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 and OCR.
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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 example
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.
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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
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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.