📚 Year 7 Cambridge Statistics: Comparing UK University Entry Requirements | 英国大学申请要求对照
Statistics is a powerful tool that helps us make sense of data. In everyday life, we use statistics to compare options, spot trends and make informed decisions. One practical example is comparing the entry requirements of different UK universities. By collecting and analysing admission data, students can better understand what grades they need and how universities differ. This topic introduces you to key Year 7 statistical skills – collecting data, making frequency tables, drawing bar charts and calculating averages and range – all through the lens of real university offers.
统计学是一种强大的工具，能帮助我们理解数据。在日常生活中，我们用统计学来比较各种选项、发现趋势并做出明智的决定。一个实际的例子是比较不同英国大学的入学要求。通过收集和分析录取数据，学生可以更好地了解他们需要什么样的成绩，以及各大学之间的差异。本主题将通过真实的大学录取数据，向你介绍英国7年级统计的关键技能——收集数据、制作频率表、绘制柱状图以及计算平均数和范围。
1. Understanding Statistics | 认识统计
Statistics is the science of collecting, organising, presenting and interpreting data. In Year 7, you will learn how to gather information, summarise it in tables and graphs, and use measures such as the mean, median, mode and range to describe the data. These skills are not just for exams – they are used by universities, employers and researchers every day.
统计学是收集、整理、展示和解读数据的科学。在7年级，你将学习如何收集信息，用表格和图表进行总结，并使用平均数、中位数、众数和范围等度量来描述数据。这些技能不仅仅用于考试——大学、雇主和研究人员每天都在使用它们。
2. Collecting University Entry Data | 收集大学申请数据
To compare UK university entry requirements, we first gathered the typical A-level offers for popular courses at ten well-known universities. Since A-level grades come as letters, we converted each offer into a numerical UCAS tariff point total: A* = 56, A = 48, B = 40, C = 32, D = 24, E = 16. This gives us a consistent set of numbers to analyse. The table below shows our data set.
为了比较英国大学的入学要求，我们首先收集了十所知名大学热门课程的典型A-level录取条件。因为A-level成绩是用字母表示的，我们将每个录取条件转换为数值型的UCAS积分总和：A* = 56分，A = 48分，B = 40分，C = 32分，D = 24分，E = 16分。这样我们就得到了一组可以用统计方法分析的数字。下表展示了我们的数据集。
| University | Typical A-level Offer | UCAS Tariff Points |
|---|---|---|
| University of Oxford | A*A*A | 160 |
| University of Cambridge | A*A*A | 160 |
| Imperial College London | A*AA | 152 |
| University College London (UCL) | A*AA | 152 |
| London School of Economics (LSE) | A*AA | 152 |
| University of Warwick | A*AA | 152 |
| University of Edinburgh | AAA | 144 |
| University of Manchester | A*AA | 152 |
| University of Leeds | AAB | 136 |
| University of Liverpool | ABB | 128 |
These tariff points now form our raw data set for statistical analysis. Notice that several universities share the same point value; this grouping will be useful when we look at frequency and the mode later.
这些关税积分现在构成了我们用于统计分析的原始数据集。注意，有几所大学的积分值是相同的；这种分组在我们后面研究频率和众数时会很有用。
3. Organising Data: Frequency Table | 整理数据：频率表
A frequency table helps us see how often each tariff point value appears. We list the distinct point values, make a tally of each occurrence and then count the tally marks to give the frequency. The table below organises our university offer data.
频率表可以让我们看清每个积分值出现了多少次。我们列出不同的积分值，用划记符号记录每次出现，然后数出划记的个数得到频数。下面的表格整理了我们的大学录取数据。
| Tariff Points | Tally | Frequency |
|---|---|---|
| 128 | I | 1 |
| 136 | I | 1 |
| 144 | I | 1 |
| 152 | IIII | 5 |
| 160 | II | 2 |
From the frequency table, we can immediately see that 152 points is the most common requirement, while the highest and lowest values appear less frequently. This summary will make it easy to build a bar chart and compute statistics.
从频率表中我们立刻可以看出，152分是最常见的录取要求，而最高分和最低分出现的次数较少。有了这个汇总表，我们就能轻松地绘制柱状图并计算统计量。
4. Visualising Data: Bar Chart | 数据可视化：柱状图
A bar chart is a great way to visualise the distribution of entry requirements. On the horizontal axis we place the tariff points (128, 136, 144, 152, 160), and on the vertical axis we show the frequency. Each category gets a bar whose height equals its frequency. For our data, the bar for 152 would be the tallest (height 5), while the bars for 128, 136 and 144 would each have height 1. The bars for 160 would reach height 2. Drawing this chart helps us quickly compare how many universities demand each points level.
柱状图是可视化入学要求分布的好方法。我们在横轴上标出积分值（128、136、144、152、160），在纵轴上表示频数。每个类别对应一个柱子，其高度等于该类的频数。对于我们的数据，152 分的柱子会是最高的（高度 5），而 128、136 和 144 分的柱子高度为 1。160 分的柱子高度为 2。画出这个图可以帮助我们快速比较有多少所大学要求每个分数水平。
To construct the bar chart yourself, you would draw and label the axes, choose a suitable scale (for example, 1 cm per university on the vertical axis), and then draw bars of equal width for each point value. Remember to leave gaps between the bars, because the categories are distinct and not part of a continuous scale.
要自己画出柱状图，你需要画出坐标轴并标上标签，选择合适的比例（例如纵轴上每厘米代表 1 所大学），然后为每个分数值画出宽度相等的柱子。记住柱与柱之间要留空隙，因为这些类别是不连续的，不像连续的尺子刻度。
5. Measure of Central Tendency: Mean | 集中趋势度量：平均数
The mean (often called the average) gives us a typical tariff point value for the whole group of universities. To find the mean, we add together all the tariff points and then divide by the total number of universities.
平均数（通常被称为平均值）可以告诉我们这组大学的一个典型入学积分值。要计算平均数，我们需要把所有大学的积分加起来，然后除以大学的总数。
The sum of all tariff points is: 160 + 160 + 152 + 152 + 152 + 152 + 144 + 152 + 136 + 128 = 1488. There are 10 universities, so we divide the total by 10.
所有积分值的总和是：160 + 160 + 152 + 152 + 152 + 152 + 144 + 152 + 136 + 128 = 1488。一共有 10 所大学，所以我们将总和除以 10。
Mean = 1488 ÷ 10 = 148.8
The mean UCAS tariff requirement for this group of universities is 148.8 points. This value sits slightly below the most common offer of 152, because the lower requirements from Leeds and Liverpool pull the mean downwards.
这组大学的平均 UCAS 积分要求是 148.8 分。这个值略低于最常见的 152 分，因为利兹大学和利物浦大学较低的要求拉低了平均数。
6. Finding the Median | 找中位数
The median is the middle value when all data points are arranged in order from smallest to largest. It is another useful average that is not influenced by very high or very low extremes.
中位数是将所有数据点从小到大排列后位于中间位置的数值。这是另一种有用的平均数，它不受极高或极低极端值的影响。
We first sort the 10 tariff points: 128, 136, 144, 152, 152, 152, 152, 152, 160, 160. Since there is an even number of values (10), the median is the mean of the 5th and 6th values. The 5th value is 152 and the 6th value is also 152.
我们先将 10 个积分值排序：128、136、144、152、152、152、152、152、160、160。因为数值的个数是偶数（10 个），中位数是第 5 个和第 6 个数值的平均数。第 5 个数值是 152，第 6 个数值也是 152。
Median = (152 + 152) ÷ 2 = 152
The median offer of 152 points confirms that half the universities require 152 or less, and half require 152 or more. Here the median equals the most frequent value, which is a helpful coincidence.
中位数 152 分表明，有一半的大学要求 152 分或以下，另一半要求 152 分或以上。这里中位数正好等于最常见的值，这是一个有用的巧合。
7. Identifying the Mode | 找众数
The mode is the data value that appears most often. It is especially useful for categorical or discrete data like university tariff points, because it shows the most typical requirement that a student may encounter.
众数是出现次数最多的数据值。对于像大学积分这种离散数据，众数尤其有用，因为它揭示了学生最可能遇到的典型录取要求。
Looking back at our frequency table, the tariff point 152 appears five times, more than any other value. Therefore, the mode is 152 points. This makes sense because five out of the ten universities in our list (Imperial, UCL, LSE, Warwick and Manchester) all ask for A*AA, which is a very common top offer.
回顾我们的频率表，152 分出现了五次，比任何其他值都多。因此，众数是 152 分。这很合理，因为我们列表中的十所大学里有五所（帝国理工、UCL、LSE、华威和曼彻斯特）都要求 A*AA，这是一个非常常见的高要求组合。
If two values tied for the highest frequency, the data set would be called ‘bimodal’. In our case, there is a clear single mode.
如果两个数值的最高频数相同，这个数据集就被称为“双众数”。在我们的例子中，有一个明确的单一众数。
8. Measure of Spread: Range | 离散度量：范围
The range tells us how spread out the data are. It is calculated by subtracting the smallest value from the largest value. A large range indicates a wide variation in university requirements, while a small range would mean the offers are very similar.
范围告诉我们数据的离散程度。它通过用最大值减去最小值来计算。范围大表明大学的入学要求差异很大，而范围小则意味着录取条件非常相似。
Our smallest tariff point value is 128 (Liverpool) and the largest is 160 (Oxford and Cambridge).
我们数据集中的最小积分值是 128（利物浦大学），最大是 160（牛津大学和剑桥大学）。
Range = 160 – 128 = 32
The range of 32 points shows that there is a noticeable
Published by TutorHao | Year 7 统计 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）