Standard Deviation Formula Explained, With Examples
Every standard deviation result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
s = √(Σ(x − x̄)² ÷ (n − 1)).
What each input means
- Numbers (separated by commas): the value you enter in the calculator.
Example
For example, with these inputs:
- Numbers (separated by commas): 12, 15, 9, 22, 15, 30
the calculator returns:
- Sample standard deviation: 7.6267
- Variance: 58.1667
- Mean: 17.1667
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
Related calculations
- Decimal to Binary Converter: Converts a base-10 number to binary, octal and hex.
- Binary to Decimal Converter: Converts binary to decimal.
- Hex to Decimal Converter: Converts hexadecimal to decimal.
- Area of a Circle Calculator: Calculates the area of a circle from the measurements you enter.
Use the Standard Deviation Calculator to plug in your own numbers.
Run your own numbers: Standard Deviation Calculator