Standard deviation (use the calculator)
A standard method from Measures of dispersion: the steps and worked examples.
Steps
- Put the calculator in statistics (SD) mode.
- Enter the data (with frequencies for a table; class marks for grouped data).
- Read σx (population standard deviation), not sx. The DSE uses σ.
- Write down the value; variance = σ².
Want to check an answer? Standard deviation calculator shows every step.
Worked examples
Example 1: Data: 4, 7, 7, 9, 13. Find the range, mean, standard deviation and variance.
range = 13 − 4 = 9
mean = 40 ÷ 5 = 8
σ = √[(16 + 1 + 1 + 1 + 25)/5] = √8.8 ≈ 2.97
variance = 8.8Example 2: NF: a test has mean 66 and standard deviation 8. A student scores 78. Find the standard score.
z = (78 − 66)/8 = 1.5.
For the whole topic, read Measures of dispersion: key points, common mistakes and how the DSE tests it.