Review and Preview

Statisticians use several tools to interpret the data. Measures of central tendencies, such as mean, median, and mode, identify the single value most representative of the data. 

To understand how far the values have spread from the mean, one can use the measures of variations, such as range and standard deviation.

Finally, to interpret each value of the data in relation to other data points, one can use the measures of relative standing.

For example, a student receives 85 percent marks on a class test. By comparing this score with the scores of his classmates, one can know whether the student's performance is excellent or poor. This relative comparison can be made by using any of the three commonly used measures of relative standing—percentile,z score,  or quartiles.

Percentiles divide data into groups of hundreds and measure where the data lies in those groups. The z score is the standard score used to find the unusual values. A quartile summarizes a group of numbers into four groups visualized using a boxplot.