📚 Year 10 Eduqas Psychology: Formulas and Principles Quick Reference Guide | Year 10 Eduqas 心理学：公式定理速查手册
This quick reference guide brings together the essential formulas, mathematical principles, and classic psychological laws that Year 10 Eduqas Psychology students need to apply in research methods and understand in key topics. From descriptive statistics to memory and perception, you will find each concept explained clearly with its formula or rule, followed by a practical example where helpful. Use this handbook to revise efficiently and build confidence for your assessments.
本速查手册汇集了 Year 10 Eduqas 心理学课程中研究方法必须掌握的核心公式、数学原理以及经典心理学定律。从描述统计到记忆与感知，每个概念都配以公式或定律的清晰解释，并在适当处给出实例。你可以利用本手册高效复习，为测评建立信心。
1. Mean | 平均值
The mean is the arithmetic average of a data set. It is calculated by adding together all the scores and dividing the total by the number of scores.
平均值是一组数据的算术平均数。计算方法是将所有分数相加，然后除以分数的个数。
Mean = Σx ÷ n
Σx represents the sum of all individual scores, and n is the total number of scores. The mean is the most sensitive measure of central tendency because it takes every value into account, but it can be distorted by extreme scores (outliers).
Σx 代表所有单个分数的总和，n 代表分数的总个数。平均值是最灵敏的集中量数，因为它考虑了每一个数值，但也容易被极端值（离群值）拉偏。
For the data set 4, 6, 7, 9, 11: Mean = (4+6+7+9+11) ÷ 5 = 37 ÷ 5 = 7.4
对于数据集 4, 6, 7, 9, 11: 平均值 = (4+6+7+9+11) ÷ 5 = 37 ÷ 5 = 7.4
2. Median | 中位数
The median is the middle value when all scores are arranged in order from smallest to largest. If there is an even number of scores, the median is the mean of the two middle values.
中位数是将所有分数按从小到大的顺序排列后位于正中间的那个数。如果分数的个数为偶数，中位数就是中间两个数的平均值。
value. 3) If n is even, median = (value at position n/2 + value at position (n/2)+1) ÷ 2.
步骤：1) 排列数据。2) 若 n 为奇数，中位数为第 (n+1)/2 个数值。3) 若 n 为偶数，中位数 = (第 n/2 个数值 + 第 (n/2)+1 个数值) ÷ 2。
The median is not affected by extreme scores, making it useful when outliers are present.
中位数不受极端分数的影响，因此在存在离群值时很有用。
=5 (odd) → median is the 3rd value = 7. For 2, 4, 6, 8: n=4 (even) → median = (4+6)/2 = 5.
例子：3, 5, 7, 12, 15 → n=5 奇数，中位数为第3个值 = 7。2, 4, 6, 8 → n=4 偶数，中位数 = (4+6)/2 = 5。
3. Mode | 众数
The mode is the score that occurs most frequently in a data set. A set may have one mode (unimodal), two modes (bimodal), more than two modes (multimodal), or no mode at all if all values appear with the same frequency.
众数是在数据集中出现频率最高的数值。一组数据可能有一个众数（单峰）、两个众数（双峰）、多个众数（多峰），或者当所有数值出现次数相同时没有众数。
The mode is the only measure of central tendency that can be used with nominal (categorical) data. However, it may not represent the centre of the data well if the most frequent value is far from the rest of the distribution.
众数是唯一可以用于称名数据（分类数据）的集中量数。不过，如果出现次数最多的数值远离其他数值，众数可能无法很好地代表数据的中心。
4. Range | 范围
The range is a simple measure of dispersion (spread). It is the difference between the highest score and the lowest score in the data set.
范围是一种简单的离差量数（反映数据分散程度）。它是数据集中最高分与最低分之间的差值。
Range = Highest score – Lowest score
The range is quick to calculate but can be misleading because it only uses the two extreme values and ignores the rest of the distribution.
范围计算简便，但可能产生误导，因为它只取决于两个极端值，而忽略了分布中的其他所有数值。
Example: Scores 8, 10, 12, 15, 22 → Range = 22 − 8 = 14.
例子：分数 8, 10, 12, 15, 22 → 范围 = 22 − 8 = 14。
5. Percentage Calculation | 百分比计算
Percentages are used frequently in psychology to describe proportions, such as the percentage of participants who showed a particular behaviour. The formula converts a part-to-whole ratio into a number out of 100.
在心理学中，百分比常用于描述比例，例如表现出某种行为的参与者所占的百分比。其公式将部分与整体的比率转化为一个百分数。
Percentage (%) = (Part ÷ Whole) × 100
Always make sure the ‘part’ and ‘whole’ refer to the same unit or the same group, and round percentages to one or two decimal places as appropriate.
务必确保“部分”与“整体”指向相同的单位或群体，并根据需要将百分比四舍五入到小数点后一位或两位。
a class of 30 students, 12 achieved grade A. Percentage of A grades = (12 ÷ 30) × 100 = 40%.
例子：一个班有 30 名学生，其中 12 人获得 A 等。A 等百分比 = (12 ÷ 30) × 100 = 40%。
6. Percentage Change | 百分比变化
Percentage change measures how much a value has increased or decreased relative to its original amount. This is helpful when analysing pre-test/post-test data or changes in behaviour over time.
百分比变化衡量一个数值相对于其原始数值的增加或减少程度。当分析前测/后测数据或行为随时间的变化时，这一计算很有用。
Percentage Change (%) = [(New value – Original value) ÷ Original value] × 100
A positive result indicates an increase; a negative result indicates a decrease. Always use the original value as the denominator.
正数结果表示增长；负数结果表示减少。务必始终以原始数值作为分母。
rom 15 words to 21 words. Percentage change = [(21 − 15) ÷ 15] × 100 = (6 ÷ 15) × 100 = 40% increase.
例子：记忆回忆单词数从 15 个提高到 21 个。百分比变化 = [(21 − 15) ÷ 15] × 100 = (6 ÷ 15) × 100 = 增长了 40%。
7. Ratio | 比率
A ratio compares the size of two quantities, showing how many times one value contains or is contained within the other. Ratios are often used in psychology to describe gender splits or condition allocations.
比率用于比较两个数量的大小，表示一个数值包含另一个数值的多少倍。心理学中常用比率描述性别分布或实验条件的分配。
Ratios can be simplified by dividing both sides by the greatest common divisor. For instance, 8:12 simplifies to 2:3. They are written with a colon but can also be expressed as fractions when computing proportions.
比率可以通过同时除以最大公约数来化简。例如 8:12 简化为 2:3。比率书写时使用冒号，但在计算比例时也可表示为分数。
r a ratio of boys to girls = 3:2, total parts = 5. Percentage of boys = (3 ÷ 5) × 100 = 60%.
若要将比率中的某一部分转换为百分比，用该部分除以两部分之和再乘以 100。例如男生与女生比率为 3:2，总份数为 5，男生百分比 = (3 ÷ 5) × 100 = 60%。
8. Normal Distribution Characteristics | 正态分布特征
A normal distribution is a bell-shaped, symmetrical frequency curve where most scores cluster around the centre and the frequencies taper off equally at both tails. In a perfectly normal distribution, the mean, median and mode are equal and lie at the peak of the curve.
正态分布是一种钟形、对称的频数曲线，大部分分数集中在中心附近，两端尾部频数对称下降。在完全正态分布中，平均值、中位数和众数相等，且都位于曲线的峰值处。
The spread of scores is measured by the standard deviation (SD). A smaller SD means scores are tightly packed around the mean; a larger SD indicates greater spread.
分数的分散程度用标准差衡量。标准差越小，分数越紧密聚集在平均值周围；标准差越大，分数越分散。
Psychological variables such as IQ scores and some personality traits are often assumed to be normally distributed in the population.
智商分数和某些人格特质等心理变量常被假定在总体中呈正态分布。
9. The Empirical Rule (68–95–99.7%) | 经验法则（68–95–99.7%）
For any normal distribution, approximately 68% of the data fall within ±1 standard deviation of the mean, about 95% fall within ±2 standard deviations, and about 99.7% thin ±3 standard deviations. This is known as the empirical rule, or the three-sigma rule.
对于任何正态分布，大约 68% 的数据落在平均值 ±1 个标准差之内，约 95% 落在 ±2 个标准差之内，约 99.7% 落在 ±3 个标准差之内。这被称为经验法则或三西格马法则。
Psychologists use this rule to determine how unusual a particular score is. For example, an IQ score more than 2 standard deviations above or below the mean (i.e. below 70 or above 130 on many tests) is considered statistically rare.
心理学家利用这一法则判断某个分数有多不寻常。例如，智商测试中超出平均值 ±2 个标准差（在许多测试中即低于 70 或高于 130）的分数被认为在统计上很罕见。
Remember that this rule only applies precisely to distributions that are normal; skewed distributions do not follow this pattern.
请记住，此法则只严格适用于正态分布；偏态分布并不遵循这一模式。
10. Central Tendency in Skewed Distributions | 偏态分布中的集中量数
When a distribution is skewed, the mean, median and mode are no longer equal. Their relative positions can tell you the direction of the skew.
当分布呈偏态时，平均值、中位数和众数不再相等。它们的相对位置可指示偏态的方向。
In a positive skew (right skew), most scores pile up on the left with a few extreme high values pulling the tail to the right. The mean is pulled in the direction of the tail, so usually: Mode < Median < Mean.
在正偏态（右偏）中，大部分分数堆积在左侧，少数极端高分将尾部拉向右侧。平均值被拉向尾部的方向，因此通常：众数 < 中位数 < 平均值。
In a negative skew (left skew), most scores pile up on the right with a tail of low scores. Here the mean is dragged downwards: Mean < Median < Mode.
在负偏态（左偏）中，大部分分数堆积在右侧，尾部为低分。此时平均值被向下拉：平均值 < 中位数 < 众数。
Because the median is less influenced by skewed tails, it is often the preferred measure of central tendency for skewed data, such as reaction times or income data.
由于中位数受偏斜尾部的影响较小，对于反应时间或收入数据这类偏态数据，中位数通常是更可取的集中量数。
11. Miller’s Magic Number 7±2 | 米勒的神奇数字 7±2
George Miller (1956) proposed that the capacity of short-term memory (STM) is limited to about 7 plus or minus 2 items or ‘chunks’ of information. This is often referred to as Miller’s Law.
乔治·米勒（1956）提出，短时记忆的容量限制约为 7±2 个项目或信息“组块”。这常被称为米勒定律。
A chunk is a meaningful unit of information. By grouping individual letters into words or words into phrases, we can expand the total amount of information held in STM. For example, the letters C, I, A, F, B, I, U, S, A can be chunked into CIA, FBI, USA – just three chunks.
组块是指有意义的信息单元。将单个字母组合成单词，或将单词组合成短语，我们就能扩展短时记忆中可容纳的信息总量。例如，字母 C, I, A, F, B, I, U, S, A 可被组块为 CIA、FBI、USA——只有三个组块。
This principle explains why we can briefly remember a 7-digit phone number but struggle with much longer sequences unless we chunk them.
这一原理解释了为什么我们能短暂记住一个 7 位数字的电话号码，但若记忆更长的序列就会感到困难，除非我们将其组块化。
12. Gestalt Principles of Perceptual Organisation | 格式塔知觉组织原则
Gestalt psychologists argued that the whole is greater than the sum of its parts, and they identified several laws by which we organise visual information automatically.
格式塔心理学家主张整体大于部分之和，他们归纳出了几条我们自动组织视觉信息的规律。
Figure-Ground: We separate a scene into a main figure that stands out and a background that recedes. Rubin’s vase is a classic example.
图形-背景：我们将场景分离为突出的主图形和后退的背景。鲁宾花瓶即是经典示例。
Similarity: Objects that look similar (in shape, colour or size) are perceived as belonging together.
相似性：在外观上相似（形状、颜色或大小）的物体被知觉为属于同一组。
Proximity: Objects that are close together tend to be grouped together.
接近性：距离较近的物体倾向于被归为一组。
Continuity: We prefer to see smooth, continuous patterns rather than abrupt changes. Lines are perceived as following the smoothest path.
连续性：我们偏好看到平滑连续的图案而非突然的变化。线条被知觉为沿着最平滑的路径延伸。
Closure: When a figure has gaps, we fill in the missing information to perceive a complete, whole object.
闭合性：当一个图形存在缺口时，我们会填补缺失的信息以知觉到一个完整的对象。
These principles help explain many visual illusions and are used extensively in design and advertising.
这些原则有助于解释众多视错觉，并在设计和广告中被广泛运用。
Published by TutorHao | Psychology Revision Series | aleveler.com
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