Median

The mean (or average) tends to be more useful when you are dealing with data that has a normal distribution, meaning there's like an even spread of data points. Imagine you had 100 students and 20 got A's, 20 got B's, 20 got C's, 20 got D's and 20 got F's. The average will be a pretty good indicator of what the average grade score was. But if you have a much more skewed data set, like say we're talking about real estate costs of houses in a city, then the average becomes less important. For instance, say 10 houses out of 100 are worth $100 million but the other 90 houses are worth between $200,000 to $400,000. Well, those $100 million houses are gonna screw up the average cost a lot, making you think all the houses are super expensive in that city. But if you use the median you get a better idea of how the costs are actually distributed. More on reddit.com

denoting or relating to a value or quantity lying at the midpoint of a frequency distribution of observed values or quantities, such that there is an equal probability of falling above or below it. More on math.answers.com

Median is one type of average. You put all the sample into order and then the median is at the halfway mark. For income it means half the population earn more and half earn less. Mean is another type of average - you add all the sample values together and then divide by the number of samples. The number might not be what any individual sample scores. Median is useful for things like income and wealth as it cuts off the outlier values. Eg for income a handful of billionaires can radically skew the result to show a much higher income or wealth than any ordinary person is realistically on. Mean is useful for a lot of statistical analysis, and for some types of average when the distribution of results follows a certain pattern and there are either no outliers or outliers are balanced. There’s another average called “Mode” - this is the value that’s most common. Mode is more for things where the samples can’t really be put into order - eg what color is the average car. Median doesn’t work. Mean would be weird. Mode is more useful here. More on reddit.com

Let’s take a set of 5 number (2, 2, 4, 6, 8). The mode is the most frequent number, so it would be 2. The median is the ‘middle’ number, as you said the 50th percentile, so if you arrange the numbers in order then go to the middle number, so at it’s a set of 5 numbers we would go to the third, so it would be 4. The mean is mathematical average, for this you add up all the numbers in the set, then divide by the numbers in the set. So 2+2+4+6+8=22, then we divide this by 5, so 4.4 These three approaches are all ways to describe a set of numbers without having to see the full set of data, however it does mean some detail is lost More on reddit.com