It is very basic question on this platform. I always found difficulty in interpreting mean to layman person. After reading few answers on SE, I found mean definition as measure of central tendency. But why it is called "central tendency"? Does tendency have specific meaning in statistical context and what does does this word represent?
My second question is how mean can be interpreted when random variable can only take two possible outcomes? Because, in such a cases it does not matter how long we continue our experiment, we will never get sample value equal to its mean value. For example, a random variable, $X$, can take two possible value either -1 or 1 with probability 0.5 each. In this case, the mean is 0. But the truth is that how long we continue to sample we will never get 0, so what 0 (mean) indicate in this case and what is relevance of it ?
I found on certain sites that interpret mean as measure of central tendency where the data seems to cluster around. But in case of uniform distribution there is no clustering of data around any specific value. So how this definition of mean is right?
My simple question is how mean[arithmetic mean] can be interpreted in simple right statistical context?