I have a large number of data. If i have to represent the data by the central tendency, which one i have to use, mean or median? The value of standard deviation is so huge too. Thanks.
As comments have pointed, mean an median answer different questions. I give an example:
There are 4 people in a very little country. The only available food is imported pizza, and one of the villagers eat one pizza a day but the other three don't eat at all. Mean of eaten pizzas is 0.25 pizzas/day/inhabitant but median is 0 pizzas/day/inhabitant.
The local food dealer needs to know how many pizzas he needs to import to the country. He would use the mean (0.25) and multiply for the population (4) and get the right daily number of pizzas to import every day (1).
The local health organisation is likely more interested in knowing how well feed is the population. The median (0) shows that at least half of the population is starving, while the mean (0.25) wouldn't show it.
In general, when we are interested in aggregate values, mean is more useful, but sometimes median is more interesting when we are more interested in the typical values.
And of course no single number can summarize the whole information of a distribution. Sometimes mean or median will be enough for a given purpose, or we can need standard deviation, histograms, percentiles and so.