Standard Deviation Examples in Statistics
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Standard Deviation.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.
Concept Recap
A measure of how spread out data values are from the mean, calculated as the typical distance from the average.
If the mean is 'home base,' standard deviation tells you how far data points typically wander from home. Small SD = data clusters close to the mean (like a tight group of friends). Large SD = data is scattered (friends spread all over town).
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Standard deviation is the typical distance of data points from the mean. A small SD means data is tightly clustered; a large SD means it is widely spread.
Common stuck point: Students confuse standard deviation with variance. Variance is the average squared distance; SD is the square root of variance and has the same units as the data.
Worked Examples
Example 1
mediumSolution
- 1 Step 1: Mean = \frac{4+8+6+2+10}{5} = 6.
- 2 Step 2: Squared deviations: (4-6)^2=4, (8-6)^2=4, (6-6)^2=0, (2-6)^2=16, (10-6)^2=16.
- 3 Step 3: Variance = \frac{4+4+0+16+16}{5} = \frac{40}{5} = 8. Standard deviation = \sqrt{8} \approx 2.83.
Answer
Example 2
hardPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
mediumExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.