📚 Year 8 WJEC Statistics: Formula & Theorem Quick Reference Handbook | Year 8 WJEC 统计：公式定理速查手册
This quick reference handbook covers the essential formulas and theorems you need for Year 8 WJEC Statistics. Each concept is explained with clear examples to help you revise efficiently and tackle exam questions with confidence.
这份速查手册涵盖了 Year 8 WJEC 统计所需的关键公式和定理。每个概念都配以清晰的示例，帮助你高效复习，自信应对考试题目。
1. Mean | 平均数
The mean is the average of a set of numbers. To calculate the mean, add up all the data values and then divide by the number of values.
平均数是一组数据的平均值。计算平均数时，将所有数据值相加，然后除以数据值的个数。
Mean = Σx ÷ n
Here Σx represents the sum of all data values and n is the number of values. The symbol Σ (sigma) means ‘sum of’.
其中 Σx 表示所有数据值的总和，n 表示数据值的个数。符号 Σ (西格玛) 意为“求和”。
Example: For the data set 4, 8, 6, 5, 7, the sum is 4+8+6+5+7 = 30, and n = 5. So the mean is 30 ÷ 5 = 6.
示例：对于数据集 4, 8, 6, 5, 7，总和为 4+8+6+5+7 = 30，n = 5。因此平均数为 30 ÷ 5 = 6。
2. Median | 中位数
The median is the middle value when the data is arranged in ascending order. It splits the data into two equal halves.
中位数是将数据按升序排列后位于中间的值。它将数据分成相等的两半。
Median position = (n + 1) ÷ 2
If n is odd, the median is the value at this position. If n is even, the median is the mean of the two middle values.
若 n 为奇数，中位数就是该位置上的值。若 n 为偶数，中位数则是中间两个值的平均数。
Example (odd n): Data 7, 2, 9, 3, 5. Ordered: 2, 3, 5, 7, 9. n=5, position=(5+1)÷2=3rd value. Median = 5.
示例 (奇数 n)：数据集 7, 2, 9, 3, 5。排序后：2, 3, 5, 7, 9。n=5，位置=(5+1)÷2=第3个值。中位数=5。
Example (even n): Data 8, 3, 6, 4. Ordered: 3, 4, 6, 8. n=4, positions 2nd and 3rd. Median = (4+6)÷2 = 5.
示例 (偶数 n)：数据集 8, 3, 6, 4。排序后：3, 4, 6, 8。n=4，第2和第3个值。中位数 = (4+6)÷2 = 5。
3. Mode | 众数
The mode is the value that appears most frequently in a data set. There can be one mode (unimodal), two modes (bimodal), or no mode if all values occur equally often.
众数是数据集中出现次数最多的值。可以有一个众数（单峰）、两个众数（双峰），或者如果没有值重复出现则无众数。
Example: In the set 3, 5, 5, 2, 7, 5, 9, the mode is 5 because it occurs three times.
示例：在数据集 3, 5, 5, 2, 7, 5, 9 中，众数为 5，因为它出现了三次。
4. Range | 极差
The range measures the spread of the data. It is the difference between the highest and lowest values.
极差衡量数据的离散程度。它是最大值与最小值之差。
Range = Highest value – Lowest value
Example: For the data set 12, 7, 22, 15, 8, the highest value is 22 and the lowest is 7. Range = 22 – 7 = 15.
示例：对于数据集 12, 7, 22, 15, 8，最高值为 22，最低值为 7。极差 = 22 – 7 = 15。
5. Mean from a Frequency Table | 从频率表求平均数
When data is given in a frequency table, multiply each value (x) by its frequency (f) to get fx. Sum these products, then divide by the total frequency.
当数据以频率表呈现时，将每个值 (x) 乘以其频数 (f) 得到 fx。求和这些乘积，再除以总频数。
Mean = Σ(fx) ÷ Σf
Example: Table: x=2 (f=3), x=5 (f=2), x=7 (f=1). Σf = 6. Σ(fx) = (2×3) + (5×2) + (7×1) = 6+10+7 = 23. Mean = 23 ÷ 6 ≈ 3.83.
示例：表格：x=2 (f=3), x=5 (f=2), x=7 (f=1)。Σf = 6。Σ(fx) = (2×3) + (5×2) + (7×1) = 6+10+7 = 23。平均数 = 23 ÷ 6 ≈ 3.83。
6. Probability | 概率
The probability of an event is a measure of how likely it is to happen. It always lies between 0 (impossible) and 1 (certain).
事件的概率是对其发生可能性的度量。它总是在 0（不可能）和 1（必然）之间。
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
For equally likely outcomes, this formula gives the theoretical probability.
对于等可能的结果，此公式给出理论概率。
Example: Rolling a fair six-sided die, P(rolling a 4) = 1/6.
示例：掷一枚公平的六面骰子，P(掷出4) = 1/6。
Complementary events: The event ‘not A’ covers all outcomes not in A. Its probability is:
互补事件：事件“非 A”包含所有不在 A 中的结果。其概率为：
P(not A) = 1 – P(A)
7. Experimental Probability | 实验概率
Experimental probability is based on actual trials or observations. It is also called relative frequency.
实验概率基于实际的试验或观察。它也称为相对频率。
Relative frequency = Number of times event occurs ÷ Total number of trials
As the number of trials increases, the experimental probability tends to get closer to the theoretical probability.
随着试验次数的增加，实验概率往往会趋近于理论概率。
Example: A coin is flipped 100 times and lands on heads 47 times. Relative frequency of heads = 47 / 100 = 0.47.
示例：一枚硬币抛掷100次，正面朝上47次。正面的相对频率 = 47 / 100 = 0.47。
8. Mutually Exclusive Events | 互斥事件
Two events are mutually exclusive if they cannot happen at the same time. For mutually exclusive events A and B:
如果两个事件不能同时发生，则它们是互斥的。对于互斥事件 A 和 B：
P(A or B) = P(A) + P(B)
Example: When drawing a card from a standard deck, the events ‘drawing a heart’ and ‘drawing a spade’ are mutually exclusive. P(heart or spade) = 1/4 + 1/4 = 1/2.
示例：从标准扑克牌中抽一张牌，事件“抽到红心”和“抽到黑桃”互斥。P(红心或黑桃) = 1/4 + 1/4 = 1/2。
9. Types of Data | 数据类型
Discrete data can only take specific values, often whole numbers or counts. There are gaps between possible values.
离散数据只能取特定的值，通常是整数或计数。可能值之间存在间隔。
Example: Number of students in a class (you cannot have 30.5 students).
示例：一个班级的学生人数（不可能有30.5个学生）。
Continuous data can take any value within a range. Measurements like height, time, and temperature are continuous.
连续数据可以在一个范围内取任意值。诸如身高、时间和温度之类的测量值是连续的。
Example: Height of a plant could be 12.3 cm, 12.35 cm, etc.
示例：植物的高度可以是 12.3 cm、12.35 cm 等。
Qualitative data describes qualities or categories (e.g. eye colour, favourite food). It is non-numeric.
定性数据描述性质或类别（例如眼睛颜色、最喜欢的食物）。它是非数值的。
Quantitative data is numerical and measures quantity. It can be discrete or continuous.
定量数据是数值型的，测量数量。它可以是离散的或连续的。
10. Charts and Diagrams Quick Reference | 图表速查
Bar chart: Used for discrete or categorical data. Bars are separated and have equal width. The height represents frequency.
条形图：用于离散或分类数据。条形分开且宽度相等。高度表示频数。
Pie chart: Shows proportions of a whole. Each sector angle is calculated as:
饼图：显示整体的比例。每个扇区的角度计算公式为：
Sector angle = (Frequency ÷ Total frequency) × 360°
Line graph: Used to show trends over time. Plot points and connect them with straight lines.
折线图：用于显示随时间变化的趋势。描点并用直线连接。
Scatter graph: Shows the relationship between two sets of data. Look for correlation:
散点图：显示两组数据之间的关系。观察相关性：
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Positive correlation: as one variable increases, the other tends to increase.
正相关：当一个变量增加时，另一个变量也倾向于增加。
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Negative correlation: as one variable increases, the other tends to decrease.
负相关：当一个变量增加时，另一个变量倾向于减少。
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No correlation: no clear pattern.
无相关：无明显模式。
Stem-and-leaf diagram: Organises data while retaining original values. Stems represent the leading digit(s) and leaves the trailing digit.
茎叶图：在保留原始数据的情况下整理数据。茎代表前导数字，叶代表末尾数字。
Published by TutorHao | Statistics Revision Series | aleveler.com
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