Learning Hub / Unit 2
Unit 2 of 6 · Round S-02 · target day 2026-11-23
Error, averages and an honest baseline
Is "tomorrow equals today" a good forecast? Before you can say yes or no you need a ruler for being wrong. This unit builds that ruler: the exact error the challenge uses, the mean absolute error (MAE), and a baseline that any forecast should beat.
"明天等于今天"算不算好预测?要回答,先得有一把衡量"错了多少"的尺子。本单元做出这把尺子:挑战赛用的精确误差、平均绝对误差(MAE),以及任何预测都应该胜过的基准。
60-minute lesson + 20-minute round touchReal data: Boston Logan, 47 daysPractice tables marked SYNTHETIC
Goals and exit evidence
- Compute one absolute error and the mean absolute error (MAE) by hand, with units.
- Use the exact challenge formula
|9t − 50F + 1600| / 90and explain why 14.0 °C against 57 °F is an error of 1/9 °C, shown as 0.11. - Explain why a baseline (persistence, M0) is a diagnostic, not a prize, and why both forecasts must be compared on the same valid days.
Exit evidence: one error table with units, valid days and working shown. It is not graded on how accurate the forecasts were.
- 手算一次绝对误差和平均绝对误差(MAE),并写上单位。
- 使用赛制精确公式
|9t − 50F + 1600| / 90,说明 14.0 °C 对 57 °F 的误差为何是 1/9 °C、显示为 0.11。 - 说明基准(持续性 M0)是诊断工具而不是奖项,以及为什么两种预测必须在同一组有效日上比较。
出口证据:一张带单位、有效日和计算过程的误差表。不按预测准不准打分。
Story hook
On 3 September 2026 a public day-ahead forecast for Boston Logan said the high would reach about 84 °F. The thermometer topped out at 73 °F. The next day the same kind of forecast said 80.9 °F and the high was 85 °F. One miss was 11 degrees too warm, the other about 4 degrees too cool. If you simply add the misses with their signs, they partly cancel and the forecast looks better than it was. How should we count?
2026 年 9 月 3 日,一份公开的提前一天预报说 Boston Logan 最高温约 84 °F,实测只到 73 °F。第二天同类预报说 80.9 °F,实测 85 °F。一次偏暖 11 度,一次偏冷约 4 度。如果带着正负号直接相加,它们会部分抵消,预报看上去比实际更好。我们应该怎样算?
Values from /learn/data/bos_logan_47d.json.
Concepts
1 · Absolute error
Error = |forecast − observed|. The bars mean "drop the sign". 2 degrees too warm and 2 degrees too cool are both an error of 2. The unit stays: °C in, °C out.
误差 = |预测 − 实测|。竖线表示"去掉正负号"。偏暖 2 度和偏冷 2 度误差都是 2。单位不变:输入 °C,误差也是 °C。
2 · Mean absolute error
MAE = (sum of absolute errors) ÷ (number of valid days). Take absolute values first, then average. Never let warm and cool misses cancel. A day without an official observation is not a day with error zero.
MAE = 绝对误差之和 ÷ 有效日数。先取绝对值,再平均,不能让偏暖和偏冷抵消。没有官方观测的日子不是"误差为 0"的日子。
3 · An honest baseline
Persistence (M0) says "tomorrow = the last complete day". At the 18:00 EST cutoff on day D−1, day D−1 is not finished, so M0 uses day D−2. A method is only interesting if it beats this on the same days.
持续性(M0):"明天 = 最后一个完整日"。D−1 日 18:00 EST 截止时,D−1 还没结束,所以 M0 用 D−2。一个方法只有在同样的日子上胜过它,才值得关注。
Why the formula has 9, 50 and 1600. You enter tenths of a degree Celsius, t (14.0 °C is t = 140). The official report is a whole °F, F. In tenths of °C the observation is (F − 32) × 50/9, so the error in °C is |t/10 − (F − 32)·5/9| = |9t − 50F + 1600| / 90. Integers only, so nothing is rounded until the very end (half-up, two decimals).
公式里为什么有 9、50 和 1600。你输入的是 0.1 °C 的整数 t(14.0 °C 记作 t = 140);官方报告是整数 °F,记作 F。换成摄氏后误差 |t/10 − (F − 32)·5/9| 正好等于 |9t − 50F + 1600| / 90。全程只用整数,直到最后一步才四舍五入(半入,两位小数)。
Worked example with real Boston data
Below are the first eight days of the 47-day classroom dataset (September 2026, °F). For each target day we compare two forecasts: the public day-ahead forecast (our stand-in for line M2) and persistence M0 (the observed high two days earlier). Errors are computed live from the data file.
下面是 47 天课堂数据的前八天(2026 年 9 月,°F)。每个目标日比较两种预测:公开的提前一天预报(这里代替 M2 线)和持续性 M0(两天前的实测最高温)。误差由页面从数据文件实时计算。
| Date | Observed °F | Forecast °F | |error| forecast | M0 = D−2 °F | |error| M0 |
|---|---|---|---|---|---|
| Loading data… | |||||
The first two days have no M0 value: there is no complete day two days earlier in this file. They are dropped from both columns so the comparison uses the same valid days. These observations come from the IEM ASOS daily summary and are preliminary; official challenge scoring uses the NWS climate report (CLI), which can differ by a degree.
前两天没有 M0 值:文件里没有两天前的完整日。它们在两列中都被剔除,保证比较用同一组有效日。这些观测来自 IEM ASOS 日汇总,属初步值;正式比赛用 NWS 气候报告(CLI)计分,两者可能差 1 度。
Activity A · The exact error calculator
Enter a forecast in °C (one decimal) and an official high in whole °F. The calculator shows every step with integers, the reduced fraction, and the two-decimal display used on results pages.
输入一个 °C 预测(一位小数)和一个官方整数 °F 最高温。计算器用整数展示每一步、约分后的分数,以及结果页使用的两位小数显示。
Activity B · Beat the baseline? (real 47 days)
Pick a window of target days. The page computes MAE for persistence (M0) and the public forecast over exactly the same valid days, in °F and in °C. Then predict before you press the button: which will win, and by how much?
选择一段目标日。页面在完全相同的有效日上计算持续性(M0)与公开预报的 MAE(°F 与 °C)。按按钮之前先写下你的预测:谁会赢,差多少?
Check for understanding
Questions 1 to 3 use the SYNTHETIC seven-day table.
| Day (SYNTHETIC) | Observed °C | Student °C | Fixed baseline °C |
|---|---|---|---|
| D1 | 12 | 12 | 10 |
| D2 | 14 | 13 | 10 |
| D3 | 13 | 13 | 10 |
| D4 | 9 | 10 | 10 |
| D5 | 8 | 9 | 10 |
| D6 | 11 | 10 | 10 |
| D7 | 10 | 11 | 10 |
1. Find each daily absolute error and the MAE for the student and for the baseline.求学生与基准逐日绝对误差和 MAE。
Answer
Student errors 0, 1, 0, 1, 1, 1, 1: sum 5, MAE = 5/7 ≈ 0.71 °C. Baseline errors 2, 4, 3, 1, 2, 1, 0: sum 13, MAE = 13/7 ≈ 1.86 °C.
学生误差 0、1、0、1、1、1、1,总和 5,MAE = 5/7 ≈ 0.71 °C。基准误差 2、4、3、1、2、1、0,总和 13,MAE = 13/7 ≈ 1.86 °C。
2. If D2's observation is missing, recompute on the same six days. May you drop D2 for the student but keep seven days for the baseline?若 D2 实测缺失,在同样的六天上重算。能否只给学生剔除 D2,而基准仍保留七天?
Answer
Student 4/6 = 2/3 ≈ 0.67 °C; baseline 9/6 = 1.5 °C; improvement 5/6 ≈ 0.83 °C. No: both series must drop the same day, or the comparison is unfair.
学生 4/6 = 2/3 ≈ 0.67 °C;基准 9/6 = 1.5 °C;改善 5/6 ≈ 0.83 °C。不能:两个序列必须剔除同一天,否则比较不公平。
3. "My average error is 0, because my warm and cool misses cancel." Rewrite this honestly."我的平均误差是 0,因为偏高和偏低抵消了。"请诚实地改写。
Answer
Take the absolute value of each day first, then average. The signed average is called bias: it tells you whether you lean warm or cool, not how big your errors are.
先逐日取绝对值再平均。带符号的平均叫偏差(bias):它告诉你整体偏暖还是偏冷,而不是误差有多大。
4. A forecast of 0.0 °C meets an official 32 °F. What does the formula give, and why?预测 0.0 °C,官方 32 °F。公式给出多少,为什么?
Answer
|9·0 − 50·32 + 1600| / 90 = 0/90 = 0, displayed 0.00. 32 °F is exactly 0 °C.
|9·0 − 50·32 + 1600| / 90 = 0/90 = 0,显示 0.00。32 °F 恰好是 0 °C。
5. You beat persistence this week. Can you say you will always beat it?这周你胜过了持续性。能说你以后总会胜过它吗?
Answer
No. You can say "on these days, under these rules, my MAE was lower". One week is a small sample; some weeks are easier than others. Season 1 has no leaderboard for exactly this reason.
不能。只能说"在这些日子、这些规则下,我的 MAE 更低"。一周样本很小,有的周更容易。首季不设排行榜正是这个原因。
Classroom: 20-minute round touch
| 0–3 | Read the round card for S-02: station, variable, unit, target day, cutoff (2026-11-22 18:00 EST = 23:00 UTC).读 S-02 题卡:站点、变量、单位、目标日、截止(2026-11-22 18:00 EST = 23:00 UTC)。 |
| 3–8 | Look at the last complete day and the public forecast; estimate a high in °C first, without AI.看最后一个完整日与公开预报;先不用 AI,独立估一个 °C 最高温。 |
| 8–13 | Seal the forecast, get a receipt, write down the first 8 characters of its sha256.封存预测,拿到回执,记下 sha256 前 8 位。 |
| 13–18 | After the reveal: compute your exact error with Activity A and compare with lines M0 and M2.揭晓后:用活动 A 算自己的精确误差,与 M0、M2 两条线对照。 |
| 18–20 | Say one thing you will change next time, and one thing you cannot conclude yet.说一件下次要改的事,和一件还不能下结论的事。 |
Full 60-minute lesson plan
| 0–8 | "Two degrees too warm" and "two degrees too cool": introduce absolute value.用"高 2 度"和"低 2 度"引出绝对值。 |
| 8–20 | Learners fill the seven-day error table; pairs cross-check one row.学生填七日误差表,两人互查一行。 |
| 20–30 | Compute both MAEs and the improvement over the baseline.计算两个 MAE 与基准改善量。 |
| 30–40 | Missing-day exercise: drop the same day from both series.缺失日练习:两列同日剔除。 |
| 40–50 | Activity B on the real 47 days: predict first, then compute.在真实 47 天上做活动 B:先预测,再计算。 |
| 50–60 | Three sentences: the result, its limit, and the next test. Hand in the exit table.三句话:结果、局限、下一次检验。交出口表。 |
Age bands
10–12
Do D1–D3 first (student 1/3 °C, baseline 3 °C), then the full table. Use the calculator for the °F conversion.
先算 D1–D3(学生 1/3 °C,基准 3 °C),再完成全表。°F 换算交给计算器。
13–15
Full table, the missing-day case and relative improvement (8/13 ≈ 61.5%). Derive the 9, 50, 1600 in the formula.
完成全表、缺失日和相对改善(8/13 ≈ 61.5%)。推导公式中的 9、50、1600。
16–17
Recompute in a spreadsheet; discuss why consecutive days are not independent and why seven days cannot show a significant edge.
用电子表格复算;讨论相邻日为何不独立,以及为何七天不能说明显著优势。
No-device alternative. Print the seven-day table on squared paper. The teacher reads the 47-day values for one week aloud; learners compute persistence errors by hand. The teacher spot-checks two rows per learner. Paper cards are stamped "classroom practice" and are never presented as server receipts.
无设备替代。把七日表印在方格纸上;教师朗读 47 天数据中的一周,学生手算持续性误差;教师每人抽查两行。纸卡盖"课堂演练",不当作服务器回执。
Five numbers (after each round)
Math map for this unit
| NS-L2-NEGORDER | Ordering negatives on the number line |
| EE-L2-EVAL | Evaluate an expression with full operations |
| MD-L2-UNITSENSE | Units and quantity sense |
| RP-L2-PCTBASE | Percent base |
| XC-L2-ASKED | Report the quantity asked |
Sources: SOURCES.json · lesson text merged from m681 lesson 2, spec 41 unit 2 and the L2 classroom line.