2.5: Measures of Position

Standard Score (z-score)

A measure of position that represents the number of standard deviations a value lies from the mean.

Interquartile Range (IQR)

A measure of variation that gives the range of the middle portion (about half) of the data by calculating the difference between the third and first quartiles.

Box-and-Whisker Plot (Boxplot)

An application of quartiles used to represent data sets that highlights the important features of a data set.

Deciles

Divide a data set into 10 equal parts.

Percentiles

Divide a data set into 100 equal parts.

Percentile that Corresponds to a Specific Data Entry, x

Divide the number of entries less than x by the total number of data entries, then multiply by 100. Round to the nearest whole number.

Quartiles

Numbers that divide an ordered data set into four equal parts. About one-quarter of the data fall on or below the first quartile. About one-half of the data fall on or below the second quartile (which is the same as the median). About three-quarters of the data fall on or below the third quartile. Divide a data set into 4 equal parts.

Fractiles

Numbers that partition, or divide an ordered data set into equal parts.

Five-Number Summary

The minimum data entry, the first quartile, the median, the third quartile, and the maximum entry.