Describing the Distribution of a Quantitative Variable · 定量变量的分布描述
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| Shape/ʃeɪp/ | 形状 | xíng zhuàng |
| Center/ˈsentə/ | 中心 | zhōng xīn |
| Spread/spred/ | 分布范围 | fēn bù fàn wéi |
| Symmetric/sɪˈmetrɪk/ | 对称 | duì chèn |
| Skewed left/skjuːd left/ | 左偏 | zuǒ piān |
| skewed right/skjuːd raɪt/ | 右偏 | yòu piān |
| clusters/ˈklʌstəz/ | 群 | qún |
| gaps/ɡæps/ | 间隙 | jiàn xì |
| outliers/ˈaʊtlaɪəz/ | 离群值 | lí qún zhí |
Telling the story of a distribution
- Once you've graphed a quantitative variable, you describe what you see — in words, in context.
- The four things to mention: shape, center, spread, and unusual features.
- Cover all four and you've summarized the distribution completely.
- "In context" means naming the variable and its units, not just abstract numbers.
讲述一个分布的故事
- 一旦你给数量变量作了图,就要描述你所见——用文字,结合情境。
- 要提的四件事:形状、中心、分散、异常特征。
- 涵盖全部四项,你就完整地汇总了分布。
- "结合情境"意味着说出变量及其单位,而非只给抽象数字。
A complete description of a distribution mentions which features? · 完整的分布描述应提及哪些特征？
Shape, center, spread, and unusual features — in context. · 形状、中心、离散度和异常特征——需置于情境中。
Shape
- Shape 形状 describes the overall form of the distribution.
- Symmetric 对称: the left and right halves roughly mirror each other.
- Skewed left 左偏: a long tail stretches to the left (low values); skewed right 右偏: a long tail to the right (high values).
- The tail's direction names the skew — skew points where the tail goes.
形状
- 形状描述分布的整体形态。
- 对称:左右两半大致互为镜像。
- 左偏:一条长尾伸向左(低值);右偏:一条长尾伸向右(高值)。
- 尾巴的方向命名偏斜——偏向尾巴所去的方向。
Reading the shape · 读取形状
A long tail to one side means the distribution is skewed that way — skew is named for the tail. · 一侧有长尾意味着分布向该方向偏斜——偏度以尾部命名。
A distribution with a long tail stretching to the left is... · 向左延伸长尾的分布是...
Skew is named for the tail direction → left. · 偏度以尾部方向命名 → 左侧。
Center and spread
- Center 中心: a typical value — roughly where the data pile up (mean or median).
- Spread 分布范围 (variability): how stretched out the values are (range, IQR, standard deviation).
- A distribution with small spread is tightly clustered; large spread is widely scattered.
- Together, center and spread answer "typical value, and how much it varies."
中心与分散
- 中心:一个典型值——数据大致堆积之处(平均数或中位数)。
- 分散(变异):值有多铺开(极差、四分位距、标准差)。
- 分散小的分布紧密聚集;分散大的广泛散布。
- 中心与分散合起来回答"典型值,以及它变化多少"。
The "center" of a distribution refers to... · 分布的“中心”指的是...
Center = typical value (mean or median). · 中心 = 典型值（均值或中位数）。
Unusual features
- Note distinctive features: clusters 群 (separate groups), gaps 间隙 (empty stretches), and possible outliers 离群值 (values far from the rest).
- Outliers may be errors, or genuinely unusual cases — flag them.
- A gap or two clusters may hint at two different sub-populations mixed together.
- Always describe these in context of the real variable.
异常特征
- 记下独特特征:簇(分开的组)、间隙(空缺的区段)、以及可能的离群值(远离其余的值)。
- 离群值可能是错误,或真正不寻常的案例——把它们标记出来。
- 一个间隙或两个簇可能暗示两个不同的子总体混在一起。
- 永远结合真实变量的情境来描述这些。
A value far from the rest of the data is a possible . · 远离其余数据的值是一个可能的。
Flag outliers as unusual features. · 将离群值标记为异常特征。
A good description states shape/center/spread in context (with the variable and units). · 良好的描述应在情境中陈述形状/中心/离散度（包含变量和单位）。
Always describe in context, not as bare numbers. · 始终在情境中描述，而非仅列裸数。
Two separate clusters with a gap between them may suggest... · 两个分离的簇及其间的空隙可能表明...
Clusters/gaps can reveal mixed sub-populations. · 簇和空隙可揭示混合的子群体。
Skew is named for the tail, not the peak. A distribution with most data on the right and a long tail trailing to the left is skewed left — even though the "bump" is on the right. And always describe shape/center/spread/unusual features in context (name the variable and units), not as bare numbers.
偏斜以尾巴命名,而非峰。 大部分数据在右、一条长尾拖向左的分布是左偏——尽管那个"隆起"在右边。而且永远结合情境(说出变量和单位)描述形状/中心/分散/异常特征,而非光秃秃的数字。
Describe household incomes in a town.
- Shape: skewed right — most incomes are moderate, with a long tail of a few very high earners.
- Center: a typical income around, say, $45{,}000 (median).
- Spread & unusual: a wide spread, with a few high outliers (the wealthiest households).
描述一个城镇的家庭收入。
- 形状: 右偏——大多数收入中等,有一条少数极高收入者的长尾。
- 中心: 典型收入约 $45{,}000(中位数)。
- 分散与异常: 分散很大,有几个高离群值(最富有的家庭)。
Describe a quantitative distribution by its shape (symmetric / skewed left / skewed right — named by the tail), center (typical value), spread (variability), and unusual features (clusters, gaps, outliers) — always in context with the variable and units.
用形状(对称 / 左偏 / 右偏——以尾巴命名)、中心(典型值)、分散(变异)、异常特征(簇、间隙、离群值)描述数量分布——永远结合情境,带上变量和单位。