KS3 Edexcel Statistics: Comparing UK University Entry Requirements | KS3 Edexcel 统计：英国大学申请要求对照

📚 KS3 Edexcel Statistics: Comparing UK University Entry Requirements | KS3 Edexcel 统计：英国大学申请要求对照

In KS3 Statistics, you learn how to collect, present and analyse data. One interesting real-life application is comparing the entry requirements for different UK universities. This helps students make informed decisions about their future studies. By using simple statistical tools, we can turn a list of A-level grades into meaningful comparisons.

在 KS3 统计课程中，你将学习如何收集、展示和分析数据。一个有趣的实际应用是比较英国不同大学的入学要求，这可以帮助学生为自己的未来学习做出明智的选择。通过运用简单的统计工具，我们可以将一列 A-level 成绩转化为有意义的比较。

1. Understanding the Question: What Are We Comparing? | 理解问题：我们在比较什么？

In statistics, we always start with a clear question. Here, our question is: ‘How do entry requirements for a Mathematics degree vary across UK universities?’ By analysing the data, we can spot patterns, identify which universities demand the highest grades and see how widely the requirements differ. This is a real-world investigation that uses skills from your KS3 data handling unit.

在统计学中，我们总是从一个明确的问题入手。这里我们的问题是：“英国各大学对数学学位的入学要求有何不同？”通过分析数据，我们可以发现规律，找出哪些大学要求最高分，并看清要求之间的差异有多大。这是一项真实世界中的调查，会用到你在 KS3 数据处理单元学到的技能。

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2. Collecting Data: University Entry Requirements | 收集数据：大学入学要求

We gathered typical A-level grade requirements for a Mathematics BSc degree from ten UK universities. The data is shown in the table below. We will use these grade combinations as our raw data set.

我们收集了十所英国大学数学理学士学位的典型 A-level 成绩要求，数据见下表。我们将使用这些成绩组合作为原始数据集。

University	A-level Offer
University of Oxford	A*A*A
University of Cambridge	A*A*A
Imperial College London	A*A*A*
UCL	A*AA
University of Manchester	A*AA
University of Warwick	A*A*A
University of Bristol	A*AA
Durham University	A*AA
University of Sheffield	AAA
University of Leicester	ABB

This table gives us qualitative data in the form of letter grades. To perform calculations, we need to convert these grades into numbers. The next section shows how we can assign points to each grade.

这张表格以字母等级的形式给出了定性数据。为了进行计算，我们需要把这些等级转换为数字。下一节将展示如何为每个等级分配分数。

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3. Converting Grades to Numerical Values | 将成绩转换为数值

We can create a simple point system: A* = 5 points, A = 4 points, B = 3 points, and C = 2 points. This turns each grade into a numerical score. Then, for each university, we add the points for the three required A-level subjects to get a total entry tariff.

我们可以建立一个简单的分数系统：A* = 5 分，A = 4 分，B = 3 分，C = 2 分。这样就把每个成绩变成了数值分数。接着，对于每所大学，我们把三门必修 A-level 科目的分数相加，得到一个总入学分值。

For example, Oxford’s requirement A*A*A means grades A*, A* and A. Using our system: 5 + 5 + 4 = 14 points. Imperial’s A*A*A* gives 5 + 5 + 5 = 15 points, and Leicester’s ABB gives 4 + 3 + 3 = 10 points. The full set of total points is shown below.

例如，牛津的要求 A*A*A 表示成绩为 A*、A* 和 A。按照我们的系统：5 + 5 + 4 = 14 分。帝国理工的 A*A*A* 得到 5 + 5 + 5 = 15 分，而莱斯特的 ABB 得到 4 + 3 + 3 = 10 分。完整的分数集合如下所示。

University	Total Points
Oxford	14
Cambridge	14
Imperial	15
UCL	13
Manchester	13
Warwick	14
Bristol	13
Durham	13
Sheffield	12
Leicester	10

Now we have numerical data that we can analyse using the statistical measures you learn in KS3: mean, median, mode and range.

现在我们有了数值数据，可以用你在 KS3 学到的统计测度进行分析：平均数、中位数、众数和极差。

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4. Organising Data in a Frequency Table | 用频数表整理数据

A frequency table helps us see how many times each total point value occurs. We list each distinct score and count how many universities achieved it. This makes it easier to spot the most common requirement.

频数表可以帮助我们看到每个总分值出现的次数。我们列出每个不同的分数，并数出有多少所大学取得了该分数。这样能更容易看出最常见的要求。

Total Points	Frequency
10	1
12	1
13	4
14	3
15	1

From the table, we can see that a total of 13 points is the most frequent, appearing for four universities. This is the mode of our data set. The frequencies also give us a quick overview of how requirements are clustered around the middle values.

从表中可以看出，总分 13 分出现的次数最多，有四所大学获得该值。这就是我们数据集的众数。频数还让我们快速了解要求是如何集中在中部数值附近的。

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5. Calculating the Mean Entry Tariff | 计算平均入学分值

The mean (or average) gives us a single value that represents the typical entry requirement across all ten universities. To find the mean, we add up all the total points and then divide by the number of universities.

平均数（或均值）为我们提供了一个代表这十所大学典型入学要求的单一数值。为求出平均数，我们先把所有总分相加，再除以大学的数量。

Sum of all points = 14 + 14 + 15 + 13 + 13 + 14 + 13 + 13 + 12 + 10 = 131

Mean = 131 ÷ 10 = 13.1

The mean entry tariff is 13.1 points. This tells us that, on average, universities expect a combination of grades that maps to roughly 13 points — somewhere between A*AA and A*A*A. The mean is useful for getting a general sense, but it can be affected by very low or very high values.

平均入学分值是 13.1 分。这告诉我们，大学平均期望的成绩组合大致相当于 13 分——介于 A*AA 和 A*A*A 之间。平均数有助于得到一个整体印象，但它可能会受到极低或极高数值的影响。

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6. Finding the Median and Mode | 求中位数和众数

The median is the middle value when the data is arranged in order. Let’s list the total points from smallest to largest: 10, 12, 13, 13, 13, 13, 14, 14, 14, 15. With ten values, the median is the average of the 5th and 6th terms. Both are 13, so the median is (13 + 13) ÷ 2 = 13.

中位数是将数据按顺序排列后位于中间的数值。让我们把总分从小到大列出：10, 12, 13, 13, 13, 13, 14, 14, 14, 15。因为有十个数值，中位数是第 5 项和第 6 项的平均值。两者都是 13，所以中位数是 (13 + 13) ÷ 2 = 13。

The mode is the value that occurs most often. From the frequency table, 13 points appears four times, making it the mode. In this data set, the median and mode are the same, which suggests a good central cluster. Both are slightly below the mean of 13.1, because the mean is pulled upward by the high score of 15.

众数是出现次数最多的数值。从频数表可知，13 分出现了四次，所以它是众数。在这个数据集中，中位数和众数相同，这表明数据集中在中部。两者都略低于平均数 13.1，这是因为平均数被高分 15 稍微拉高了。

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7. Measuring Spread: Range | 度量分散程度：全距

The range tells us how spread out the data is. It is calculated by subtracting the smallest value from the largest value. Here, the highest total points value is 15 (Imperial) and the lowest is 10 (Leicester).

极差告诉我们数据的分散程度。它的计算方法是用最大值减去最小值。这里最高总分是 15（帝国理工），最低是 10（莱斯特）。

Range = 15 − 10 = 5 points

A range of 5 points means that the entry standards can differ noticeably. In terms of A-level grades, 5 points is about the difference between ABB and A*A*A*, which is a significant gap. The range helps students understand that not all universities demand the same level of achievement, even for the same degree subject.

极差为 5 分，意味着入学标准可能有明显差异。就 A-level 成绩而言，5 分大致相当于 ABB 和 A*A*A* 之间的差别，这个差距相当大。极差有助于学生理解，即使是同一个学位科目，不是所有大学都要求同样的成绩水平。

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8. Bar Chart Comparison of Universities | 大学录取要求的条形图比较

Drawing a bar chart is an excellent way to visualise the differences. On the horizontal axis we place the universities, and on the vertical axis we plot the total points. Each university gets a bar whose height equals its total tariff. For instance, Imperial’s bar reaches 15, while Leicester’s stops at 10. The three universities with 13 points would have bars of equal medium height.

绘制条形图是直观显示差异的好方法。在横轴上我们放置大学名称，在纵轴上标出总分数。每所大学对应一个条形，其高度等于它的总入学分值。例如，帝国理工的条形会达到 15，而莱斯特的止于 10。三所得分为 13 的大学的条形则具有相同的中等高度。

In a classroom setting, you would use squared paper or software to draw the chart accurately, ensuring the bars are of equal width and clearly labelled. From the chart, you could instantly pick out the most and least competitive universities for Mathematics, and see the overall distribution at a glance.

在课堂环境中，你会用方格纸或软件来精确绘制图表，确保条形宽度一致、标记清晰。从图表中可以立刻找出数学专业最具竞争力和最不具竞争力的大学，并一目了然地看到整体分布情况。

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9. Interpreting the Data: Which University Is Most Competitive? | 解读数据：哪所大学最具竞争力？

Based on our analysis, Imperial College London appears to be the most competitive, with a top score of 15 points (A*A*A*). The University of Leicester is the least competitive in this group, asking for 10 points (ABB

Published by TutorHao | KS3 统计 Revision Series | aleveler.com

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