Standard Deviation
Square root of variance; typical spread.
Key idea
Square root of variance; typical spread.
In depth
The standard deviation is the square root of the variance, restoring the original units. It is roughly the typical distance of data from the mean. A small value means data cluster tightly.
Worked example
Variance 2.67 gives SD ≈ 1.63.
Formula
Real-world uses
- Describing how far typical heights are from the average
- Judging the consistency of quality tests
Common mistake
Thinking the SD is the average absolute deviation; it is not the same.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Standard Deviation?
Square root of variance; typical spread. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Standard Deviation?
The key formula is σ = √(Σ(x−μ)²/n).
Where is Standard Deviation used in real life?
Real-world examples: Describing how far typical heights are from the average; Judging the consistency of quality tests.
What should I learn before Standard Deviation?
Make sure you are comfortable with Variance, the previous topic in Probability & Statistics.
What is a common mistake with Standard Deviation?
Thinking the SD is the average absolute deviation; it is not the same.
How can I practise Standard Deviation?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Standard Deviation?
Move on to Sample vs Population Variance next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Sample vs Population Variance – Divide by n−1 for sample variance.
- Weighted Mean – Average where values have different importance.