Pros and Cons

The median has its own set of advantages and disadvantages. Here they are:

Robust to Outliers: The median is less sensitive to outliers and skewed data compared to the mean. A single extreme value can dramatically affect the mean but will have no effect on the median.
Simple to Understand: The concept of "the middle value" is easy to grasp, making the median an accessible measure for people without a strong statistical background.
Easy to Compute for Small Data Sets: For small data sets, the median can be quickly computed by sorting the data and finding the middle value.
Applicable to Ordinal Data: Unlike the mean, the median can be used for ordinal data, which can be ranked but not quantitatively measured (e.g., a satisfaction survey with options like "poor," "fair," "good").
Better for Skewed Distributions: In a skewed distribution, the median will give a better "central location" of the data than the mean.

Ignores the Rest of the Data: The median only considers the middle value(s), ignoring all other data points. This can be a problem when you need to consider the entire data distribution.
Not Algebraically Manipulable: Unlike the mean, the median cannot be algebraically manipulated, which limits its utility in mathematical and statistical modeling.
Computational Complexity for Large Data: For large data sets, computing the median requires the data to be sorted first, which can be computationally intensive.
Ambiguity in Even-Sized Data Sets: When the data set has an even number of observations, the median is the average of the two middle numbers, which may not always be a clear-cut representative of the data.
Less Popular in Statistical Analysis: In some statistical techniques, especially those that require mathematical modeling, the mean is generally preferred over the median.

Understanding these pros and cons can help you decide when it's most appropriate to use the median as a measure of central tendency.