Standard deviation calculator
Enter a set of data, separated by commas or spaces. The calculator works out the mean, variance and standard deviation and shows every step in a table, the same way the DSE does.
How it works
- Work out the mean x̄ = Σx / n.
- Find how far each value is from the mean, x − x̄, and square it.
- Add the squares and divide by the number of values n to get the variance σ².
- The standard deviation σ is the square root of the variance.
- x̄ = 40 / 8 = 5
- The squared differences are 9, 1, 1, 1, 0, 0, 4 and 16, which add up to 32.
- σ² = 32 / 8 = 4
The DSE uses the population standard deviation, dividing by n. The s or σₙ₋₁ on a calculator is the sample standard deviation, which divides by n − 1 and gives a different answer.
To learn it properly, read Measures of dispersion: key points, steps and worked examples.
Frequently asked questions
What does the standard deviation tell you?
It measures how spread out the data are from the mean. The larger the standard deviation, the more spread out the data; if every value is the same, it is 0.
Why does my calculator give a different answer?
Most calculators have both σₓ (divide by n) and sₓ (divide by n − 1). The DSE Mathematics Compulsory Part uses σₓ, the population standard deviation.
How do I work with grouped data?
Use the class mark of each class to stand for that class, then weight by the frequencies. In the exam you usually enter the class marks and frequencies in your calculator's statistics mode.