📚 Year 9 Edexcel Statistics: Formula & Theorem Quick Reference Handbook | 九年级爱德思统计：公式定理速查手册
This handbook provides a concise summary of essential formulas and theorems for Year 9 Edexcel Statistics. It covers measures of central tendency, spread, data representation, probability, and bivariate data, helping you revise key concepts and calculation methods efficiently.
本手册为九年级爱德思统计课程提供核心公式与定理的简明总结。内容涵盖集中趋势量数、离散程度、数据表示、概率和双变量数据，帮助你高效复习关键概念和计算方法。
1. Mean, Median, Mode, and Range | 平均数、中位数、众数和极差
The mean is the average value. It is calculated by adding all the data values and dividing by the number of values.
平均数就是均值。计算方法是将所有数据值相加，再除以数据个数。
Mean = (∑x) / n
这里 ∑x 表示所有数据值的总和，n 表示数据的个数。
Example: For the data set 3, 7, 8, 10, the mean is (3+7+8+10)/4 = 28/4 = 7.
示例：数据集 3, 7, 8, 10 的平均数是 (3+7+8+10)/4 = 28/4 = 7。
The median is the middle value when the data are arranged in order. If there are two middle values, take their average.
中位数是将数据排序后位于中间的值。如果中间有两个值，则取它们的平均数。
To find the median position, use (n+1)/2. For example, with n=5, position = 3rd value.
中位数的位置用 (n+1)/2 来确定。例如，n=5 时，位置是第3个数据。
The mode is the value that appears most frequently. A data set can have no mode, one mode, or multiple modes.
众数是出现次数最多的值。一组数据可以没有众数、有一个众数或多个众数。
The range measures spread. Range = Maximum value − Minimum value.
极差衡量数据的分散程度。极差 = 最大值 − 最小值。
2. Mean from a Frequency Table | 从频数表计算平均数
When data are grouped in a frequency table, the mean is estimated using midpoints of class intervals multiplied by frequencies.
当数据以频数表的形式给出时，用组中值乘以频数来估算平均数。
Mean = (∑ f × x) / ∑ f
其中 f 是频数，x 是组中值（或具体的值），∑ f × x 是频数与数值乘积的总和，∑ f 是总频数。
vidual values, x is simply the data value. Add a column for f×x, find totals, then divide.
对于单值频数表，x 就是数据值本身。添加一列 f×x，计算总和，然后相除。
appears 3 times, value 6 appears 5 times. Mean = (5×3 + 6×5) / (3+5) = (15+30)/8 = 5.625.
示例：数值5出现3次，数值6出现5次。平均数 = (5×3 + 6×5) / (3+5) = 45/8 = 5.625。
3. Quartiles and Interquartile Range | 四分位数与四分位距
The lower quartile (Q₁) is the median of the lower half of data. The upper quartile (Q₃) is the median of the upper half.
下四分位数 (Q₁) 是数据下半部分的中位数。上四分位数 (Q₃) 是数据上半部分的中位数。
To calculate quartiles: order the data, find the median (Q₂), then split into two halves. If n is odd, do not include the median in either half.
计算四分位数的方法：排序，找出中位数 (Q₂)，然后将数据分成两半。如果 n 是奇数，两半都不包含中位数。
Interquartile range (IQR) = Q₃ − Q₁
The IQR measures the spread of the middle 50% of data and is not affected by extreme values.
四分位距衡量中间50%数据的分散程度，且不受极端值影响。
4. Box Plots | 箱线图
A box plot (or box-and-whisker plot) displays the five-number summary: minimum, Q₁, median, Q₃, and maximum.
箱线图（盒须图）展示五数概括：最小值、Q₁、中位数、Q₃ 和最大值。
Draw a box from Q₁ to Q₃ with a line at the median. Whiskers extend to the minimum and maximum, unless outliers are defined.
绘制从 Q₁ 到 Q₃ 的矩形，并在中位数处画一条竖线。须线延伸到最小值和最大值（除非定义了异常值）。
Box plots are useful for comparing distributions and identifying skewness.
箱线图在比较分布和识别偏态时很有用。
5. Stem and Leaf Diagrams | 茎叶图
A stem-and-leaf diagram keeps original data visible while showing distribution shape. Each number splits into a stem (tens) and leaf (units).
茎叶图在展示分布形态的同时保留原始数据。每个数分解为茎（十位数）和叶（个位数）。
Always include a key, e.g., '2 | 3 means 23'. Order the leaves in ascending order.
必须包含图例，例如 '2 | 3 表示 23'。叶子按升序排列。
Back-to-back stem-and-leaf diagrams compare two related datasets using a common stem.
背靠背茎叶图使用共同的茎来比较两组相关数据。
6. Probability Basics |
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