In statistics, several tools are used to interpret the data. Measures of central tendency represent the characteristics of the data, such as mean, median, and mode. Additionally, measures of variance like standard deviation and range are used to find the spread of data from the mean. Relative standing measures the distance between data locations. Commonly used measures of relative standings are percentile, z score, and quartiles.
Percentiles are a type of fractile that partition data into groups with roughly the same number of values. Percentile divides data into 100 groups, with about 1% of the values in each group.
z scores are measures of position in that they describe the location of a value in terms of standard deviations relative to the mean. A z score of 2 indicates that a data value is two standard deviations above the mean, and a negative 3 z score indicates that a value is three standard deviations below the mean.
Quartiles are numbers that divide data into quarters. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data.
This text is adapted from Openstax, Introductory Statistics, Section 2.3 Measures of the Location of the Data and 2.7 Measures of the Spread of the Data
