German Gymnasium Klasse 10 / Mathematics Thüringen / Curriculum
Stochastik: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 10.
单元
练习前按清晰顺序掌握本章核心概念。
Before calculating, identify what each value measures, the population, and whether the sample is representative.
Mean, median, range, and probability answer different questions. Give the value together with a contextual interpretation.
A graph needs a valid scale and a probability must lie from 0 to 1. These checks immediately expose inconsistent answers.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics Thüringen
逐步查看方法，并理解每一步为何成立。
For the data 5, 3, 8, 5, 8, find the mean and range.
Mean 5.8, range 5.
Before calculating, explain the key idea from “Mehrstufige Experimente” and which conditions must be checked.
The answer should show not only which rule is used for “Mehrstufige Experimente”, but also why it is valid here.
Stochastik
八道分层练习，从基础熟练到考试应用。请先独立完成，再查看提示或答案。
Data: 9, 2, 9, 2. Find mean and range.
Mean = sum/count.
mean = 5.5, range = 7.
Order 9, 5, 20, 4, 5 and find the median.
The median is the middle ordered value.
4, 5, 5, 9, 20; median = 5.
A bag contains 8 blue and 6 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 8/14.
In 60 trials, an outcome occurred 12 times. Find relative frequency and percentage.
Divide frequency by number of trials.
12/60 = 0.2 = 20%.
Values 7, 5 have frequencies 5, 7. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(7·5 + 5·7)/12 = 5.83.
Two samples have the same mean but ranges 3 and 6. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 3 is more consistent because its values are less spread out.
Choose a suitable graph for “Baumdiagramme” and justify axes, scale, and title.
Decide whether data are categorical, discrete, or continuous.
A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
Explain why correlation between two variables does not prove causation.
A third factor or reverse relationship may exist.
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
Stochastik
六道不同作业，从基础到挑战，包含预计用时、提示和答案指南。
Homework 1: Data: 5, 3, 5, 3. Find mean and range.
Mean = sum/count.
mean = 4.0, range = 2.
Homework 2: Order 13, 8, 40, 5, 8 and find the median.
The median is the middle ordered value.
5, 8, 8, 13, 40; median = 8.
Homework 3: A bag contains 4 blue and 2 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 4/6.
Homework 4: In 140 trials, an outcome occurred 28 times. Find relative frequency and percentage.
Divide frequency by number of trials.
28/140 = 0.2 = 20%.
Homework 5: Values 3, 6 have frequencies 6, 3. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(3·6 + 6·3)/9 = 4.00.
Homework 6: Two samples have the same mean but ranges 6 and 18. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 6 is more consistent because its values are less spread out.
50 分钟 / 40 分
带计时器、完整分值和参考答案的章节自测。
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Data: 3, 3, 3, 3. Find mean and range.
2 分mean = 3.0, range = 0.
2. Order 11, 6, 30, 5, 6 and find the median.
3 分5, 6, 6, 11, 30; median = 6.
3. A bag contains 9 blue and 2 yellow counters. Find P(blue).
3 分P = 9/11.
4. In 100 trials, an outcome occurred 20 times. Find relative frequency and percentage.
4 分20/100 = 0.2 = 20%.
5. Values 8, 6 have frequencies 6, 8. Find the weighted mean.
4 分(8·6 + 6·8)/14 = 6.86.
6. Two samples have the same mean but ranges 4 and 12. Which is more consistent and why?
4 分The sample with range 4 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Baumdiagramme” and justify axes, scale, and title.
5 分A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
8. Explain why correlation between two variables does not prove causation.
5 分Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Statistische Kennwerte”: population, sample, variables, and possible bias.
5 分A complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Prüfungsaufgaben” using sample size, spread, and limitations.
5 分The evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
单元
课程参考来源；教学顺序请始终与学校和老师确认。
Mathematics Thüringen
German Gymnasium Klasse 10: 数学与物理的结构化路线，包含章节、练习和下一步。
结构跟随教材，用来帮助组织学习。
通常容易出错或需要更多复习的部分。
从教材、daily material、PDFs、videos 和 worked examples 开始。
进入 full tests 前先做 targeted practice，让覆盖情况更清楚。
如何衡量本章进度，以及何时加入综合 mock。
完成本章后该做什么，以及它如何连接到下一单元。
说明：每学年的正式考试范围请始终以学校、老师和当前官方来源为准。
