Consider a set of N observations consisting of $k$ distinct values, each of frequency $f_{1}, f_{2},...,f_{k}$. The above $k$ observations once each is added to get a modified sample of $N+k$ observations with frequency$f_{i}+1$.
Then what would be change in mean, median, mode and variance.
I understand that mode will remain the same. For mean, I visualised that the frequency curve of the modified sample would shift 1 point vertically up. Can I hence say that new mean will be less than or equal to original mean? and that median will be greater than or equal to original median. I also took a few observations, 1,2,2,4,4 (original) to check my claim. Am I right?
Which is the right method to do such problems?