📚 Cumulative Frequency & Box Plots | 累积频率与箱线图
In Edexcel IGCSE Mathematics, cumulative frequency and box plots are essential tools for analysing grouped data. They allow you to estimate key statistical measures such as the median, quartiles, and interquartile range, and provide a clear visual summary of a distribution. This article covers everything you need to know for the exam, from constructing tables to interpreting box plots.
在 Edexcel IGCSE 数学中，累积频率和箱线图是分析分组数据的重要工具。它们能够帮助你估计中位数、四分位数和四分位距等关键统计量，并清晰地呈现数据分布的可视化总结。本文涵盖考试所需的所有知识点，从构建表格到解读箱线图。
1. What is Cumulative Frequency? | 什么是累积频率？
Cumulative frequency is the running total of frequencies up to a certain value in a data set. When data are grouped into classes, you can add up the frequencies sequentially to see how many data points lie below each upper class boundary. It is particularly useful for finding medians and quartiles without needing the original raw data.
累积频率是数据集中到某个值为止的频率累计总和。当数据被分成组时，你可以按顺序累加各组的频数，以了解有多少数据点低于每个组的上限。这在不需要原始原始数据的情况下，对求中位数和四分位数特别有用。
2. Constructing a Cumulative Frequency Table | 构建累积频率表
To build a cumulative frequency table, start with a grouped frequency distribution. Add a third column and, for each row, sum the frequency of that class with the cumulative frequency of the previous row. The final cumulative frequency should equal the total number of observations, n.
要构建累积频率表，从分组频率分布开始。添加第三列，对于每一行，将该组的频数与前一行的累积频率相加。最终的累积频率应等于观测总数 n。
Example: Ages of participants in a survey: 0-10 (freq 4), 10-20 (7), 20-30 (10), 30-40 (5), 40-50 (3). Cumulative frequencies: 4, 11, 21, 26, 29. The upper boundaries are 10, 20, 30, 40, 50.
示例：某调查参与者年龄：0-10 (频数4), 10-20 (7), 20-30 (10), 30-40 (5), 40-50 (3)。累积频率：4, 11, 21, 26, 29。上界为10, 20, 30, 40, 50。
3. Drawing a Cumulative Frequency Curve | 绘制累积频率曲线
Plot the cumulative frequency against the upper boundary of each class. Use a smooth curve to connect the points; never join them with straight line segments. The curve should start at the lower boundary of the first class (with cumulative frequency 0) and end at the last upper boundary with cumulative frequency n. Often, the lower boundary of the first interval is included as (lower bound, 0).
以每个组的上界为横坐标，累积频率为纵坐标描点。用平滑曲线连接这些点；切勿用直线段连接。曲线应从第一个组的下界（累积频率为0）开始，到最后一个上界处累积频率为 n 结束。通常会把第一个区间的下界作为点 (下界, 0) 加入。
Remember to label axes clearly: x-axis with the variable and unit, y-axis 'Cumulative frequency'.
切记清晰地标注坐标轴：x 轴标上变量及单位，y 轴标上 'Cumulative frequency'。
4. Estimating the Median | 估算中位数
The median is the value that splits the ordered data into two equal halves. From the cumulative frequency graph, find the position of the median: n/2. Draw a horizontal line from n/2 on the cumulative frequency axis to the curve, then drop a vertical line to the x-axis. The reading on the x-axis is the estimated
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