📚 Year 10 WJEC Statistics: Quick Reference Handbook for Formulas and Theorems | Year 10 WJEC 统计：公式定理速查手册
This handbook consolidates essential formulas and theorems for the Year 10 WJEC Statistics syllabus. Mastering these will streamline your revision and boost exam confidence.
本手册整合了 Year 10 WJEC 统计考试大纲中的核心公式与定理。掌握这些内容能帮助你有条理地复习，增强应试信心。
1. Key Notation | 关键符号
The symbols below appear frequently in WJEC Statistics. Familiarity with them ensures you interpret questions correctly from the start.
以下符号在 WJEC 统计中频繁出现，熟悉它们是准确理解题目的第一步。
| Symbol & Name (English) | 含义 (中文) |
|---|---|
| x̄ (x-bar) – sample mean | 样本均值 |
| μ (mu) – population mean | 总体均值 |
| s – sample standard deviation | 样本标准差 |
| σ (sigma) – population standard deviation | 总体标准差 |
| n – sample size (number of data values) | 样本容量（数据个数） |
| N – population size | 总体容量 |
| f – frequency | 频数 |
| Σ (capital sigma) – sum of | 求和 |
| Q₁ – lower quartile | 下四分位数 |
| Q₃ – upper quartile | 上四分位数 |
| IQR – interquartile range | 四分位距 |
| r – correlation coefficient | 相关系数 |
| P(A) – probability of event A | 事件 A 的概率 |
2. Measures of Central Tendency | 集中趋势的量数
The mean, median and mode summarise the centre of a dataset. Choosing the right measure depends on the data type and the presence of outliers.
均值、中位数和众数用以概括数据集的中心。选择哪种量数取决于数据类型和是否存在异常值。
For ungrouped data, the arithmetic mean is calculated as the sum of all values divided by the number of values.
对于未分组数据，算术均值的计算公式是所有数值之和除以数值的个数。
x̄ = Σx / n
The median is the middle value when the data are arranged in order. If n is even, the median is the average of the two middle numbers.
中位数是将数据排序后位于正中间的值；若 n 为偶数，则为中间两个数的平均值。
The mode is the value that occurs most frequently. A data set may have one mode, more than one mode (bimodal) or no mode.
众数是出现次数最多的值。一组数据可能有一个众数、多个众数（双峰）或无众数。
3. Measures of Spread | 离差的量数
Spread tells us how varied or consistent the data are. The simplest measure is the range.
离差告诉我们数据有多分散或多一致。最简单的量数是极差（全距）。
Range = Maximum value − Minimum value
The interquartile range (IQR) is the range of the middle 50% of the data and is less affected by outliers.
四分位距 (IQR) 是中间 50% 数据的极差，较少受异常值的影响。
IQR = Q₃ − Q₁
The standard deviation measures the average distance of each data point from the mean. For a sample, the formula uses n−1 as the divisor (sample standard deviation).
标准差衡量每个数据点与均值的平均距离。对于样本，公式使用 n−1 作为除数（样本标准差）。
s = √[ Σ(x − x̄)² / (n − 1) ]
If the data represent the entire population, use N instead of n−1 and μ instead of x̄.
如果数据代表整个总体，则将分母换为 N，均值换为 μ。
σ = √[ Σ(x − μ)² / N ]
4. Frequency Tables & Grouped Data | 频数表与分组数据
For data organised in a frequency table, multiply each value (or midpoint for grouped data) by its frequency.
对于频数表组织的数据，用每个值（或分组数据的组中值）乘以它对应的频数。
Estimated mean x̄ = Σfx / Σf
When only class intervals are given, use the class midpoint x. This gives an estimate of the mean.
若只给出了组距，则用组中值 x。计算得到的是均值的估计值。
To find the median from a grouped frequency table, use linear interpolation. The formula locates the median within its class interval.
要从分组频数表求中位数，使用线性插值。该公式将中位数定位在其所在组区间内。
Median = L + [ (n/2 − F) / f ] × w
L = lower boundary of the median class, F = cumulative frequency before the median class, f = frequency of the median class, w = class width.
L 为中位数组的组下限，F 为中位数组之前的累积频数，f 为中位数组的频数，w 为组距。
The same interpolation method works for quartiles: for Q₁ use n/4, for Q₃ use 3n/4.
相同的插值法也适用于四分位数：Q₁ 用 n/4，Q₃ 用 3n/4。
5. Probability Basics | 概率基础
Probability describes how likely an event is to occur and is always a number between 0 and 1 inclusive.
概率描述事件发生的可能性，总是在 0 到 1 之间（含端点）。
P(A) = Number of favourable outcomes / Total number of possible outcomes
The probability of an event not occurring is the complement.
事件不发生的概率是其对立事件（补事件）的概率。
P(not A) = 1 − P(A)
All probabilities from a sample space sum to 1.
样本空间中所有结果的概率之和为 1。
6. Combined Probability | 组合概率
When two events, A and B, are mutually exclusive (cannot happen at the same time), the probability of either occurring is simply the sum.
当两个事件 A 和 B 互斥（不能同时发生）时，任一事件发生的概率即为两者之和。
P(A or B) = P(A) + P(B) [if mutually exclusive]
If the events can both occur, we must subtract the intersection to avoid double counting.
如果两事件可以同时发生，我们必须减去交集的概率以避免重复计数。
P(A or B) = P(A) + P(B) − P(A and B)
For independent events, the probability of both occurring is the product of their individual probabilities.
对于独立事件，两事件同时发生的概率等于各自概率的乘积。
P(A and B) = P(A) × P(B) [if independent]
Tree diagrams can help visualise combined probabilities and include multiplication along branches.
树状图有助于将组合概率可视化，沿着分支使用乘法法则。
7. Relative Frequency & Expectation | 相对频率与期望
Relative frequency is an estimate of probability based on experiment or survey results.
相对频率是基于试验或调查结果对概率的估计。
Relative frequency = Number of successful trials / Total number of trials
The expected number of occurrences of an event in a given number of trials is the probability multiplied by the number of trials.
在给定的试验次数中，事件预期的发生次数是概率乘以试验总次数。
Expected frequency = P(event) × Number of trials
8. Scatter Graphs & Correlation | 散点图与相关
A scatter graph shows the relationship between two variables. Correlation measures the strength and direction of a linear relationship.
散点图展示两个变量之间的关系。相关性衡量线性关系的强度和方向。
Spearman’s rank correlation coefficient is often used when data are ranked or when the relationship is monotonic.
斯皮尔曼等级相关系数常用于数据为等级数据或关系为单调关系时。
rₛ = 1 − 6Σd² / [ n(n² − 1) ]
d = difference between the ranks of each pair, n = number of data pairs. The value lies between −1 and +1.
d 为每一对数据的等级之差，n 为数据对的数量。该值介于 –1 到 +1 之间。
Pearson’s product moment correlation coefficient is also used for linear relationships and can be found using a calculator.
皮尔逊积矩相关系数也用于线性关系，可以利用计算器求得。
9. Line of Best Fit & Regression | 最佳拟合直线与回归
When a scatter graph suggests a linear trend, a line of best fit can be drawn by eye. For accurate predictions, the least squares regression line is used.
当散点图呈现线性趋势时，可以凭目测画出最佳拟合直线。为了精确预测，则使用最小二乘回归直线。
The regression line has the equation y = a + bx, where b is the slope and a is the y-intercept.
回归直线的方程为 y = a + bx，其中 b 为
Published by TutorHao | Year 10 统计 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply