📚 Year 7 AQA Statistics: Formula & Theorem Quick Reference | 7年级AQA统计：公式定理速查手册
This quick reference handbook covers all the essential formulas, key concepts, and definitions for Year 7 Statistics following the AQA framework. It brings together data handling, averages, charts, and probability into one handy revision guide.
本速查手册涵盖了AQA体系下7年级统计所需的所有基本公式、关键概念和定义，将数据处理、平均数、图表和概率总结成一本便捷的复习指南。
1. Types of Data and Data Collection | 数据类型与数据收集
Discrete data can only take certain values. You get discrete data by counting things, such as the number of pets or shoe sizes.
离散数据只能取特定的值。通过计数获得离散数据，比如宠物数量或鞋码。
Continuous data can take any value in a range. You get continuous data by measuring, for example height, mass or temperature.
连续数据可以取某个范围内的任何值。通过测量获得连续数据，比如身高、质量或温度。
Primary data is data you collect yourself for a specific purpose. Secondary data is data collected by someone else for another reason, like information from a book or website.
一手数据是为特定目的自己收集的数据。二手数据是别人为其他原因收集的数据，比如来自书籍或网站的信息。
When designing a questionnaire, keep questions short and clear. Avoid leading questions that push people towards a particular answer.
设计问卷时，问题要简短清晰。避免引导性问题，不要把人推向某个特定答案。
2. Frequency Tables and Cumulative Frequency | 频数表与累积频数
A frequency table shows how many times each data value occurs. Tally marks help you count before you write the frequency.
频数表显示每个数据值出现了多少次。划记符号帮助你在写下频数之前进行计数。
Cumulative frequency is the running total of frequencies. Add each frequency to the sum of the previous ones to find the cumulative frequency.
累积频数是频数的累加总和。把每个频数加到之前所有频数的和上，就得到累积频数。
You can use cumulative frequency to find how many values are below, or above, a certain point in a data set.
你可以使用累积频数找出数据集中有多少个值低于或高于某个特定点。
3. Pictograms and Bar Charts | 象形图与条形图
A pictogram uses a small picture or symbol to represent a certain number of items. You must include a key that shows what one picture stands for.
象形图使用小图片或符号来代表一定数量的物体。必须包含图例说明一个图片代表多少。
A bar chart shows data using bars of equal width. The bars do not touch each other, and the height of each bar matches its frequency.
条形图用等宽的条形表示数据。条形之间不接触，每个条形的高度与它的频数相匹配。
A dual bar chart compares two related sets of data. Draw two bars side by side for each category, using a key to show which colour belongs to which set.
双重条形图用于比较两组相关联的数据。每个类别旁边并列绘制两个条形，并用图例说明每种颜色属于哪一组数据。
4. Pie Charts | 饼图
A pie chart shows proportions of a whole. The size of each sector is proportional to the frequency of the data it represents.
饼图显示整体中各部分的比例。每个扇区的大小与其所代表数据的频数成正比。
Sector angle = (Frequency of category ÷ Total frequency) × 360°
扇区角度 = (类别频数 ÷ 总频数) × 360°
Follow these four steps: find the total frequency; calculate the angle for each category using the formula; draw a circle and draw the first radius; then use a protractor to measure and draw each sector.
遵循四个步骤：求出总频数；用公式计算每个类别的角度；画一个圆并画出第一条半径；然后用量角器量出并画出每个扇区。
Always label each sector of the pie chart clearly so that the reader can see what each slice represents.
始终清晰地标注饼图的每个扇区，让读者能看出每一块代表什么。
5. Stem and Leaf Diagrams | 茎叶图
A stem and leaf diagram keeps all original data values while showing their distribution. The stem represents the leading digit, and the leaf shows the final digit.
茎叶图保留了所有原始数据值，同时展示它们的分布。茎代表前导数字，叶代表最后一位数字。
To create a stem and leaf diagram, first split each number into a stem and a leaf. Write the stems in a vertical column and draw a vertical line. Then write the leaves in order next to their stem, and always provide a key.
制作茎叶图时，首先把每个数拆分成茎和叶。将茎写在垂直列中，画一条竖线。然后按大小顺序将叶子写在对应茎的旁边，并一定要给出图例说明。
From an ordered stem and leaf diagram you can easily read off the median, mode and range. The median is the middle value when the leaves are listed in order.
从一个有序的茎叶图中，你可以轻松读取中位数、众数和极差。当叶子按顺序列出时，中位数是中间的数值。
6. Mean, Median, Mode and Range | 均值、中位数、众数和极差
The mean is the average you get by sharing the total equally. It is sometimes called the arithmetic mean.
均值是把总数平均分配后得到的平均数，有时也叫算术平均值。
Mean = Sum of all data values ÷ Number of data values
均值 = 所有数据值之和 ÷ 数据值的个数
The median is the middle number when the data is sorted in order. If there are two middle numbers, the median is the mean of those two numbers.
中位数是将数据按顺序排列后的中间数。如果有两个中间数，中位数是这两个数的平均数。
The mode is the data value that appears most often. There can be one mode, no mode, or more than one mode.
众数是出现次数最多的数据值。可以有一个众数、没有众数或多个众数。
The range measures how spread out the data is. A small range means the data are close together, and a large range means they are spread out.
极差衡量数据的分散程度。极差小表示数据比较集中，极差大表示数据比较分散。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
7. Mean from a Frequency Table | 频数表求均值
When data is in a frequency table, you can find the mean without listing every value. Multiply each value by its frequency, add these products, then divide by the total frequency.
当数据以频数表形式呈现时，无需列出每个值也能求出均值。将每个值乘以其频数，把这些积相加，再除以总频数。
Mean = Σ(f × x) ÷ Σf
均值 = Σ(f × x) ÷ Σf
In this formula, f stands for frequency and x stands for the data value. The symbol Σ means ‘the sum of’.
在这个公式中，f 代表频数，x 代表数据值。符号 Σ 表示“……的总和”。
Always add a third column to your table labelled ‘f × x’ to help you organize the multiplication and addition.
始终在表格中添加第三列并标注为 ‘f × x’，帮助你有条理地进行乘法和加法运算。
8. Line Graphs and Time Series | 折线图与时间序列
A line graph shows how data changes over a period of time. Plot each point and join them with straight line segments. The horizontal axis usually represents time.
折线图显示数据在一段时间内如何变化。描出每个点并用直线线段连接起来。横轴通常代表时间。
A time series is a sequence of data measured at regular time intervals, like every hour or every day. You can use it to spot upward or downward trends.
时间序列是以固定时间间隔（如每小时或每天）测量的一系列数据。你可以用它来发现上升或下降趋势。
Sometimes you can see seasonal patterns in a time series, for example ice cream sales increasing in summer months. Use a time series graph to visualize these changes.
有时候可以在时间序列中看到季节性模式，比如冰淇淋销量在夏季月份上升。使用时间序列图使这些变化可视化。
9. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph plots paired data on two axes. Each point shows the values of two related variables, such as height and arm span.
散点图在两个轴上绘制成对的数据。每个点显示两个相关变量的值，比如身高和臂展。
Correlation describes the relationship between the two variables. If one goes up while the other also goes up, there is positive correlation. If one goes up while the other goes down, there is negative correlation.
相关性描述两个变量之间的关系。如果一个上升另一个也上升，就是正相关。如果一个上升而另一个下降，就是负相关。
If points are scattered with no clear pattern, there is no correlation. An outlier is a point that lies far away from the general pattern of the other points.
如果点分布散乱没有明显规律，就是没有相关性。异常值是远离其他点分布规律的某个点。
A line of best fit can be drawn through the points to show the trend. Even if not all points lie exactly on the line, the line should follow the general direction.
可以在这些点之间画一条最佳拟合线来显示趋势。即使并非所有点都精确落在线上，这条线也应沿着总体方向。
10. Basic Probability | 概率基础
Probability is a measure of how likely an event is to happen. It always takes a value between 0 and 1, where 0 means impossible and 1 means certain.
概率衡量一个事件发生的可能性有多大。它的取值总是在 0 到 1 之间，0 表示不可能，1 表示必然发生。
Probability = Number of favourable outcomes ÷ Total number of possible outcomes
概率 = 有利结果的数量 ÷ 所有可能结果的总数
The probability scale helps you describe likelihood with words: impossible (0), unlikely, even chance (½), likely, and certain (1). Place events on this scale to compare their chances.
概率尺度帮助用词语描述可能性：不可能(0)、不太可能、等可能性(½)、很可能、一定发生(1)。将事件放在这个尺度上比较其发生的机会。
Outcomes are mutually exclusive if they cannot happen at the same time, such as rolling a 3 and a 5 on a single dice throw. The sum of probabilities of all mutually exclusive outcomes in a trial equals 1.
如果几个结果不会同时发生，它们就是互斥的，比如掷一个骰子时不可能同时得到3点和5点。一次试验中所有互斥结果的概率之和等于1。
Use fractions, decimals or percentages to express probability, but always simplify fractions where possible.
可以用分数、小数或百分数来表示概率，但分数要尽可能化简。
Published by TutorHao | Statistics Revision Series | aleveler.com
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