📚 Year 7 Cambridge Statistics: Core Concepts Review | Year 7 剑桥统计：核心知识点梳理
Statistics helps us make sense of the world by turning raw numbers into clear pictures and useful summaries. In Year 7 Cambridge Mathematics, you learn the core skills of collecting, displaying and interpreting data. This article revisits all the key ideas you need to master, from types of data to averages and range, giving you a solid foundation for future studies.
统计学通过将原始数字转化为清晰的图表和有用的总结，帮助我们理解世界。在 Year 7 剑桥数学课程中，你将学习收集、展示和解读数据的基本技能。本文回顾所有你需要掌握的核心概念，从数据类型到平均数和极差，为今后的学习打下坚实基础。
1. What is Statistics? | 什么是统计？
Statistics is the science of collecting, organising, presenting, analysing and interpreting data. It allows us to answer questions, spot trends and make informed decisions in everyday life, from weather forecasts to sports performance.
统计学是一门收集、整理、展示、分析和解释数据的科学。它让我们能够回答问题、发现趋势并做出明智的决策，无论是天气预报还是体育表现分析，都离不开统计。
In Year 7, you focus on small data sets that you can manage by hand. The aim is to understand how data is handled honestly and how to draw sensible conclusions without being misled by charts or numbers.
在 Year 7，你主要处理可以手工管理的小型数据集。目的是理解如何诚实地处理数据，以及如何得出合理的结论而不被图表或数字误导。
2. Types of Data | 数据类型
Data can be qualitative or quantitative. Qualitative data describes qualities or categories that cannot be measured with numbers, such as favourite colour, eye colour or type of pet.
数据可以分为定性数据和定量数据。定性数据描述无法用数字测量的性质或类别，例如最喜欢的颜色、眼睛颜色或宠物种类。
Quantitative data consists of numerical values that can be counted or measured. Quantitative data is further split into discrete data, which can only take certain fixed values (like the number of students in a class), and continuous data, which can take any value within a range (like height or temperature).
定量数据由可计数或可测量的数值组成。定量数据又分为离散数据和连续数据。离散数据只能取某些固定的值（如班级学生人数），连续数据可以在一个范围内取任意值（如身高或温度）。
Recognising the type of data is the first step in choosing the right chart and the most suitable average later.
识别数据类型是之后选择合适图表和适当平均数的第一步。
3. Collecting Data | 收集数据
Data can be collected through surveys, questionnaires, observations or experiments. A well-designed data collection sheet or tally chart helps you record information systematically and avoid mistakes.
数据可以通过调查、问卷、观察或实验来收集。一张设计良好的数据记录表或计数表可以帮助你有条理地记录信息，避免错误。
When designing a questionnaire, questions should be clear, unbiased and easy to answer. For example, asking 'How many hours of sport do you do each week?' is better than a vague 'Do you like sport?' because the first gives quantitative data that is much easier to analyse.
在设计问卷时，问题应当清晰、无偏向且容易回答。例如，问“你每周运动多少小时？”比含糊地问“你喜欢运动吗？”更好，因为前者能得到更容易分析的定量数据。
In Year 7, you usually work with primary data you have collected yourself or secondary data from newspapers and books. Understanding where data comes from is essential for judging how reliable it is.
在 Year 7，你通常使用自己收集的一手数据或来自报纸和书籍的二手数据。了解数据的来源对于判断其可靠性至关重要。
4. Frequency Tables | 频数表
A frequency table lists each data value or category and shows how many times it occurs (its frequency). Tally marks are commonly used to count while collecting data, with every fifth mark drawn diagonally to make groups of five easy to count.
频数表列出每个数据值或类别，并显示它出现的次数（即频数）。在收集数据时通常使用计数符号，每第五个标记画成斜线，以便五个一组计数。
For example, a survey of favourite fruits might produce a frequency table with 'Apple' having tally marks |||| || for a frequency of 7, and 'Banana' having ||| for a frequency of 3. A frequency table quickly organises raw data so you can see patterns and calculate totals.
例如，一项关于最喜欢水果的调查可能产生一张频数表，其中“苹果”的计数符号为 |||| ||，表示频数为 7，“香蕉”为 |||，频数为 3。频数表能快速整理原始数据，让你看到规律并计算总数。
Frequency tables can also be used to construct grouped frequency tables for continuous data, though in Year 7 you mostly work with ungrouped discrete data.
频数表也可用于为连续数据构建分组频数表，不过在 Year 7 你主要处理不分组的离散数据。
5. Bar Charts | 条形图
A bar chart displays categorical data with rectangular bars. The height or length of each bar represents the frequency of that category. Bars must be of equal width and there should be equal gaps between them to show that the categories are separate.
条形图用矩形长条展示分类数据。每个长条的高度或长度代表该类别的频数。长条必须等宽，且长条之间应有相等的间距，以表明类别是分开的。
You label each axis clearly: the horizontal axis shows the categories, and the vertical axis shows the frequency. The scale on the vertical axis must start at zero and increase in equal steps, or the chart can become misleading.
你需要清晰地标记每个坐标轴：横轴显示类别，纵轴显示频数。纵轴的刻度必须从零开始并以等步长增加，否则图表可能会产生误导。
Bar charts make it easy to compare frequencies at a glance. For instance, a bar chart of pet ownership shows immediately which pet is most and least popular.
条形图能够让人一目了然地比较频数。例如，宠物拥有情况的条形图能立即显示哪种宠物最受欢迎、哪种最不受欢迎。
6. Pictograms | 象形图
o tell the reader what each symbol stands for, for example one book symbol = 5 books read.
象形图使用小图片或符号来代表一定数量的项目。图例是必不可少的，它告诉读者每个符号代表什么，例如一个书本符号 = 5 本已读书籍。
When drawing a pictogram, symbols must be the same size and spaced evenly. If a frequency is not an exact multiple of the key value, you may show a part of a symbol, like half a book to represent 2.5 books rounded appropriately.
绘制象形图时，符号必须大小相同且均匀排列。如果某个频数不是图例数值的整数倍，你可以展示部分符号，比如用半个书本符号代表适当取整后的 2.5 本书。
Pictograms are visually appealing and useful for making data more engaging, but they can be less precise than bar charts when exact comparisons are needed.
象形图在视觉上很有吸引力，有助于让数据更生动有趣，但在需要精确比较时，它的精度可能不如条形图。
7. Line Graphs | 折线图
A line graph is used to show how a quantity changes over time or across ordered categories. Data points are plotted and connected with straight line segments to reveal trends.
折线图用于显示一个量随时间或有序类别的变化。将数据点描出并用直线段连接起来，以揭示变化趋势。
The horizontal axis usually represents time (such as days, months or years), and the vertical axis represents the variable being measured. You must choose a sensible scale that spreads the data across the graph and makes trends visible.
横轴通常表示时间（如天、月或年），纵轴表示被测量的变量。你需要选择合理的刻度，让数据点分布在图上，使趋势清晰可见。
For example, a line graph of daily maximum temperature over a week can show whether the weather is warming or cooling. Line graphs are not suitable for categorical data that has no natural order.
例如，一周内每日最高气温的折线图可以显示天气是在变暖还是变冷。折线图不适合用于没有自然顺序的分类数据。
8. Pie Charts | 饼图
A pie chart displays data as sectors of a circle, where each sector represents a category' size of each sector is determined by its angle, calculated as (frequency / total) × 360°.
饼图将数据展示为圆中的扇形，每个扇形代表一个类别在整体中所占的比例。每个扇形的大小由其角度决定，计算公式为 (频数 ÷ 总数) × 360°。
Pie charts are excellent for showing relative shares, such as how a budget is split or the composition of a class by eye colour. All sectors together must add up to 360°, and percentages can be added to help interpretation.
饼图非常适合于展示相对份额，例如预算如何分配，或按眼睛颜色划分的班级构成。所有扇形加起来必须等于 360°，并且可以加上百分比以帮助理解。
In Year 7, you learn to draw simple pie charts using a protractor and compass, and to interpret given charts by working backwards from angles to frequencies.
在 Year 7，你将学习使用量角器和圆规绘制简单的饼图，并学会通过从角度反推频数来解读给定的饼图。
9. Mean (Average) | 平均数
The mean is the most common measure of average. It is calculated by adding up all the data values and then dividing by the number of values.
Mean = (sum of all values) ÷ (number of values)
平均数是衡量集中趋势最常用的指标。计算方法是：将所有数据值相加，再除以数据的个数。
平均数 = 所有数值之和 ÷ 数值个数
The mean gives a single number that represents the entire data set. However, it can be heavily influenced by unusually large or small values, called outliers. If a data set contains an outlier, the mean might not give a typical picture.
平均数是一个能代表整个数据集的单一数值。但它可能受到异常大或异常小的值（即离群值）的严重影响。如果数据集中含有离群值，平均数可能无法反映典型情况。
10. Median | 中位数
The median is the middle value when the data is arranged in order from smallest to largest. For an odd number of values, the median is the exact middle value. For an even number of values, it is the mean of the two middle values.
中位数是将数据从小到大排列后位于中间的值。如果数据个数为奇数，中位数就是正中间的那个值；如果数据个数为偶数，则中位数是中间两个数的平均数。
s not affected by outliers, so it often describes the typical value better when data is skewed.
例如，在数据集 2, 3, 5, 7, 8 中，中位数是 5。在数据集 2, 3, 5, 7, 8, 10 中，中位数是 (5 + 7) ÷ 2 = 6。中位数不受离群值影响，因此当数据分布偏斜时，它通常能更好地描述典型值。
11. Mode | 众数
The mode is the value that appears most often in a data set. There can be one mode, more than one mode (bimodal or multimodal), or no mode at all if all values occur with the same frequency.
众数是数据集中出现次数最多的值。可以有一个众数、多个众数（双众数或多众数），或者如果所有值出现次数相同，则没有众数。
The mode is the only measure of average that can be used for qualitative data, such as finding the most common favourite colour. It is easy to spot from a frequency table or bar chart.
众数是唯一可以用于定性数据的平均数指标，例如找出最常见的最喜欢的颜色。它很容易从频数表或条形图中发现。
12. Range | 极差
The range is a simple measure of how spread out the data is. It is calculated by subtracting the smallest value from the largest value.
Range = largest value – smallest value
极差是衡量数据分散程度的一种简单指标。计算方法是用最大值减去最小值。
极差 = 最大值 – 最小值
A larger range indicates that the data values are more spread out, while a smaller range suggests they are closely bunched together. Used alongside the mean or median, the range helps describe the consistency of a data set.
极差较大表明数据值更加分散，极差较小则表明数据值紧密聚集。与平均数或中位数一起使用时，极差有助于描述数据集的一致性。
Published by TutorHao | Statistics Revision Series | aleveler.com
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