What is Difference Between Z-Score and Standard Deviation?

The standard deviation measures the dispersion of data in a distribution, while the Z-score indicates how many standard deviations a particular data point is from the mean of that distribution.

Let’s look at the difference between Z-score and standard deviations.

Aspect	Standard Deviation	Z-Score
Definition	Measures the dispersion or spread of a data set.	Standardizes individual data points in terms of how many standard deviations they are from the mean.
Symbol	σ (sigma)	Z (Z-score)
Formula	σ = √ [(Σ(xi – μ)²) / n]	​Z = X–μ/σ
Interpretation	Provides information about the spread of data points around the mean.	Indicates the relative position of a data point within a distribution. A positive Z-score means above the mean, and a negative Z-score means below the mean.
Unit of Measurement	Same unit as the data points being measured.	Dimensionless (no unit).

where:

• N is the number of data points.
• X_i is each individual data point.
• [Tex]\bar{X}[/Tex] is the mean of the data set.
• X is the individual data point.
• μ is the mean of the distribution.
• σ is the standard deviation of the distribution.

In summary, while the standard deviation gives a measure of how spread out the data is, the Z-score allows for a standardized comparison of individual data points in terms of their deviation from the mean.