# Which is better, replacement by mean and replacement by median?

I'm doing a project that involves replacing missing values in a set of data (first time doing this). This involves using two methods replacement by mean and replacement by median to fill in the missing values. There is not a lot of difference between the results of the minimum, median, maximum, mean and standard deviation of the data using both methods and I was wondering which method is better and how can I make a decision to which one is better using the results produced?

• If you replace missings with means, naturally the mean is preserved. Ditto medians. Nor will the extremes change. The SDs will typically be reduced slightly, but it would be reduced greatly if you do this a lot. These are predictable consequences of what you do and not ipso facto indications that the method is good. – Nick Cox Mar 27 '15 at 15:54
• Analysts plugging missing values (MVs) with automatic "solutions" like this aren't thinking through the consequences. It's just an easily implemented approach. This "solution" introduces as many problems as it solves since an otherwise typically smooth pdf ends up with a large spike at the plugged value, as a function of the number of MVs, of course. Model-based imputations are demonstrably superior and less biasing than any automated approach. @NickCox can't be ignorant of this, despite what his suggestion implies. – Mike Hunter Mar 18 '17 at 17:20
• :@DJohnson ... not ipso facto indications that the method is good. Not clear enough? – Nick Cox Mar 18 '17 at 19:46
• Categorical values are generally imputed with the mode as it represents the value that is the most common for the given column. – Sandeep Kar Jan 12 at 21:33
• Replacement by mean or median --- or mode -- is in effect saying that you have no information on what a missing value might be. It is hard to know why imputation is though to help in that circumstance. Much hinges on whether the variable with missing values is regarded as a response or outcome to be predicted or as a predictor, and naturally it may have different roles for different purposes. What can make sense is to see whether the observations with missing values on this variable are systematically different on the variables that are known from the observations with non-missing values. – Nick Cox Jun 4 at 8:39

If some assumptions are met (for example, if the probability of a variable having a missing value does not depend on the value itself, technically called "missing at random") and your study involves multiple variables, you might be better off using multiple imputation rather than replacements by means or medians. In multiple imputation, known values of all variables are used to provide several sets of estimates of the missing data. This approach can provide better estimates both of the underlying relations among the variables and of the reliability of your estimates. See questions on this site having the multiple-imputation tag for more information.