These measures are used to describe the position of a value with respect to the rest of the values of the data set.

To compute quartiles and percentiles, but not to compute z-scores, the data must be sorted by value.

Quartiles

Percentiles and

Standardized scores (z-scores).

Standardized scores, commonly known as z-scores, are independent of the units in which the data values are measured.

They are useful when comparing observations measured on different scales.

A z-score gives the distance between the measurement and the mean in terms of the number of standard deviations.

A negative z-score indicates that the measurement is smaller than the mean.

A positive z-score indicates that the measurement is larger than the mean.