📚 Year 9 SQA Statistics: Quick Reference Handbook of Formulas and Theorems | Year 9 SQA 统计：公式定理速查手册
This handbook provides a concise summary of essential formulas, definitions, and theorems for Year 9 Statistics following the SQA curriculum. Use it as a quick reference during revision to reinforce key concepts and solve problems efficiently.
本手册简明扼要地总结了遵循SQA课程的九年级统计基本公式、定义和定理。可作为复习时的快速参考，帮助强化关键概念并高效解题。
1. Measures of Central Tendency | 集中趋势度量
Central tendency summarises a data set by identifying a typical value. The three main measures are mean, median, and mode.
集中趋势通过确定典型值来概括数据集。三种主要度量是平均数、中位数和众数。
Mean: The arithmetic average, calculated by summing all data values and dividing by the total number of values.
平均数：算术平均值，通过将所有数据值相加并除以数值总个数来计算得出。
x̄ = Σx / n
x̄ = Σx / n
Where Σx is the sum of all values and n is the number of observations.
其中Σx是所有值的总和，n是观测值个数。
Median: The middle value when data are ordered from smallest to largest. If n is odd, the median is the (n+1)/2-th value; if even, it is the average of the two middle values.
中位数：将数据从小到大排序后位于中间的值。如果n为奇数，中位数是第(n+1)/2个值；如果n为偶数，则是中间两个值的平均数。
Median position = (n+1) / 2
中位数位置 = (n+1) / 2
Mode: The value that appears most frequently. A data set may have one mode, more than one mode (bimodal, multimodal), or no mode at all.
众数：出现次数最多的值。一个数据集可能有一个众数、多个众数（双峰、多峰）或没有众数。
2. Mean from a Frequency Table | 频数表求平均数
When data are presented in a frequency table, the mean is found using the grouped data formula.
当数据以频数表呈现时，使用分组数据公式求平均数。
x̄ = Σfx / Σf
x̄ = Σfx / Σf
Here f is the frequency of each value (or class midpoint) and x is the data value or midpoint.
其中f是每个值（或组中值）的频数，x是数据值或组中值。
Multiply each x by its frequency, sum these products to get Σfx, and divide by the total frequency Σf.
将每个x乘以其频数，求和得到Σfx，再除以总频数Σf。
3. Median and Mode from Frequency Tables | 频数表求中位数与众数
For an ungrouped frequency table, the median is found by locating the cumulative frequency that reaches or exceeds half the total frequency.
对于未分组的频数表，通过找出累积频数达到或超过总频数一半的位置来确定中位数。
r the first value where cumulative frequency ≥ Σf/2 (method may vary; check SQA guidance).
增加一列累积频数。中位数是对应于位置(Σf+1)/2的值，或者是累积频数首次≥ Σf/2的值（方法可能不同，请参照SQA指导）。
The mode is simply the value with the highest frequency.
众数只是频数最高的那个值。
4. Range and Interquartile Range (IQR) | 极差与四分位距
Range: The difference between the maximum and minimum values in a data set.
极差：数据集中最大值与最小值之差。
Range = Max − Min
极差 = 最大值 − 最小值
Interquartile Range (IQR): Published by TutorHao | Year 9 统计 Revision Series | aleveler.com
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