Comparing Distributions of a Quantitative Variable · 比较定量变量的分布
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| parallel boxplots/ˈpærəlel ˈbɒksplɒts/ | 平行箱线图 | píng xíng xiāng xiàn tú |
Putting two groups side by side
- Often the real question is a comparison: do boys and girls, or two treatments, differ?
- Show the groups together with parallel boxplots 平行箱线图 or back-to-back displays.
- Then compare them explicitly, feature by feature.
- A good comparison names the difference and its direction, in context.
把两组并排放
- 真正的问题常是比较:男生和女生,或两种处理,有区别吗?
- 用并列箱线图或背靠背图把各组放在一起。
- 然后明确地逐特征比较它们。
- 好的比较说出差异及其方向,结合情境。
One group's boxplot · 一组的箱线图
Placing two boxplots side by side lets you compare their centers, spreads, and shapes explicitly. · 并排放置两个箱线图可明确比较它们的中心、离散度和形状。
Parallel boxplots are a good way to compare two or more distributions. · 平行箱线图是比较两个或多个分布的好方法。
They align groups on the same scale. · 它们在同一尺度上对齐各组。
Compare shape, center, spread
- Shape: is each group symmetric or skewed? Do they differ in form?
- Center: which group has the higher median (or mean)? By how much?
- Spread: which group is more variable (bigger IQR or SD)?
- Address all three — a comparison that mentions only the center is incomplete.
比较形状、中心、分散
- 形状: 每组对称还是偏斜?它们在形态上有区别吗?
- 中心: 哪组的中位数(或平均数)更高?高多少?
- 分散: 哪组更变异(更大的 IQR 或标准差)?
- 三项都要处理——只提中心的比较是不完整的。
A complete comparison of two groups addresses which features? · 两组完整比较涉及哪些特征？
Shape, center, spread, and unusual features for both groups. · 两组的形状、中心、离散度和异常特征。
A wider box (larger IQR) means a group is... · 更宽的箱体（更大的 IQR）意味着一组...
Bigger IQR = more spread = more variable. · IQR 越大 = 离散度越大 = 变异性越大。
Use comparative language
- Say it comparatively: "Group A's median is greater than Group B's," or "Group A is more variable than Group B."
- Vague statements ("they're different") earn no credit — be specific about what differs and which way.
- Always tie the comparison to the context (the actual variable and groups).
- Comparative words — greater, less, more spread out — are what graders look for.
使用比较性语言
- 比较性地说:"A 组的中位数大于 B 组的",或"A 组比 B 组更变异"。
- 含糊的陈述("它们不同")拿不到分——要具体说什么不同、朝哪个方向。
- 永远把比较系于情境(实际变量和组)。
- 比较性词语——更大、更小、更分散——正是评分者所看的。
Which statement earns credit on the AP exam? · 哪项陈述能在 AP 考试中得分？
Explicit, directional, in context. · 明确、定向、置于情境中。
Comparisons should be ____ — stating which group is greater and by how much. · 比较应是____——说明哪组更大及大多少。
Directional, quantified, in context. · 定向、量化、置于情境中。
Note outliers and unusual features
- Do the groups differ in outliers or other unusual features?
- One group might have a high outlier the other lacks, or a gap.
- Mention these differences too — they can be the most interesting finding.
- A complete comparison covers shape, center, spread, and unusual features for both groups.
记下离群值与异常特征
- 各组在离群值或其他异常特征上有区别吗?
- 一组可能有另一组没有的高离群值,或一个间隙。
- 这些差异也要提——它们可能是最有趣的发现。
- 完整的比较对两组都涵盖形状、中心、分散和异常特征。
If one group has a low outlier the other lacks, you should... · 若一组有低离群值而另一组没有，你应该...
Differences in outliers are part of a complete comparison. · 离群值的差异是完整比较的一部分。
Comparisons must be explicit and directional: "Group A's median (72) is higher than Group B's (65)" — not just "the medians are different." State which group is greater/more variable, by roughly how much, in context. Merely describing each group separately, without comparing, misses the point.
比较必须明确且有方向:"A 组的中位数(72)高于 B 组的(65)"——而不只是"中位数不同"。说出哪组更大/更变异、大约多少,结合情境。仅分别描述每组、不作比较,就没抓住要点。
Parallel boxplots of test scores for Class A and Class B.
- Center: Class A's median ($78$) is greater than Class B's ($70$).
- Spread: Class B is more variable (a wider box/IQR).
- Shape/unusual: both roughly symmetric, but Class B has a low outlier that Class A lacks.
A 班和 B 班考试分数的并列箱线图。
- 中心: A 班的中位数($78$)大于 B 班的($70$)。
- 分散: B 班更变异(更宽的箱/IQR)。
- 形状/异常: 两者大致对称,但 B 班有一个 A 班没有的低离群值。
Compare distributions with parallel boxplots (or back-to-back plots), addressing shape, center, spread, and unusual features for both groups. Use explicit comparative language ("greater than," "more variable than") with direction and context — not just "they differ."
用并列箱线图(或背靠背图)比较分布,对两组都处理形状、中心、分散和异常特征。使用明确的比较性语言("大于""更变异")并带方向和情境——而不只是"它们不同"。