge | A*A*A | 160 |
| Imperial | A*A*A | 160 |
| UCL | A*A*A | 160 |
| LSE | A*AA | 152 |
| Manchester | A*AA | 152 |
| Keele | ABB | 128 |
Looking at the table, you can already see that four of the seven universities require the same 160 points, two require 152 points, and Keele asks for 128 points. The data is now ready for statistical analysis.
观察表格，你已经能够看到七所大学中有四所要求相同的 160 分，两所要求 152 分，基尔大学要求 128 分。现在数据已经准备就绪，可以进行统计分析了。
6. Creating a Bar Chart | 创建条形图
A bar chart is an excellent way to visualise categorical data like university names alongside numerical data like tariff points. Each university would be a category on the horizontal axis, and the height of each bar shows its UCAS points. Because the data is not grouped into intervals, this is a simple bar chart for discrete data.
条形图是展示类别数据（如大学名称）与数值数据（如 tariff 分数）的绝佳方式。每所大学将作为水平轴上的一个类别，每个条形的高度表示其 UCAS 分数。由于数据没有被分组成区间，这是一个针对离散数据的简单条形图。
If we were to sketch the chart, the bars for Oxford, Cambridge, Imperial and UCL would all reach 160. LSE and Manchester would be slightly shorter at 152, while Keele would be noticeably lower at 128. This immediately shows a gap between the more selective institutions and the rest.
如果我们要绘制此图，牛津、剑桥、帝国理工和 UCL 的条形都将达到 160。LSE 和曼彻斯特的条形会稍短，为 152，而基尔的条形会明显更低，为 128。这立即显示出更具选拔性的院校与其他院校之间的差距。
When you draw bar charts in class, remember to label the axes, give the chart a title, and keep the bars the same width. The bars must not touch, since the categories are separate.
当你在课堂上绘制条形图时，记得标注坐标轴、为图表添加标题，并保持条形宽度一致。条形之间不要挨着，因为各个类别是独立的。
7. Calculating the Mean UCAS Tariff | 计算平均 UCAS 分数
The mean (average) gives us a single value that represents the typical UCAS points required. To find it, we add all the tariff points together and then divide by the number of universities.
平均数（均值）给我们一个代表典型所需 UCAS 分数的单一数值。要计算它，我们将所有 tariff 分数相加，然后除以大学的数目。
Let us add the values: 160 + 160 + 160 + 160 + 152 + 152 + 128 = 1072. There are 7 universities, so we divide 1072 by 7.
让我们将数值相加：160 + 160 + 160 + 160 + 152 + 152 + 128 = 1072。共有 7 所大学，因此我们将 1072 除以 7。
Mean = 1072 ÷ 7 ≈ 153.1 UCAS points (to one decimal place)
平均数 = 1072 ÷ 7 ≈ 153.1 UCAS 分（保留一位小数）
The mean tariff of about 153 is pulled up by the four top universities but pulled down by Keele. This tells us that the ‘centre’ of our data is closer to the A*AA universities than to the highest ones.
平均 tariff 约为 153，这一数值被四所顶尖大学拉高，但又被基尔大学拉低。这说明我们数据的“中心”更靠近 A*AA 类大学，而非最高要求的那几所。
8. Finding the Range | 查找极差
The range measures how spread out the data is. It is simply the difference between the largest and the smallest tariff point.
极差衡量数据的分散程度。它就是最大 tariff 分数与最小分数之间的差值。
From our table, the highest value is 160 (Oxford, Cambridge, Imperial, UCL) and the lowest is 128 (Keele). So the range is:
从我们的表格来看，最高值是 160（牛津、剑桥、帝国、UCL），最低值是 128（基尔）。因此极差为：
Range = 160 − 128 = 32 points
极差 = 160 − 128 = 32 分
A range of 32 shows that there is considerable variation among UK universities for Mathematics. Some ask for very high grades, while others are more accessible. The range does not tell us about the clustering of values, but it indicates the overall spread.
32 分的极差表明，英国大学在数学专业上的要求存在相当大的差异。有的要求非常高的成绩，而有的则更易进入。极差并不能反映数值的聚集情况，但它体现了总的分布广度。
9. Median and Mode of Offers | 录取条件的中位数和众数
To find the median, we first sort the tariff points in ascending order:
要找到中位数，我们首先将 tariff 分数按升序排列：
128, 152, 152, 160, 160, 160, 160
The middle value, since there are 7 numbers, is the 4th value. The 4th value is 160. Thus, the median offer is 160 points.
因为有 7 个数，中间的值是第 4 个值。第 4 个值是 160。因此，中位录取条件是 160 分。
The mode is the most frequently occurring tariff point. Here, 160 appears four times, 152 appears twice, and 128 appears once. So the mode is 160 points, which corresponds to an A*A*A offer.
众数是出现频率最高的 tariff 分数。在这里，160 出现四次，152 出现两次，128 出现一次。因此众数是 160 分，对应 A*A*A 的录取要求。
The median and mode both being 160 suggest that high-grade offers are common in our sample, even though the mean was slightly lower due to Keele. This is why we use more than one average – each tells a slightly different story.
中位数和众数都是 160，这提示在我们的样本中高成绩要求很常见，尽管平均数因基尔大学而略低。这就是为什么我们要使用不止一种平均数——每一种都传递略有不同的信息。
10. Comparing STEM and Humanities Requirements | 比较 STEM 与人文学科要求
Does the picture change if we look at a Humanities subject like English Literature? To find out, we could collect a second set of data. Suppose we check typical offers for English Literature at the same universities and convert them to tariff points.
如果我们看一门像英语文学这样的人文学科，情况是否会改变？为了弄明白，我们可以收集第二组数据。假设我们查看相同大学英语文学专业的典型录取条件，并将其转化为 tariff 分数。
Hypothetical data for English Literature: Oxford AAA → 144, Cambridge A*AA → 152, Imperial – does not offer pure English, so we replace with Durham AAA → 144, UCL AAA → 144, LSE – no English, so we use Edinburgh AAA → 144, Manchester AAB → 136, Keele ABB → 128. Let us calculate the mean: (144+152+144+144+144+136+128) ÷ 7 ≈ 141.7 points.
英语文学假设数据：牛津 AAA → 144，剑桥 A*AA → 152，帝国理工不提供纯英语，因此用杜伦大学 AAA → 144 代替，UCL AAA → 144，LSE 无英语，用爱丁堡大学 AAA → 144 代替，曼彻斯特 AAB → 136，基尔 ABB → 128。计算均值：(144+152+144+144+144+136+128) ÷ 7 ≈ 141.7 分。
Clearly, the mean for Mathematics (153.1) is higher than for English Literature (141.7). This suggests that, in our small sample, top universities demand slightly higher tariff points for STEM subjects. However, entry requirements depend on many factors, and we must be careful not to draw sweeping conclusions from limited data.
显然，数学的平均分（153.1）高于英语文学（141.7）。这表明，在我们的小样本中，顶尖大学对 STEM 专业要求的 tariff 分数略高。然而，入学要求取决于许多因素，我们不应从有限数据中得出过于绝对的结论。
11. Drawing Conclusions from the Data | 从数据中得出结论
From our investigation, we can conclude that for Mathematics, most of the highly selective universities we examined look for offers worth 160 UCAS points, which is equivalent to A*A*A. The mean (153.1) is dragged downwards by Keele, but the median and mode both point to 160. The range of 32 shows variety exists, so students have options at different levels.
从我们的调查中我们可以得出结论：对于数学专业，我们考察的大多数选拔性强的大学都倾向于价值 160 UCAS 分的录取条件，相当于 A*A*A。平均数（153.1）被基尔大学拉低，但中位数和众数都指向 160。32 分的极差显示了多样性的存在，因此学生在不同层级都有选择。
Comparing Mathematics with English Literature suggested that STEM offers might be slightly higher on average, but a more comprehensive dataset with more universities and subjects would be needed to confirm this. A good statistician always acknowledges the limitations of the data.
数学与英语文学的比较显示，STEM 的录取条件可能平均略高，但需要有包含更多大学和专业的更全面数据集来证实这一点。一位好的统计学家总是会承认数据的局限性。
This project demonstrates how basic Year 7 statistics – tables, bar charts, mean, median, mode and range – can turn raw information into a clear picture that helps you understand real-world choices.
这个项目展示了 Year 7 基础统计学——表格、条形图、平均数、中位数、众数和极差——如何将原始信息转化为清晰的图景，帮助你理解现实世界中的选择。
12. How This Helps Year 7 Students | 这对 Year 7 学生有何帮助
Even though university applications are several years away, this exercise builds essential skills. You learn to plan a data collection, organise numbers, calculate statistics, and present findings. These skills are part of the CAIE lower secondary statistics curriculum and also give you an early glimpse of how grades matter for future pathways.
尽管大学申请还是好几年后的事情，这个练习能培养关键技能。你学会了规划数据收集、整理数字、计算统计量并展示发现。这些技能是 CAIE 初中统计课程的一部分，同时也让你提前一窥成绩对未来的重要性。
By practising with real data, you also become a more critical reader of information. When you see university league tables or course entry requirements, you will know how to compare them using averages and spread, rather than just looking at one number.
通过使用真实数据进行练习，你还会成为一个更具批判性的信息读者。当你看到大学排名表或课程入学要求时，你就会知道如何使用平均数和分散度来比较它们，而不只是看单个数字。
Keep exploring data around you – sports scores, weather temperatures, class test results – and apply the statistical toolkit from today. The more you practise, the more confident you will become in handling numbers and making evidence-based decisions.
继续探索你身边的数据——体育比分、气温、课堂测验成绩——并运用今天学到的统计工具。你练习得越多，处理数字和做出基于证据的决策就越有信心。
Published by TutorHao | Statistics Revision Series | aleveler.com
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