Question

what are the measures of central tendency ? Why arithmetic mean is considered as ideal measure?

Answer 1

Mean is considered as the best measure of central tendency because of the following reasons :

It is rigidly defined. Median might not be rigid when there are even number of observations and mode cannot be considered as rigid either when there are more than one value with the highest frequency or frequency density.
Only the mean directly uses all the observations; it changes when any one of the observations is changed.
The mean is generally the one that is the least affected by sampling fluctuations.

Answer 2

Arithmetic mean has become the most widely used measure of central tendency of data. ... That is why arithmetic mean is regarded as the ideal measure of central tendency. One demerit of arithmetic mean is that it is affected by the extreme value (of observed data).