契苾小优_雅思陪练_2026-10-02_数学_比例会骗人：当比例开始骗人

➗比例会骗当比例开始骗人

外语自言自语陪练 ｜ 雅思冲分 ｜ 2026-10-02 周五 ｜ 2026-10-02

本系列为「契苾小优」雅思备考专用输出，转载请注明出处。

外语自言自语｜场景：清晨书房·国庆长假日更静｜语言：英语为主（English-led）

陪练对象：小优（契苾小优，古凉州今武威）

日期：2026年10月2日（周五）· 国庆假期第二天

外语独白

This morning the house is quiet, the kind of quiet you only get on a long holiday. I sat with a pie chart, the one showing how the world's people are spread out. And I caught myself doing the thing I always do: I looked at Asia taking up more than half the circle and thought, well, that looks about right, doesn't it. Then I paused. 嗯，这就是元认知：不是去算比例，是察觉自己「以为懂了」其实没细想。Meta-cognition sounds fancy, but it is just standing above your own thinking and watching it work. Do I actually know why Asia is 56 per cent, or did I only nod because the number felt familiar?

The word that trips me up again is proportion versus percentage. They are cousins; proportion is the relationship itself, percentage is that relationship times a hundred. I keep saying "the proportion is 56 per cent", which is fine, but then I slip into "the percentage rate" for no reason at all. percentage is not a rate. 这俩我老混，percentage 不是 rate，rate 是 per unit time，percentage 只是 per hundred。小错，可一开口就露怯。

What I like about today's maths is that it feeds straight back into knowing myself. A proportion can look calm on a pie and still hide a wild swing if the sample is small. So when I say "most people think X", am I quoting a real survey, or just the three friends rattling around in my own head? That is the meta part: catching the gap between what I claim to know and what I actually checked. 这词儿是之前统计期学的 sample，今天捡回来用，倍儿顺手。

I am still slow at saying "the margin of error widens as the sample shrinks" in one clean breath. Give me a few more mornings.

语法笔记

比比例、比份额，看图写作天天用。说 "A 是 B 的两倍大" 正式写作用 twice as large as，不推荐 two times larger than；说差距大用 far larger than 或 considerably greater。百分比前可加 roughly / just over / just under 调精度：Asia accounted for just over half。注意 more bigger 是错的，big 本身已是比较级形态，直接 bigger。另：the + 比较级…，the + 比较级… 是今天的主打句型（样本越大，误差越小），前后两个比较级要成对，别只写一半。

中式英语易错

❌ 中式英语 the proportion is 56% rate

✅ 地道表达 the proportion is 56%

percentage 不是 rate，别写 56% rate

❌ 中式英语 most of people think so

✅ 地道表达 most people think so

most 后不接 of，除非 most of the people

❌ 中式英语 I very know this

✅ 地道表达 I know this very well

very 不能修饰动词 know

❌ 中式英语 data is clear

✅ 地道表达 the data show a clear pattern

IELTS 多数据点倾向复数 show；单条统计量可用 shows

❌ 中式英语 a percent of

✅ 地道表达 a percentage of

percent 一般不单独加 a 前置，写作用 percentage

❌ 中式英语 my intuition tell me

✅ 地道表达 my intuition tells me

intuition 当单数

同义替换

• proportion → share / fraction / slice（份额 / 部分 / 一块）

• roughly → approximately / about / just over（大约 / 差不多 / 略超）

• know → be aware / realize / grasp（意识到 / 领悟 / 掌握）

• gap → discrepancy / mismatch / blind spot（差异 / 不符 / 盲区）

• estimate → gauge / work out / put a number on（估量 / 算出 / 给个数）

• misleading → deceptive / bent / off（误导的 / 偏的 / 不对的）

今日新词

•proportion/prəˈpɔːʃn/ (n. 比例、份额) — pro- + portio (Latin, a part); family: portion, proportional. Eg. The proportion of Asia was 56% in 2019.

•percentage/pəˈsentɪdʒ/ (n. 百分比) — per centum (Latin, by the hundred) + -age. Eg. Only a small percentage of samples were checked.

•sample/ˈsɑːmpl/ (n. 样本、抽样) — *sam- (take one out); family: example. Eg. We drew a random sample of 1,000 people.

•margin/ˈmɑːdʒɪn/ (n. 余量、误差幅度) — margo (Latin, edge); family: marginal. Eg. The margin of error was plus or minus 3%.

•cognitive/ˈkɒɡnətɪv/ (adj. 认知的) — cognoscere (Latin, to know); family: recognise, cognition. Eg. This is a cognitive skill you can train.

•bias/ˈbaɪəs/ (n. 偏差、偏见) — from Greek "oblique". Eg. A small sample can introduce bias.

•statistic/stəˈtɪstɪk/ (n. 统计量、数据) — status (Latin, state); family: state, status. Eg. That statistic comes from UN DESA.

•intuition/ˌɪntjuˈɪʃn/ (n. 直觉) — intueri (Latin, to look within); family: intuitive. Eg. Trust intuition, but check it.

今日句型

• 新学 1：The larger the sample, the narrower the margin of error.（样本越大，误差幅度越窄。）the + 比较级…，the + 比较级…，今天的主打。

• 新学 2：It is easy to mistake a familiar number for a checked one.（容易把一个眼熟的数当成核实过的数。）元认知句式，给今日饼图用。

• 旧句回扣：the more you practise, the more it sticks（回扣 09-28 健康期 the more…the more）；well-connected（回扣 09-24 工作期，今日指「样本连成整体才靠谱」）。

今日表达 TOP3

•spot your own blind spot— see where you cannot see. The most meta-cognitive line of the day: first notice the place you do not see.

•a number can lie by being lonely— a figure misleads when its sample is too small. This puts sample size into plain words.

•nod along without checking— agree without verifying. That is exactly what I did with today's pie chart.

一词多义 · 小心熟词生义

•sample：今日义"样本（统计）"；另一常见义"样品、试听曲"，如 I got a free sample at the store. / a sample of the song.

•rate：今日义"比率、速率"；另一常见义"等级、价格"，如 a first-rate hotel / the exchange rate.

•margin：今日义"误差幅度、余量"；另一常见义"页边空白、利润"，如 write notes in the margin / profit margin.

•bias：今日义"偏差、偏见"；另一常见义"斜裁（布料）"，如 cut the cloth on the bias.

•figure：今日义"数字、图表"；另一常见义"人物、身形"，如 a historical figure / she has a fine figure.

•share：今日义"份额、占比"；另一常见义"分享、股份"，如 share the cake / buy shares.

•note：今日义"注意、注解"；另一常见义"音符、钞票"，如 play a note / a ten-pound note.

注意：统计话题最易踩 sample / rate / margin / figure 的熟词生义；写作 Task 1 里 figure 指「图表」、rate 指「比率」时，别顺手写成「人物」或「价格」。

学科短文

Statistics is, at heart, a discipline of humility. When we report that Asia housed 56.1 per cent of humanity in 2019, the number looks exact, yet it hides a thousand quiet choices: which borders count, how migrants are assigned, what "region" even means. The English word proportion comes from Latin pro portione, "according to a portion", and percentage from per centum, "by the hundred" — both are just ratios dressed up for comparison. Probability, from Latin probabilitas (to test, probare), was never a promise about one single toss but a statement about many. This is where meta-cognition enters: knowing that a single familiar statistic can masquerade as a verified fact. To think statistically is to keep asking whether the sample was broad, the margin honest, and one's own intuition checked. A number is not wisdom; it is only a prompt to look closer.

重点词点拨：

•masquerade as— 冒充、伪装成（此处指「眼熟的数假装成核实过的数」）。

•humility— 谦逊；此处指承认数字有局限、别把比例当真理。

•dressed up for comparison— 为比较而包装（比喻：比例和百分比本质都是比值，只是写法不同）。

•prompt— 提示、引子；此处指数字只是「让你再靠近看一眼」的由头。

•assign— 归类、指派；此处指把迁移者算进哪个区域是人为约定。

词根串联复习

今天的新词成一张网：proportion / portion / proportional 同走 portio（部分）；percentage / cent 同走 centum（一百）；sample / example 同走 sam-（取出的一份）；margin / marginal 同走 margo（边缘）；cognitive / recognise / cognition 同走 cognoscere（知道）；statistic / state / status 同走 status（站立、状态）；intuition / intuitive 同走 intueri（内省）。老词也来：09-24 工作期的 representative（代表，词根 praesent-* 在场）正好接今天的 sample，样本要能代表整体，才算数；09-28 健康期的 cumulative（累积，词根 cumulare 堆）今天换成比例语言：小样本叠不出大真相。

艾宾浩斯复习

Due words from old drills, run through today's new content.

The 09-28 health drill built "a buffer of fitness"; today that becomes the margin of error, the buffer of uncertainty: a small sample means a thin buffer and a shaky conclusion.

The 10-01 health drill used derivative for "heart-rate change rate"; today rate means "proportion", same word, one for time, one for share, so do not cross the wires.

The 09-25 education drill used cumulative; today it is proportion, both turn the scattered into the whole. Old words are not lost; they just come back in new clothes.

今日话题词卡

数学 · 数据与统计线（5–8 条，带词根）：

• proportion /prəˈpɔːʃn/ n. 比例 — 词根 pro- + portio（部分）

• percentage /pəˈsentɪdʒ/ n. 百分比 — 词根 centum（一百）

• sample /ˈsɑːmpl/ n. 样本 — 词根 *sam-（取出的一份）

• margin (of error) /ˈmɑːdʒɪn/ n. 误差幅度 — 词根 margo（边缘）

• bias /ˈbaɪəs/ n. 偏差 — 希腊语「斜的」

• statistic /stəˈtɪstɪk/ n. 统计量 — 词根 status（状态）

• cognitive /ˈkɒɡnətɪv/ adj. 认知的 — 词根 cognoscere（知道）

• intuition /ˌɪntjuˈɪʃn/ n. 直觉 — 词根 intueri（内省）

⚡ ⚡ 一嘴反应训练

Part 1 即兴，只给关键词，不写稿：

• Q：Do you think numbers can be misleading? — A 关键词：yes / small samples / familiar ≠ checked.

• Q：How do you check if a fact is true? — A 关键词：source / compare / ask why.

• Q：Are you good at noticing your own mistakes? — A 关键词：sometimes / meta / blind spot.

️ ️ 发音 / 连读提示

•proportion：母语音标 /prəˈpɔːʃn/ → 国际IPA /prəˈpɔːʃn/（重音在第二音节，尾音 ʃn 别丢成 ʃən）。

•cognitive：母语音标 /ˈkɒɡnətɪv/ → 国际IPA /ˈkɒɡnətɪv/（首音节 ɒ 是圆唇短 o，别读成 ʌ）。

•percentage：母语音标 /pəˈsentɪdʒ/ → 国际IPA /pəˈsentɪdʒ/（tʃ 破擦，别读成 dʒ；重音在第二音节）。

连读：the larger the sample，两个 the 之间轻读，larger 的 r 与 the 连成 /ðə ˈlɑːdʒə/，顺下来才像 native。

多语种句尾

Numeri non cogitant. (Latin, Leibniz: numbers do not think for themselves; it is the reader who thinks. Mathematics is only a tool, and meta-cognition is the hand that holds it.)

✍️ ✍️ 写作联动 · 看图写作

Task 1 写作任务（150 词 / 20 分钟）

The pie chart shows the share of the world's population by major region in 2019, based on UN DESA data. Summarise the information by selecting and reporting the main features, and make comparisons where relevant. 必须写 overview（整体最大的一块是谁）与 key features（Asia 过半、Africa 第二、其余合计不到一半），并按「大块 vs 小块」做分组比较。

本期图型描述句型（取自饼图句型包）

• The largest slice was held by Asia at 56.1%, followed by Africa at 20.5%.

• Asia and Africa together accounted for more than three quarters of the world's population.

• The proportion of Oceania was negligible at just 0.5%.

• Europe and Northern America made up 14.4%, while Latin America and the Caribbean stood at 8.4%.

• The remaining regions, taken together, represented less than a fifth of the total.

范文要点（3–4 条）

1. Overview：Asia alone held just over half of humanity；the circle is heavily lopsided.

2. Key feature 1：Africa was a clear second at about a fifth；the two top regions surpassed 75%.

3. Key feature 2：Europe & Northern America (14.4%) and Latin America & the Caribbean (8.4%) formed a middle band.

4. Key feature 3：Oceania was tiny at 0.5% — almost invisible on the chart.

统计旁注（几十字）

饼图把一个整体的 100% 切成扇区，看「部分占整体」的比例。易错：人眼比角很难，本图 5 块且口径混合（欧洲与北美合并为一区），类别偏多时宜改条形图；只有差异明显、块数少，饼图才清楚。

引导理解（从凉州看世界）

Liangzhou Lotus Mountain (Guzang Purple Mountain) has stayed green for a thousand years, and the people at its foot still live with the mountain to this day. Mathematics was never just a study ornament. The former-Liang Zhang Gui bronze galloping horse, known as 前凉张轨铜奔马, came from the Leitai tomb in ancient Liangzhou, 武威古凉州的雷台墓, cast with piece-moulds and an iron core inside the legs, the so-called 铁骨铜腿, iron bone and bronze legs. That horse, with three hooves off the ground, is pure calculation of proportion and mechanics. Which step of dividing the mould, joining it, and pouring the metal does not need a number? Wuwei, ancient Liangzhou, a six-dynasty capital and the chief city of the northwest, turned proportion into craft long ago. Today I compute the proportion of the world's population; the ancients computed the centre of gravity of a bronze horse. To know that a proportion can lie, and to know how to use proportion to make a horse stand, that is roughly what meta-cognition looks like in practice. The Liangzhou Leitai scenic area, 凉州雷台景区, also displays the bronze chariot-and-horse procession from that tomb, the 铜车马仪仗队, enlarged to six times the original size. Proportion, once more, this time scaled up big enough to walk through. 数学这件事，凉州人做了快两千年，知道比例会骗人，也知道怎么用比例把一匹马立住。

一词一世界，词根即思维。明天接着聊 (◕‿◕)