Statistics
Standardising a single value
Recentre then rescale. The result carries no units because the numerator and denominator share them.
The Formula
z = (x - mean) / SD
Recentre then rescale. The result carries no units because the numerator and denominator share them.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| x | Value being standardised | — | Must come from the same distribution as the mean and SD used. |
| mean | Arithmetic average of the distribution | — | Recentres the scale so the average sits at zero. |
| SD | Standard deviation | same as x | Either population or sample form, used consistently and stated when reported. |
What Each Symbol Means
x
Value being standardised
Must come from the same distribution as the mean and SD used.
mean
Arithmetic average of the distribution
Recentres the scale so the average sits at zero.
SDsame as x
Standard deviation
Either population or sample form, used consistently and stated when reported.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a z-score page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Z-Score, filed under Math. Every number the guide produces comes from substituting into this one line.