📚 Year 7 SQA Statistics: Core Knowledge Review | Year 7 SQA 统计：核心知识点梳理
Statistics is all about collecting, organising, displaying and interpreting data to make sense of the world around us. For Year 7 students following the SQA curriculum, building a strong foundation in statistical concepts is essential. This article reviews the core topics you will encounter, including types of data, tally charts, frequency tables, a variety of graphs and key measures such as mean, median, mode and range. Each concept is explained with clear examples to help you understand and apply your skills confidently.
统计学是关于收集、整理、展示和解读数据，从而理解我们周围世界的一门学问。对于学习 SQA 课程的 Year 7 学生来说，打好统计学基础至关重要。本文梳理了你将学到的核心知识点，包括数据类型、计数符号、频数表、多种统计图表，以及均值、中位数、众数和范围等关键统计量。每个概念都配有清晰的例子，帮助你透彻理解并自信地运用这些技能。
1. Types of Data | 数据类型
Data can be split into two main categories: qualitative (or categorical) data and quantitative (or numerical) data. Qualitative data describes qualities or categories, such as eye colour, favourite subject or types of pet. Quantitative data consists of numbers that can be measured or counted, like height, shoe size or number of siblings.
数据可以分为两大类：定性（或分类）数据与定量（或数值）数据。定性数据描述的是性质或类别，例如眼睛颜色、最喜欢的学科或宠物种类。定量数据则是可以测量或计数的数字，比如身高、鞋码或兄弟姐妹的数量。
Quantitative data can be further divided into discrete data and continuous data. Discrete data can only take certain separate values – for example, the number of students in a class (you cannot have half a student). Continuous data can take any value within a given range, such as height, mass or time, which can be measured to different levels of precision.
定量数据还可以进一步细分为离散数据和连续数据。离散数据只能取某些分离开的数值，例如一个班级的学生人数（你不可能有半个学生）。连续数据则可以取某个范围内的任意值，比如身高、质量或时间，它们可以测量到不同的精度。
2. Collecting Data: Surveys and Tally Marks | 收集数据：调查与计数符号
When we want to collect original data, we often carry out a survey or an experiment. A survey might ask people about their preferences or habits. It is important to design questions that are clear, unbiased and easy to answer. For example, ‘What is your favourite sport?’ is a good open question, while a leading question like ‘Don’t you think football is the best sport?’ should be avoided.
当我们想要收集原始数据时，通常会进行调查或实验。调查可能会询问人们的偏好或习惯。设计清晰、无偏见且容易回答的问题非常重要。比如，“你最喜欢的运动是什么？”是一个好的开放性问题，而像“难道你不觉得足球是最好的运动吗？”这样的引导性问题则应避免。
Before numbers are organised into tables, we often use tally marks to record responses as they come in. A tally is a quick way of counting by drawing marks in groups of five – the fifth mark crosses the previous four. This makes counting up the totals much faster.
在把数字整理到表格之前，我们通常会用计数符号按顺序记录回答。计数是一种快速计数的办法，以五个为一组画记号——第五个记号画一条斜线穿过前面四个。这样能让统计总数快得多。
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A group of four vertical lines with a diagonal line through them represents 5. So a tally like |||| || represents 7, and |||| |||| ||| represents 13.
一组四条竖线加一条斜线穿过代表 5。因此，像 |||| || 这样的计数代表 7，而 |||| |||| ||| 代表 13。
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Tables with tally columns help you transfer data directly into frequency columns without making mistakes.
带有计数栏的表格可以帮助你准确无误地将数据直接填入频数栏。
3. Frequency Tables | 频数表
A frequency table is used to summarise data by showing how often each value or category occurs. Once you have finished tallying, you write the total as the frequency. A frequency table provides a neat overview and is often the first step before drawing a graph.
频数表用来总结数据，显示每个数值或类别出现的次数。当你完成计数后，就把总数作为频数写入表格。频数表提供了一个整洁的概览，通常是绘制图表前的第一步。
Consider a survey in which 30 students were asked their favourite colour. The results recorded as tallies and frequencies might look like this:
假设一项调查询问了 30 名学生最喜欢的颜色。用计数和频数记录的结果可能如下表所示：
| Colour | Tally | Frequency |
|---|---|---|
| Red | |||| || | 7 |
| Blue | |||| |||| | 10 |
| Green | |||| | 4 |
| Yellow | |||| | | 6 |
| Other | ||| | 3 |
From this table you can quickly see that blue is the most popular colour and that ‘Other’ was chosen only three times.
从这个表格你可以快速看出蓝色是最受欢迎的颜色，而“其他”只被选了三次。
4. Bar Charts | 条形图
A bar chart displays categorical data with rectangular bars. The height of each bar represents the frequency for that category. The bars should be of equal width and should not touch each other, because the categories are separate.
条形图用矩形条展示分类数据。每个条形的高度代表对应类别的频数。这些条形的宽度应当相等且彼此不相连，因为各个类别是分开的。
When drawing a bar chart, always label both axes clearly. The horizontal axis shows the categories, while the vertical axis shows the frequency. Make sure the scale on the vertical axis is even and starts from zero, so that the heights are not misleading.
绘制条形图时，一定要清楚地标明两条坐标轴。横轴显示类别，纵轴显示频数。确保纵轴的刻度均匀且从零开始，这样条形的高度才不会产生误导。
Bar charts can also be drawn horizontally, especially when category names are long. In all cases, the length of the bar is proportional to the frequency.
条形图也可以水平绘制，特别是当类别名称很长的时候。无论哪种情况，条形的长度都与频数成正比。
5. Pictograms | 象形图
A pictogram uses small pictures or symbols to represent data. Each symbol stands for a certain number of items. Pictograms are eye-catching and give a quick visual impression, but you must always include a key to explain what each symbol represents.
象形图使用小图画或符号来表示数据。每个符号代表一定数量的项目。象形图非常醒目，能快速传递视觉印象，但你一定别忘了加上图例，说明每个符号代表多少项目。
For example, if you were showing the number of books read by five friends, you might use one book symbol to represent 2 books. To show 7 books, you would draw three and a half books. The key must say: 1 symbol = 2 books.
例如，如果你要展示五个朋友阅读的书籍数量，你可以用一个书本符号代表 2 本书。而要表示 7 本书，你就要画三个半书本符号。图例必须写明：1 个符号 = 2 本书。
When interpreting pictograms, be careful with partial symbols. Often, a half symbol or a quarter symbol is used to show values that are not multiples of the unit chosen.
解读象形图时，要当心不完整的符号。通常会使用半个或四分之一个符号来表示不是所选单位倍数的数值。
6. Line Graphs | 折线图
Line graphs are used to display data that changes over time or shows a trend. Points are plotted to represent individual data pairs, and these points are joined by straight line segments. The horizontal axis usually shows time, and the vertical axis shows the measured quantity, such as temperature or distance.
折线图用来展示随时间变化或呈现某种趋势的数据。首先标出代表各个数据对的点，然后用直线段把这些点连接起来。横轴通常表示时间，纵轴表示测量的数量，比如温度或距离。
When drawing a line graph, it is important to choose sensible scales so that the graph makes good use of the space and the trend is easy to see. Always plot the points carefully and then connect them in order.
绘制折线图时，选择合理的刻度很重要，这样既能充分利用图表空间，又能让趋势易于观察。一定要仔细标出数据点，然后按顺序连接它们。
Line graphs can help you spot increases, decreases and periods where the value stays the same. They are often used in science experiments and in displaying weather data.
折线图能帮助你发现上升、下降以及数值保持不变的阶段。它们常用于科学实验和天气数据的展示。
7. Pie Charts | 饼状图
A pie chart is a circular diagram divided into sectors. Each sector represents a category, and its angle (or area) is proportional to the frequency of that category. Pie charts are excellent for showing how a whole is divided into parts, and for comparing proportions at a glance.
饼状图是一个被分成多个扇区的圆形图。每个扇区代表一个类别，其圆心角（或面积）与该类别的频数成正比。饼状图非常适合展示一个整体如何被划分成若干部分，并让人一眼就能比较各部分的比例。
To construct a pie chart, you first calculate the total frequency. Then, for each category, you compute the sector angle using the formula: Sector angle = (Frequency of category / Total frequency) × 360°. Here is a simple calculation:
要绘制饼状图，首先计算总频数。然后，对每个类别，用下面的公式计算扇区角度：扇区角度 = (该类别的频数 / 总频数) × 360°。下面是一个简单的计算：
Sector angle = (Category frequency ÷ Total frequency) × 360°
For instance, if 20 students were asked their favourite season and 8 chose Spring, the sector for Spring would be (8 ÷ 20) × 360° = 144°. You then draw the sectors using a protractor and label them clearly.
例如，如果调查了 20 名学生最喜欢的季节，有 8 人选择了春季，那么春季的扇区角度为 (8 ÷ 20) × 360° = 144°。然后你用量角器画出扇区并清楚地标示出来。
8. Mode: The Most Frequent Value | 众数：出现最频繁的值
The mode is the value that appears most often in a data set. It is a measure of central tendency that is especially useful for categorical data. A set of data can have one mode, more than one mode, or no mode at all if all values occur equally often.
众数是数据集中出现最频繁的值。它是一种集中趋势的度量，对分类数据尤其有用。一组数据可以有一个众数、多个众数，或者没有众数（如果所有数值出现的次数相同）。
For example, in the list 2, 3, 5, 3, 8, 3, the mode is 3 because it occurs three times. In the list 1, 4, 6, 4, 6, the modes are 4 and 6 – this is called bimodal. In the list 9, 7, 3, 5, every number appears once, so there is no mode.
例如，在数列 2, 3, 5, 3, 8, 3 中，众数是 3，因为它出现了三次。在数列 1, 4, 6, 4, 6 中，众数是 4 和 6，这称为双众数。在数列 9, 7, 3, 5 中，每个数字都只出现一次，因此没有众数。
9. Median: The Middle Value | 中位数：中间值
The median is the middle number in an ordered set of data. To find the median, you first arrange all numbers from smallest to largest. If there is an odd number of data values, the median is the exact middle one. If there is an even number, the median is the mean of the two middle numbers.
中位数是一组有序数据中间的那个数。要找到中位数，你需要先把所有数字从小到大排列。如果有奇数个数据值，中位数就是正中间的那一个。如果有偶数个，中位数则是中间两个数的平均数。
Take the data set: 12, 7, 9, 20, 4. First, order it: 4, 7, 9, 12, 20. The middle number is 9, so the median is 9. For an even set like 3, 8, 2, 6, order to get 2, 3, 6, 8. The two middle numbers are 3 and 6; the median is (3 + 6) ÷ 2 = 4.5.
以数据集 12, 7, 9, 20, 4 为例。首先排序：4, 7, 9, 12, 20。中间的数是 9，所以中位数是 9。对于偶数个的数据集，如 3, 8, 2, 6，排序得 2, 3, 6, 8。中间的两个数是 3 和 6，中位数是 (3 + 6) ÷ 2 = 4.5。
The median is not affected by extremely high or low values, making it a good average to use when data contains outliers.
中位数不受极端高值或低值的影响，因此当数据包含异常值时，它是一个很好的平均数选择。
10. Mean: The Average | 均值：平均数
The mean is what most people think of as the ‘average’. It is calculated by adding up all the data values and then dividing the total by the number of values. The mean takes every piece of data into account, which makes it very useful but also sensitive to outliers.
均值就是大多数人所说的“平均数”。它的计算方法是把所有数据值加起来，再将总和除以数据的个数。均值考虑了每一个数据，这使其非常有用，但也容易受到异常值的影响。
The formula for the mean can be written as:
均值的计算公式可以写成：
Mean = (Sum of all data values) ÷ (Number of data values)
For the numbers 5, 8, 12, 4, and 6, the sum is 5 + 8 + 12 + 4 + 6 = 35. There are 5 values, so the mean is 35 ÷ 5 = 7.
对于数字 5, 8, 12, 4 和 6，总和是 5 + 8 + 12 + 4 + 6 = 35。有 5 个数值，因此均值是 35 ÷ 5 = 7。
In everyday situations, the mean is used to find average scores, temperatures or prices. Always check your answer to see if it makes sense in the context of the data.
在日常生活中，均值被用来计算平均分数、平均温度或平均价格。得出答案后，一定要检查它是否在数据背景下有意义。
11. Range: Spread of Data | 范围：数据的离散程度
The range measures how spread out a set of data is. It is simply the difference between the largest value and the smallest value. A larger range indicates that the data are more spread out, while a smaller range shows that the values are more consistent.
范围衡量一组数据的分散程度。它就是最大值与最小值之间的差。范围越大说明数据越分散，范围越小则说明数值越集中。
Range = Largest value – Smallest value
Range = Maximum value − Minimum value
Given the set 4, 7, 1, 9, 3, the largest value is 9, the smallest is 1, so the range is 9 − 1 = 8. The range tells you at a glance how much the numbers vary, but it does not give any information about the values in between.
给定数据集 4, 7, 1, 9, 3，最大值是 9，最小值是 1，所以范围是 9 − 1 = 8。范围能让你一眼看出这些数字的变动幅度，但它不提供中间数值的任何信息。
12. Interpreting Graphs and Comparing Data | 解释图表和比较数据
Being able to read and interpret different graphs is just as important as being able to draw them. When you look at a bar chart, line graph or pie chart, you should be able to identify the highest and lowest frequencies, spot trends, and compare categories or time periods.
能够阅读和解读不同的图表与能够绘制它们同等重要。当你查看条形图、折线图或饼状图时，你应该能够找出最高和最低的频数，发现趋势，并比较不同的类别或时间段。
When comparing two sets of data, it is helpful to calculate and compare their averages and ranges. For example, two classes could have the same mean score on a test, but one class might have a much larger range, meaning the scores are less consistent. The median can also give a better picture if the data are skewed.
在比较两组数据时，计算和比较它们的平均数和范围会很有帮助。例如，两个班级在一次测验中的平均分可能相同，但其中一个班级的分数范围要大得多，这意味着成绩不太稳定。如果数据是偏态的，使用中位数可能会更有代表性。
Always read the title and labels on a graph, and pay attention to the scale used. A scale that does not start at zero or that uses different intervals can sometimes make differences look larger or smaller than they really are.
阅读图表时一定要看标题和标签，并注意所用的刻度。一个不是从零开始的刻度或用了不同间隔的刻度，有时会让差异显得比实际情况更大或更小。
Published by TutorHao | Statistics Revision Series | aleveler.com
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