📚 6C Presenting Data | 数据展示
Data presentation is not just about creating graphs - it is about selecting the most meaningful way to display information so that patterns, trends, and unusual features become visible. In IB Mathematics, mastering data presentation enables you to interpret real-world situations, compare distributions, and communicate statistical findings clearly and accurately.
数据展示不仅仅是绘制图表——它是选择最有意义的方式来显示信息，以便让模式、趋势和不寻常的特征显现出来。在IB数学中，掌握数据展示能够使你解释现实情况、比较分布，并清晰准确地传达统计结果。
1. Organising Raw Data | 整理原始数据
essential to define interval boundaries precisely and to use consistent notation, such as 0 ≤ x < 10.
在可视化数据之前，第一步是将原始数值整理成频率表。对于取值较少的离散数据，简单的频率表列出每个值及其计数。对于连续数据或取值较多的离散数据，我们将数据分组到区间中。必须精确定义区间边界，并使用一致的表示法，例如 0 ≤ x < 10。
When constructing grouped frequency tables, we often include columns for class midpoint (to be used later for calculating an estimate of the mean), cumulative frequency, and relative frequency. The midpoint of an interval is calculated as (lower bound + upper bound) / 2. Cumulative frequency is the running total of frequencies.
在构建分组频率表时，我们通常加入组中点（用于后续估计平均值）、累积频率和相对频率列。区间的组中点计算为（下限 + 上限）÷ 2。累积频率是频率的累计总和。
Example: The following table organises test scores for 30 students.
示例：下表整理了30名学生的考试成绩。
| Score interval 分数区间 | Frequency 频率 | Midpoint 组中点 | Cumulative frequency 累积频率 |
|---|---|---|---|
| 0 ≤ x < 10 | 2 | 5 | 2 |
| 10 ≤ x < 20 | 5 | 15 | 7 |
| 20 ≤ x < 30 | 8 | 25 | 15 |
| 30 ≤ x < 40 | 10 | 35 | 25 |
| 40 ≤ x < 50 | 5 | 45 | 30 |
This table already gives an idea of the distribution: scores are concentrated in the 30–40 interval. The cumulative frequency column will be used to draw a cumulative frequency graph.
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