Averages & Spread — GCSE Mathematics Revision
Revise Averages & Spread for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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Go to Scatter Graphs & CorrelationWhat is Averages & Spread?
The three averages are mean, median and mode. The mean is the sum of values divided by the count. The median is the middle value when data is ordered. The mode is the most frequent value. Range measures spread (highest - lowest). For grouped data, you estimate the mean using midpoints and cannot find the exact median — only the class containing the median.
Step-by-step explanationWorked examples
Worked example 1: Core method
Data: 3, 5, 7, 7, 8, 10. Mean = (3+5+7+7+8+10)/6 = 40/6 = 6.67 (2 d.p.). Median = (7+7)/2 = 7. Mode = 7. Range = 10-3 = 7.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Averages & Spread idea being tested, show the method or evidence, then explain why it answers the command word. This helps GCSE Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Averages & Spread idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Averages & Spread
1. Understand the core idea
The three averages are mean, median and mode. The mean is the sum of values divided by the count.
Can you explain Averages & Spread without copying the notes?
2. Turn it into marks
Data: 3, 5, 7, 7, 8, 10. Mean = (3+5+7+7+8+10)/6 = 40/6 = 6.
Underline the method, evidence, or command-word move that would earn credit in GCSE Statistics.
3. Fix the likely mark leak
Watch for this mistake: Not ordering the data before finding the median.
Write one correction rule before doing another practice question.
Practise this topic
Jump into adaptive, exam-style questions for Averages & Spread. Free to start; sign in to save progress.
Mini quiz: Averages & Spread
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one GCSE sentence, explain what Averages & Spread is testing.
Answer: The three averages are mean, median and mode. The mean is the sum of values divided by the count.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Averages & Spread question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Not ordering the data before finding the median." What should their next repair task be?
Answer: Do one Averages & Spread question and review the mistake type.
Mark focus: Error correction and next-step practice.
Averages & Spread flashcards
Core idea
What is the main idea in Averages & Spread?
The three averages are mean, median and mode. The mean is the sum of values divided by the count.
Common mistake
What mistake should you avoid in Averages & Spread?
Not ordering the data before finding the median.
Practice
What is one useful practice task for Averages & Spread?
Answer one Averages & Spread question and review the mistake type.
Exam board
How should you use board notes for Averages & Spread?
Use your own GCSE specification for exact paper wording and depth.
Common mistakes
- 1Not ordering the data before finding the median.
- 2Using the frequency as the data value when calculating the mean from a frequency table (multiply value × frequency first).
- 3Forgetting to divide by the total frequency, not the number of classes, when finding the mean from grouped data.
- 4Stating the modal class frequency instead of the modal class interval.
Averages & Spread exam questions
Exam-style questions for Averages & Spread with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Averages & Spread
Core concept
The three averages are mean, median and mode. The mean is the sum of values divided by the count. The median is the middle value when data is ordered. The mode is the most frequent value. Range measur…
Frequently asked questions
Which average should I use?
Mean uses all data but is affected by outliers. Median is not affected by outliers and is best for skewed data. Mode is useful for categorical data. The question will usually tell you which to find.
How do I find the median from a frequency table?
Find the total frequency n. The median is the (n+1)/2 th value. Use cumulative frequency to find which class or value this falls in.