Given a sample (the scope is 72 elements) with mode=54 mean=55,7 median=54,5. The 73th value of the extended sample is 56. What can I say about the mode, median and mean of the extended sample?
Well, the updated mean is easy to calculate.
To make a statement about the median I know the 36th and the 37th value, since the mean of those two values gives me the median, because I have an even number of observations. I would get the equation (x+y)/2=54,5 which doesnt help me in working out the 37th value from what I see.
There have to be at least two values of 54, so that it could be the mode of the sample (assuming all other values appear just one time in the sample).