Final answer:
The difference of the medians refers to the subtraction of the median value of one data set from the median of another. Medians are central values that divide ordered data into two halves and are less sensitive to extreme values or outliers than means. To find the difference, calculate each median and then subtract them.
Step-by-step explanation:
When assessing the difference of the medians, it means we are looking at the difference between the median values of two data sets. The median is the value that separates the orderly arranged data into two equal halves, where half of the values are equal to or smaller than the median, and the other half of the values are equal to or larger than the median.
In a given distribution, if the data set has an odd number of observations, the median will be the middle value, whereas if there is an even number of observations, the median is calculated as the average of the two middle values. Importantly, the median is resistant to the influence of outliers or skewed data. For example, in a dataset with a high-income outlier, the median will give a more representative measure of the typical income than the mean, which can be significantly affected by the outlier.
To illustrate with an example, in a dataset representing the longevity of patients after a new treatment (from 3 to 47 months), finding the median requires ordering the data and identifying the central value (which is not necessarily part of the dataset). If comparing two such data sets for treatment efficacy, we would calculate the median for each and then subtract one from the other to obtain the difference of the medians.