Is it meaningful to do a average operation on a set of numbers ??
By set, I mean something which will not have duplicate elements.
Let us assume that a car travels at 1 Km/hr for one hour, 4 Km/hr for next hour and then again at 1 Km/hr for the third hour. Average speed is is (1 + 4 + 1)/3 = 2 Km/hr. This means that, the kind of travelling that the person did (as mentioned above) is equivalent to travelling at travelling at a constant speed of 2 Km/hr for 3 continuous hours.
Now in another case, let us remove the duplicate elements while calculating the average. So new average is (1 + 4)/2 = 2.5 Km/hr.... I guess this number 2.5 Km/hr has no real world meaning. No one can make use of this value in any algorithm or other way to understand or analyse systems. Am I right??
This act of removing duplicates while calculating the average of any group of numbers is not going to result in a meaningful answer for any physical quantity(not just with speed-diatance-time thing). Am I right??
And I guess the same is the case with standard deviation operation.
I guess I conveyed what I wanted to ask properly...In other words, I just wanted to know whether there is a bizarre case in which one removes duplicates from a group of numbers and finds average and uses it as a meaningful data for further analysis....
Yes, there is an example, namely sampling from a finite population.
Suppose you are interested in the average height of a group of people of $N$ people. You take a sample size $n$ with replacement (e.g. choose one at random $n$ times).
The natural estimator of the group is the mean of your sample measurements, and this is an unbiased estimator.
But if you deduplicate the individuals who are sampled more than once (suppose that measuring an individual twice gives the same answer each time and no pair of people share precisely the same height), then the sample deduplicated average will be tend to be closer to the population average than the sample average with duplicates is, especially if $n$ is large relative to $N$.
(Note: if $n=1$ there can be no duplication, and if $n=2$ then deduplicating makes no difference)