📚 Year 10 CCEA Psychology: Formula & Theorem Quick Reference Guide | Year 10 CCEA 心理学：公式定理速查手册
This quick reference guide covers the essential formulas and theorems you'll encounter in Year 10 CCEA GCSE Psychology. From statistical measures used in research methods to key psychophysical laws, these formulas will help you analyse data and understand core psychological principles. Keep this handbook handy for revision and exam preparation!
本速查手册涵盖 Year 10 CCEA GCSE 心理学中涉及的基本公式与定理，从研究方法中使用的统计量到关键的心理物理定律，这些公式有助于分析数据并理解核心心理学原理。备考复习时请随身携带本手册！
1. Arithmetic Mean | 算术平均数
The arithmetic mean (often just called the mean) is the sum of all values divided by the total number of values. It is the most common measure of central tendency. The Greek letter sigma (Σ) means 'sum', x represents each individual score, and n is the sample size.
算术平均数（简称平均数）是所有数值的总和除以数值的个数，是最常用的集中量数。希腊字母 Σ 表示求和，x 代表每个分数，n 是样本量。
Mean = Σx / n
For example, the mean of scores 4, 7, 9, 12 is (4+7+9+12) / 4 = 32 / 4 = 8.
例如，分数 4、7、9、12 的平均数为 (4+7+9+12) / 4 = 32 / 4 = 8。
2. Median | 中位数
The median is the middle value when all scores are arranged in ascending (or descending) order. If there is an odd number of scores, the median is the central score. If the number is even, the median is the mean of the two central scores.
中位数是将所有分数按升序（或降序）排列后位于中间的值。若分数个数为奇数，中位数就是正中间的那个分数；若个数为偶数，中位数为中间两个分数的平均数。
Median position = (n + 1) / 2
n odd set: 3, 5, 9 → median = 5. For an even set: 2, 4, 7, 9 → median = (4 + 7) / 2 = 5.5.
奇数个数据：3, 5, 9 → 中位数 = 5。偶数个数据：2, 4, 7, 9 → 中位数 = (4 + 7) / 2 = 5.5。
3. Mode | 众数
The mode is the score that occurs most frequently in a dataset. A set of scores can have one mode (unimodal), two modes (bimodal), several modes (multimodal), or no mode if all values appear only once.
众数是数据集中出现频率最高的分数。数据集可以有一个众数（单峰）、两个众数（双峰）、多个众数（多峰），或者若所有值都只出现一次则没有众数。
In the data set 2, 3, 3, 5, 7, 7, 7, 9, the mode is 7 because it appears three times.
在数据 2, 3, 3, 5, 7, 7, 7, 9 中，众数是 7，因为它出现了三次。
4. Range | 全距
The range is the simplest measure of dispersion (spread). It shows the distance between the highest and lowest scores in a dataset.
全距是最简单的离散量数，表示数据集中最高分与最低分之间的距离。
Range = Max − Min
If the highest score is 95 and the lowest is 21, the range is 95 − 21 = 74.
若最高分为 95，最低分为 21，则全距为 95 − 21 = 74。
5. Percentage Change | 百分比变化
Percentage change expresses how much a quantity has increased or decreased relative to its original value. A positive result indicates an increase, while a negative result indicates a decrease.
百分比变化表示某一数量相对于原值增加或减少的幅度。正值表示增加，负值表示减少。
Percentage Change = ((New − Original) / Original) × 100%
If a memory score rises from 40 to 52, the percentage change is ((52 − 40) / 40) × 100% = 30% increase.
如果记忆分数从 40 提升到 52，百分比变化为 ((52 − 40) / 40) × 100% = 30% 增长。
6. Converting Fractions, Decimals & Percentages | 分数、小数和百分比的转换
In psychological research, data may appear as fractions, decimals or percentages. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100. Reverse conversions: divide a percentage by 100 to get a decimal; write a decimal as a fraction over a power of ten and simplify.
在心理学研究中，数据可能以分数、小数或百分比的形式出现。将分数转换为小数，用分子除以分母；将小数转换为百分比，乘以 100。反向转换：百分比除以 100 得到小数；将小数写成分母为 10 的幂的分数并约分。
1/4 = 0.25 = 25% 3/5 = 0.6 = 60%
These conversions are essential when interpreting graphs or calculating proportional data.
这些转换在解读图表或计算比例数据时至关重要。
7. Ratios & Proportions | 比率与比例
A ratio compares two quantities and is written as a:b. To simplify a ratio, divide both sides by their greatest common factor. A proportion represents a part of a whole, often expressed as a fraction or percentage.
比率用于比较两个数量，写作 a:b。化简比率时，将两边同时除以最大公因数。比例表示部分与整体的关系，通常用分数或百分比表示。
If 18 out of 60 participants correctly recalled a word, the proportion is 18/60 = 0.3 = 30%, and the ratio of correct to incorrect is 18:42, which simplifies to 3:7.
如果 60 名参与者中有 18 人正确回忆了一个词，比例为 18/60 = 0.3 = 30%，正确与不正确的比率为 18:42，化简后为 3:7。
8. Weber's Law | 韦伯定律
Weber's Law describes the just noticeable difference (JND) – the smallest change in a stimulus that can be detected 50% of the time. The formula shows that the JND is a constant proportion of the initial stimulus intensity.
韦伯定律描述了最小可觉差——即在 50% 的情况下能被察觉到的最小刺激变化。该公式表明，最小可觉差与初始刺激强度的比值是一个常数。
ΔI / I = k
0.02, meaning if you hold 100 g, you would need to add about 2 g to notice the difference.
ΔI 是可察觉的变化量，I 是初始刺激强度，k 是韦伯常数。对于举重，k ≈ 0.02，也就是说当你拿着 100 克重物时，需要增加约 2 克才能察觉变化。
9. Normal Distribution Empirical Rule | 正态分布经验法则
Many psychological variables, such as IQ scores, are normally distributed, forming a symmetrical bell-shaped curve around the mean. The empirical rule tells us the approximate percentage of data falling within certain standard deviations (SD) of the mean.
许多心理变量（如智商分数）服从正态分布，形成以均值为中心的对称钟形曲线。经验法则告诉我们数据落在均值附近多少个标准差范围内的近似百分比。
Approximately 68% of data lie within ±1 SD of the mean, about 95% within ±2 SD, and about 99.7% within ±3 SD. This rule helps identify unusually high or low scores.
大约 68% 的数据落在均值 ±1 个标准差内，约 95% 落在 ±2 个标准差内，约 99.7% 落在 ±3 个标准差内。该法则有助于识别异常高分或低分。
10. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law states that performance increases with physiological or mental arousal, but only up to an optimal point. Beyond that, further arousal leads to a decline in performance. The graph forms an inverted U-shape.
耶克斯-多德森定律指出，随着生理或心理唤醒水平的提高，表现会提升，但仅达到最佳唤醒点为止；超过该点后，唤醒进一步提高反而导致表现下降。其图形呈倒 U 形。
Optimal arousal depends on task difficulty: simple or well-learned tasks require higher arousal for peak performance, whereas complex or new tasks are best performed with lower arousal.
最佳唤醒水平取决于任务难度：简单或熟练的任务需要较高唤醒才能达到最佳表现，而复杂或新任务则在较低唤醒时表现最好。
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