# Measures of Central Tendency

One of the main goals of data analysis is to describe data in a succinct manner so that it is easily understandable; this is called data reduction. To succinctly describe data, measures of central tendency (that is, mean, median, and mode) can be used. For example, suppose you collect data on the arrest records of inmates in a particular region. From your data, you might want to determine the most common offenses committed by inmates. If each offense is measured nominally (for example, armed robbery = 1, murder = 2, and aggravated assault = 3), determining the mode would show which offense is committed most frequently. You might also want to determine the number of offenses typically committed by inmates (ratio level of measurement) prior to being sentenced to prison. To do this, you could calculate the mean, or the average number of offenses committed by inmates. You also could rank the number of offenses from the highest to the lowest to determine the middle number, or the median number of offenses committed by inmates.

Before choosing which measure of central tendency to use, it is important to consider the level of measurement that applies to the variable. For instance, it would not make sense to find the mean or median of a variable, such as gender, that is measured nominally. As you complete the following Discussion, keep in mind that not all measures of central tendency are appropriate for all levels of measurement.