Цілі навчання
- Recognise, explain, and apply “Tables”.
- Recognise, explain, and apply “Bar charts”.
- Recognise, explain, and apply “Line graphs”.
- Recognise, explain, and apply “Pictograms”.
- Recognise, explain, and apply “Mean, median, mode, range”.
KS3 Year 7 / Mathematics / Curriculum
Statistics and probability
Statistics and probability: structured theory, worked examples, answered practice, and a mastery checklist for KS3 Year 7.
Ключові ідеї та перевірки
- I choose an appropriate statistic.
- I calculate and interpret probabilities.
- Every solution or explanation for “Statistics and probability” should include a method, justification, and final check.
Розділ
Основна теорія
Ключові ідеї глави у зрозумілій послідовності перед практикою.
Data and population
Before calculating, identify what each value measures, the population, and whether the sample is representative.
Statistic with interpretation
Mean, median, range, and probability answer different questions. Give the value together with a contextual interpretation.
Scale and probability check
A graph needs a valid scale and a probability must lie from 0 to 1. These checks immediately expose inconsistent answers.
Tables
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.
Bar charts
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.
Line graphs
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.
Pictograms
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.
Mean, median, mode, range
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
Розв'язані приклади
Дотримуйтесь методу крок за кроком і перевіряйте обґрунтування.
Worked data example
For the data 5, 3, 8, 5, 8, find the mean and range.
- 1Sum = 29 and count = 5.
- 2Mean = 29/5.
- 3Range = maximum - minimum.
Mean 5.8, range 5.
Reasoning example
Before calculating, explain the key idea from “Tables” and which conditions must be checked.
- 1Define the idea in one clear sentence.
- 2Connect it to a representation, law, or formula.
- 3State a restriction, unit, or final check that makes the solution valid.
The answer should show not only which rule is used for “Tables”, but also why it is valid here.
Statistics and probability
Практика з відповідями
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
Базова навичка4 хвилин
Data: 9, 2, 9, 2. Find mean and range.
Підказка
Mean = sum/count.
Відповідь
mean = 5.5, range = 7.
Базова навичка5 хвилин
Order 9, 5, 20, 4, 5 and find the median.
Підказка
The median is the middle ordered value.
Відповідь
4, 5, 5, 9, 20; median = 5.
Застосування6 хвилин
A bag contains 8 blue and 6 yellow counters. Find P(blue).
Підказка
Favourable outcomes / total outcomes.
Відповідь
P = 8/14.
Застосування7 хвилин
In 60 trials, an outcome occurred 12 times. Find relative frequency and percentage.
Підказка
Divide frequency by number of trials.
Відповідь
12/60 = 0.2 = 20%.
Обґрунтування8 хвилин
Values 7, 5 have frequencies 5, 7. Find the weighted mean.
Підказка
Sum value×frequency and divide by total frequency.
Відповідь
(7·5 + 5·7)/12 = 5.83.
Обґрунтування9 хвилин
Two samples have the same mean but ranges 3 and 6. Which is more consistent and why?
Підказка
Lower spread means greater consistency.
Відповідь
The sample with range 3 is more consistent because its values are less spread out.
Екзаменаційний10 хвилин
Choose a suitable graph for “Equally likely outcomes” and justify axes, scale, and title.
Підказка
Decide whether data are categorical, discrete, or continuous.
Відповідь
A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
Екзаменаційний12 хвилин
Explain why correlation between two variables does not prove causation.
Підказка
A third factor or reverse relationship may exist.
Відповідь
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
Типові помилки
- Using the mean when outliers distort the result.
- Using the wrong denominator in a probability.
- Drawing a graph without title, units, or consistent scale.
Перевірка розуміння
- I choose an appropriate statistic.
- I calculate and interpret probabilities.
- I check sample and graph quality.
Statistics and probability
Домашня робота до розділу
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
Базовий8 хвилин
Homework 1: Data: 5, 3, 5, 3. Find mean and range.
Підказка
Mean = sum/count.
Відповідь
mean = 4.0, range = 2.
Базовий10 хвилин
Homework 2: Order 13, 8, 40, 5, 8 and find the median.
Підказка
The median is the middle ordered value.
Відповідь
5, 8, 8, 13, 40; median = 8.
Поглиблений12 хвилин
Homework 3: A bag contains 4 blue and 2 yellow counters. Find P(blue).
Підказка
Favourable outcomes / total outcomes.
Відповідь
P = 4/6.
Поглиблений15 хвилин
Homework 4: In 140 trials, an outcome occurred 28 times. Find relative frequency and percentage.
Підказка
Divide frequency by number of trials.
Відповідь
28/140 = 0.2 = 20%.
Складний18 хвилин
Homework 5: Values 3, 6 have frequencies 6, 3. Find the weighted mean.
Підказка
Sum value×frequency and divide by total frequency.
Відповідь
(3·6 + 6·3)/9 = 4.00.
Складний20 хвилин
Homework 6: Two samples have the same mean but ranges 6 and 18. Which is more consistent and why?
Підказка
Lower spread means greater consistency.
Відповідь
The sample with range 6 is more consistent because its values are less spread out.
50 хвилин / 40 балів
Повний тест розділу
Повний тест із таймером, балами та зразками відповідей.
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 балівВідповідь
mean = 3.0, range = 0.
2. Order 11, 6, 30, 5, 6 and find the median.
3 балівВідповідь
5, 6, 6, 11, 30; median = 6.
3. A bag contains 9 blue and 2 yellow counters. Find P(blue).
3 балівВідповідь
P = 9/11.
4. In 100 trials, an outcome occurred 20 times. Find relative frequency and percentage.
4 балівВідповідь
20/100 = 0.2 = 20%.
5. Values 8, 6 have frequencies 6, 8. Find the weighted mean.
4 балівВідповідь
(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 балівВідповідь
The sample with range 4 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Equally likely outcomes” and justify axes, scale, and title.
5 балівВідповідь
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 балівВідповідь
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Tables”: population, sample, variables, and possible bias.
5 балівВідповідь
A complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Bar charts” using sample size, spread, and limitations.
5 балівВідповідь
The evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
Розділ
Офіційні джерела
Джерела програми; порядок тем уточнюйте у школі та викладача.
Mathematics
KS3 Year 7: структурований маршрут з математики та фізики з розділами, практикою і наступними кроками.
Що покриває глава
Структура відповідає підручнику й допомагає організувати вивчення теми.
Tables
Bar charts
Line graphs
Pictograms
Mean, median, mode, range
Probability scale
Equally likely outcomes
Simple probability experiments
На чому сфокусуватися
Теми, де найчастіше виникають помилки або потрібна додаткова практика.
I choose an appropriate statistic.
I calculate and interpret probabilities.
I check sample and graph quality.
Джерела, щоденні матеріали та ресурси
З чого почати: підручник, daily material, PDFs, videos і worked examples.
Start from the official textbook or specification referenced on the subject page.
Use the notes and examples as support, not as a replacement for the official syllabus.
Check the current syllabus version before exam preparation.
Практика за підтемами
Цільова практика перед full tests, щоб coverage було зрозумілим.
Data: 9, 2, 9, 2. Find mean and range.
Order 9, 5, 20, 4, 5 and find the median.
A bag contains 8 blue and 6 yellow counters. Find P(blue).
In 60 trials, an outcome occurred 12 times. Find relative frequency and percentage.
Values 7, 5 have frequencies 5, 7. Find the weighted mean.
Two samples have the same mean but ranges 3 and 6. Which is more consistent and why?
Choose a suitable graph for “Equally likely outcomes” and justify axes, scale, and title.
Explain why correlation between two variables does not prove causation.
Mocks і перевірка прогресу
Як вимірювати прогрес у главі і коли додавати її до загального mock.
Start with untimed practice by subtopic.
Move to a short timed checkpoint only after completing the mastery checklist.
Record each error with the correct method and revisit it after 48 hours.
Наступний крок
Що робити після глави і як вона пов'язана з наступним розділом.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Примітка: офіційну екзаменаційну програму кожного року завжди уточнюйте у школі, викладача та за поточними офіційними джерелами.