Standard score (NF)
A standard method from Measures of dispersion: the steps and worked examples.
Steps
z = (x − mean) ÷ standard deviation. Higher z means better relative performance.
- Find the mean and standard deviation of the group.
- Work out z = (x − mean) ÷ standard deviation.
- Compare standard scores, not raw marks: the higher z is the better result relative to the group.
Want to check an answer? Standard deviation calculator shows every step.
Worked examples
Example 1: 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.