Standard Deviation
Standard deviation measures how spread out data values are from the mean. A small standard deviation means data is clustered closely; a large one means it is more spread out.
What You Need to Know
Key Concept Diagram
Standard deviation measures the typical distance of values from the mean
A low standard deviation means data is clustered near the mean
A high standard deviation means data is more spread out
Standard deviation is always non-negative; it equals zero only when all values are the same
Key Vocabulary
Standard deviation
A measure of how spread out values in a data set are from the mean
Mean
The average of a data set; sum divided by count
Variance
The average of the squared deviations from the mean; standard deviation is its square root
Spread
How far data values are distributed from the centre
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Dataset A has standard deviation 1.2; Dataset B has standard deviation 8.5. Which is more spread out?
Question 2
Two classes both score a mean of 70% on a test. Class 1 has standard deviation 3, Class 2 has standard deviation 15. What can you conclude?
Question 3
A dataset has values 5, 5, 5, 5, 5. What is the standard deviation?
Key Concepts Summary
- ●Standard deviation measures the typical distance of values from the mean
- ●A low standard deviation means data is clustered near the mean
- ●A high standard deviation means data is more spread out
- ●Standard deviation is always non-negative; it equals zero only when all values are the same