German Gymnasium Klasse 8 / Mathematics / Curriculum
Daten und Zufall: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 8.
CHAPTER PLAN
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Estimated active study time
209 minutes
Objectives, key ideas, and structured theory.
Open →Worked examples that explain every step.
Open →Graded tasks with hints and answer guidance.
Open →Assignments from core work to challenge.
Open →A timed, marked test with solution guidance.
Open →Progress is stored only in this browser and does not require AI credits.
Unit
The essential chapter ideas in a clear sequence before practice.
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
Follow the method step by step and check why every step is valid.
For the data 4, 6, 10, 8, 7, find the mean and range.
Mean 7.0, range 6.
Before calculating, explain the key idea from “Mehrstufige Zufallsexperimente” and which conditions must be checked.
The answer should show not only which rule is used for “Mehrstufige Zufallsexperimente”, but also why it is valid here.
Daten und Zufall
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Data: 6, 5, 6, 5. Find mean and range.
Mean = sum/count.
mean = 5.5, range = 1.
Order 11, 9, 18, 2, 9 and find the median.
The median is the middle ordered value.
2, 9, 9, 11, 18; median = 9.
A bag contains 5 blue and 4 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 5/9.
In 240 trials, an outcome occurred 48 times. Find relative frequency and percentage.
Divide frequency by number of trials.
48/240 = 0.2 = 20%.
Values 4, 3 have frequencies 3, 4. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(4·3 + 3·4)/7 = 3.43.
Two samples have the same mean but ranges 7 and 35. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 7 is more consistent because its values are less spread out.
Choose a suitable graph for “Baumdiagramme introduction” 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.
Daten und Zufall
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Data: 9, 6, 9, 6. Find mean and range.
Mean = sum/count.
mean = 7.5, range = 3.
Homework 2: Order 8, 5, 15, 3, 5 and find the median.
The median is the middle ordered value.
3, 5, 5, 8, 15; median = 5.
Homework 3: A bag contains 8 blue and 5 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 8/13.
Homework 4: In 40 trials, an outcome occurred 8 times. Find relative frequency and percentage.
Divide frequency by number of trials.
8/40 = 0.2 = 20%.
Homework 5: Values 7, 4 have frequencies 4, 7. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(7·4 + 4·7)/11 = 5.09.
Homework 6: Two samples have the same mean but ranges 3 and 18. 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.
50 minutes / 40 marks
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Data: 7, 6, 7, 6. Find mean and range.
2 marksmean = 6.5, range = 1.
2. Order 6, 3, 9, 3, 3 and find the median.
3 marks3, 3, 3, 6, 9; median = 3.
3. A bag contains 6 blue and 5 yellow counters. Find P(blue).
3 marksP = 6/11.
4. In 90 trials, an outcome occurred 18 times. Find relative frequency and percentage.
4 marks18/90 = 0.2 = 20%.
5. Values 5, 4 have frequencies 4, 5. Find the weighted mean.
4 marks(5·4 + 4·5)/9 = 4.44.
6. Two samples have the same mean but ranges 8 and 48. Which is more consistent and why?
4 marksThe sample with range 8 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Baumdiagramme introduction” and justify axes, scale, and title.
5 marksA 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 marksCorrelation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Mittelwerte”: population, sample, variables, and possible bias.
5 marksA complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Relative Häufigkeit” using sample size, spread, and limitations.
5 marksThe evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Keep each unit in GR/DE: concept, German term, example, exercise, recap.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.
