How you know the mean is the really insightful about the current analysis?

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The book. How to Lie with Statistics. From the author Darrel Huff. Give some tips to the newcomers in statistics class or somebody trying to learn about the information and how they can be manipulated.
About 2/3 of the book it's about the central tendency and how to get that mean, or mode, or median, a real value for the information required and the problems with the mean value.

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For example, and ilustration, see below:
If you have a set of numbers t = {0,1,2,4,4,5,5,6,6,6,7};
The mean value will be the sum of the numbers, divided by the total of values on the population. In this case the population is really small and we don't need to make a sample to analysis the whole.
So:
u = sum(population)/number(population),
with
u=(0+1+2+4+4+5+5+6+6+6+7)/(11)
=46/11
=4.18. The mean value is 4,18.

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For find the mode you pick the number that appears the most on the set, or in other words, have most frequency.
In this set is 6, because have frequency 3.

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For find the median you need to order first your set in increasing value. After that you divide apart in two subgroups the set. And if the set has one central number, the median is that number. Else if appears two numbers in central value, you sum them and divide by two.
In this example the median is 5. After the search process.

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So what number i use to value the central tendency?

If you have median, mode and mean, in different value. You don't have a symmetrical distribution. So every central tendency number will be different, and for the conclusion of some research with this numbers need to appoint this.