📚 Year 10 AQA Psychology: Formula & Theorem Quick Reference Guide | Year 10 AQA 心理学：公式定理速查手册
Mastering the mathematical requirements is essential for success in Year 10 AQA Psychology. This quick reference guide brings together every formula and key statistical theorem you need when analysing data in psychological research, from calculating measures of central tendency to interpreting distribution shapes. Keep it handy when completing worksheets, analysing experimental results, or preparing for assessments.
掌握数学要求对 Year 10 AQA 心理学的成功至关重要。本速查手册汇集了你在分析心理学研究数据时所需的所有公式和关键统计定理，涵盖集中趋势的计算、分布形状的解读等。在做练习题、分析实验结果或备考评估时，请随时查阅。
1. Mean Formula & Its Theorem | 平均数公式与相关定理
The mean (often called the average) is the most sensitive measure of central tendency because it uses every score in a dataset. The formula is:
平均数（通常称为均值）是最灵敏的集中趋势度量，因为它使用了数据集中的每个分数。公式为：
Mean = Σx ÷ n
where Σ (sigma) means 'sum of' mber of scores. For example, with scores 4, 7, 9, 10: Σx = 30, n = 4, mean = 30 ÷ 4 = 7.5.
其中 Σ（西格玛）表示“总和”，x 代表每个原始分数，n 是分数的总数。例如，分数为 4, 7, 9, 10：Σx = 30，n = 4，平均数 = 30 ÷ 4 = 7.5。
A crucially important theorem about the mean is that it is easily distorted by extreme scores (outliers). This means that if one participant gives a very high or very low score, the mean may no longer represent the typical value. In such cases, researchers often prefer the median.
关于平均数的一个至关重要的定理是它易受极端值（异常值）的影响。这意味着如果某个参与者给出了非常高或非常低的分数，平均数可能不再代表典型值。在这种情况下，研究者往往更倾向于使用中位数。
| Strength | Limitation |
|---|---|
| Uses all data, making it more representative. | Distorted by outliers. |
优势：使用所有数据，更具代表性。局限：易被异常值扭曲。
2. Median Formula & Theorem | 中位数公式与定理
The median is the middle value when all scores are arranged in ascending order. If the number of scores (n) is odd, the median is the middle score; if n is even, the median is the mean of the two middle scores. This rule can be considered the 'median theorem'.
中位数是将所有分数按升序排列后的中间值。如果分数个数 (n) 是奇数，中位数即为正中间的分数；如果 n 是偶数，中位数则是中间两个分数的平均数。这一规则可视为“中位数定理”。
For odd n: Median = score at position (n+1) ÷ 2
For even n: Median = (score at n/2 + score at n/2+1) ÷ 2
5, 6, 9 (n=4, even): scores at 2nd and 3rd positions are 5 and 6, median = (5+6)÷2 = 5.5.
例：分数 3, 5, 6, 9, 11（n=5，奇数）。位置 = (5+1)÷2 = 第 3 个分数 → 6。对于 3, 5, 6, 9（n=4，偶数）：第 2 和第 3 个分数为 5 和 6，中位数 = (5+6)÷2 = 5.5。
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