Most papers present mean value for their samples though some present median value. What is the difference?
When to use the arithmetic mean or the median depends on the research question. Use the mean if you need the average value of your observations. Use the median if you need the value of the typical observation. Peter Feinsinger provides an interesting example (“Designing Field Studies for Biodiversity Conservation”). Suppose you measure the number of fruits that is removed each night (presumably by bats) from a species of tree. You find that in most trees just a few fruits is removed while in a few trees the rate of fruit removal is high. Obviously, the values of the mean and the median are very different. In this case, the mean represents the average number of fruits that is removed per tree. The median represents the number of fruits that is removed from the typical tree. The mean represents the point of view of the bat, e.g. it is an index of the number of fruits that is consumed by the population of bats. The median represents the point of view of the tree, e.g. it suggests that the typical tree in the tree population has dispersed few seeds.
In statistics, parametric tests are used when data is normally distributed (i.e. "symmetrical" and mean is present) and non-parametric tests are used when data is skewed (median is present).
Just to clarify. If your data is skewed you don´t necessarily need to do a non-parametric analysis. You can also use generalized linear models based on other distributions than the normal. I think you can still use the mean in such cases, along with asymmetrical Wald confidence intervals.
Median is useful when you want to show the central tendency and you have some outliers (extreme values) which influences the mean a lot (i.e. the estimated mean does not represent the central tendency).
A follow up question: Is there any situation where the mode (i.e. most common value) would be the preferred central tendency measure for illustrating results?
The arithmetic mean is the sum of a collection of measurement values divided by the number of measurements, while the median is the numerical value separating the higher half of a data set from the lower half.
In my opinion, it is advisable to use the arithmetic mean (together with standard deviation) for data that meets the requirements for parametric statistics and the median (with quartiles or range) for data that were evaluated by non-parametric statistics.
When to use the arithmetic mean or the median depends on the research question. Use the mean if you need the average value of your observations. Use the median if you need the value of the typical observation. Peter Feinsinger provides an interesting example (“Designing Field Studies for Biodiversity Conservation”). Suppose you measure the number of fruits that is removed each night (presumably by bats) from a species of tree. You find that in most trees just a few fruits is removed while in a few trees the rate of fruit removal is high. Obviously, the values of the mean and the median are very different. In this case, the mean represents the average number of fruits that is removed per tree. The median represents the number of fruits that is removed from the typical tree. The mean represents the point of view of the bat, e.g. it is an index of the number of fruits that is consumed by the population of bats. The median represents the point of view of the tree, e.g. it suggests that the typical tree in the tree population has dispersed few seeds.
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