Representing a Quantitative Variable with Graphs · 用图表表示定量变量
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| histogram/ˈhɪstəɡræm/ | 直方图 | zhí fāng tú |
| dotplot/ˈdɒtplɒt/ | 点图 | diǎn tú |
| stem-and-leaf plot/stem ænd liːf plɒt/ | 茎叶图 | jīng yè tú |
| bins/bɪnz/ | 组距 | zǔ jù |
| ogive/ˈɒɡɪv/ | 累积频率图 | lěi jī pín lǜ tú |
Seeing the shape of numbers
- For a quantitative variable, we want to see how the values are distributed — clustered, spread, symmetric?
- Three standard displays reveal this: the histogram 直方图, dotplot 点图, and stem-and-leaf plot 茎叶图.
- Each shows the same data differently, but all reveal the overall shape.
- Reading these plots is where "describing a distribution" begins.
看出数字的形状
- 对数量变量,我们想看值是如何分布的——聚集、分散、对称?
- 三种标准图揭示这点:直方图、点图、茎叶图。
- 每种用不同方式展示同一数据,但都揭示整体形状。
- 阅读这些图正是"描述分布"的起点。
Histograms and bins
- A histogram groups values into intervals called bins 组距, then draws a bar for each bin's count.
- Unlike a bar chart, the bars touch — the scale is continuous.
- Bin choice matters: too few bins hide the shape; too many make it noisy. Aim for a number that reveals the real pattern.
- Taller bars = more data in that interval.
直方图与组距
- 直方图把值分组到叫组距的区间,再为每个组距的计数画一根条。
- 与条形图不同,条是相接的——刻度是连续的。
- 组距的选择很重要: 太少组距会隐藏形状;太多会显得杂乱。目标是能揭示真实规律的数目。
- 更高的条 = 该区间里更多数据。
A histogram's shape · 直方图的形状
A histogram groups values into touching bins — the bar heights reveal where the data pile up. · 直方图将值分组到相连的区间中——条形高度揭示了数据堆积的位置。
A histogram's bars touch because the scale is continuous. · 直方图的条形相连是因为刻度是连续的。
Touching bars distinguish it from a categorical bar chart. · 相连的条形将其与分类条形图区分开来。
Choosing too few bins in a histogram tends to... · 直方图选择的区间过少倾向于……
Too few bins over-smooth and hide features. · 区间过少会导致过度平滑并掩盖特征。
The intervals that group a histogram's values are called . · 将直方图数值分组的区间称为。
Each bin becomes one bar. · 每个组对应一个条形。
Dotplots and stem-and-leaf
- A dotplot stacks one dot per value above a number line — great for small data sets, keeps every value.
- A stem-and-leaf plot splits each number into a stem (leading digits) and leaf (last digit), so you see shape and the actual values.
- Both are best for small-to-moderate data; a histogram handles large sets.
- All three answer "where do the values pile up?"
点图与茎叶图
- 点图在数轴上方每个值堆一个点——对小数据集很好,保留每个值。
- 茎叶图把每个数拆成茎(前导数字)和叶(末位数字),所以你既看到形状又看到实际值。
- 两者对中小数据最好;直方图处理大数据集。
- 三者都回答"值堆积在哪里?"
A stem-and-leaf plot shows the shape and keeps the actual data values. · 茎叶图展示分布形状并保留实际数据值。
The leaves are the actual last digits. · 叶是实际的末位数字。
Cumulative graphs (ogives)
- A cumulative relative frequency graph (ogive 累积频率图) plots the running total proportion up to each value.
- It rises from $0$ to $1$ (or $0\%$ to $100\%$).
- Read a percentile from it: go up to a value, read across to the proportion below it.
- Great for questions like "what score is the $75$th percentile?"
累积图(累积频率曲线)
- 累积相对频率图(累积频率图)绘制直到每个值的累计比例。
- 它从 $0$ 升到 $1$(或 $0\%$ 到 $100\%$)。
- 从它读百分位数:上到某个值,横向读出它以下的比例。
- 非常适合"哪个分数是第 $75$ 百分位?"这类问题。
A cumulative relative frequency graph (ogive) is used to read... · 累积相对频率图（Ogive）用于读取……
Read across from a proportion to find a percentile. · 从比例横读以找到百分位数。
An ogive (cumulative relative frequency graph) rises from... · 累积频率图（累积相对频率图）从...上升...
It accumulates proportions from $0$ up to $1$. · 它从 $0$ 累积至 $1$ 的比例。
A histogram is for quantitative data — its bars touch (a continuous scale), unlike a categorical bar chart's separated bars. And your bin width shapes the picture: too wide erases features, too narrow adds noise. Try a sensible number of bins that shows the true shape, and state the bin width you used.
直方图用于数量数据——它的条是相接的(连续刻度),不同于分类条形图分开的条。而你的组距宽度塑造图形:太宽抹去特征,太窄增添噪声。试一个能显示真实形状的合理组距数,并说明你用的组距宽度。
Test scores: $62, 65, 71, 71, 73, 78, 82, 85, 91$.
- Stem-and-leaf (stems = tens): $6\,|\,2\,5$; $7\,|\,1\,1\,3\,8$; $8\,|\,2\,5$; $9\,|\,1$.
- The shape is roughly symmetric, centered around the $70$s.
- A histogram with bins of width $10$ would show the same clustering.
考试分数:$62, 65, 71, 71, 73, 78, 82, 85, 91$。
- 茎叶图(茎 = 十位):$6\,|\,2\,5$;$7\,|\,1\,1\,3\,8$;$8\,|\,2\,5$;$9\,|\,1$。
- 形状大致对称,中心在 $70$ 多。
- 组距宽度为 $10$ 的直方图会显示相同的聚集。
Display a quantitative variable with a histogram (bars touch; choose sensible bins), a dotplot, or a stem-and-leaf plot — all reveal the shape. A cumulative relative frequency graph (ogive) rises from $0$ to $1$ and lets you read percentiles. Histogram bars touch, unlike categorical bar charts.
用直方图(条相接;选合理组距)、点图或茎叶图展示数量变量——都揭示形状。累积相对频率图(累积频率曲线)从 $0$ 升到 $1$,让你读百分位数。直方图的条相接,不同于分类条形图。