What does it tell us?
The mean tells you the average. The standard deviation tells you how spread out the values are from that average.
Both sets have a mean of 50, but Set B is far more spread out.
- Small standard deviation means the values are close together. The data is less varied.
- Large standard deviation means the values are spread out. The data is more varied.
- A standard deviation of 0 means every value is the same.
The formula
the mean
nhow many values there are
Σ"add them all up"
This formula is given on your exam formulae list, so you don't need to memorise it. You do need to know how to use it.
Worked example
Find the standard deviation of: 4, 6, 7, 8, 10
⚠ Show the full calculation. Keep the fraction visible as you work: formula → numbers in the fraction → calculator value → final answer. Don't round until the last line.
0 of 0 complete
Your turn
Use a calculator. Stuck? Tap Need a hint? and you'll get one clue at a time. Each worked solution shows where the marks are given.
Past paper questions
Ready for exam-style questions? Use these links to practise mean and standard deviation questions from real SQA papers. Remember: calculate first, then write two comparison statements that link to the context of the question.
Mean & standard deviation: past paper questions by topic Every SQA past paper and specimen question on this topic in one PDF, with answers. Start here. maths.scot · PDF Open ↗ (opens in a new tab) Standard deviation: SQA question bank Every National 5 standard deviation question from SQA papers (2014 onwards), each with a link to its marking scheme. Includes Applications of Maths questions too. The method is exactly the same. dynamicmaths.co.uk Open ↗ (opens in a new tab)