Today I read an interesting statement, which I am not sure about its correctness.
Assume we are looking at a data set with one column $H$ that is numeric. It has a bunch of missing values. Now let's say I just replace the missing value in column $H$ by the mean of this column (calculated by excluding the missing value). This method is good in the sense that it won't change the mean of column H. But it also has some problems. I was told that this will lessen the correlation with other numeric columns.
This is something I don't understand. I think the extreme case. Assume that column H only has 2 non-missing value, then I use the average of these 2 numbers to replace all the missing values in column H, then this will make the column H almost like a constant, which has variance close to 0. Then the correlation between this almost constant variable and other numeric column will be infinity? or undefined? or zero?