How to find correlation between categorical data and continuous data
For your specific case I would recommend the &quot;grouped mode&quot; because that would be the value you are interested in imputing (I did the same for this kaggle challenge).
On more general terms we have to understand the scale of each variable. We often talk about categorical data but in more detail we have to differentiate between &quot;nominal data&quot; and &quot;ordinal data&quot;.
Income brackets are ordinal, that means there is a clear numerical hierarchy, while other data such as the &quot;Embarkment&quot; here is more nominal, that means there is no order or numerical relation.
Therefore a correlation is impossible and it is more helpful to think in terms of grouped distributions.
What does that mean for imputation
Finally besides simply imputing the grouped mode (that is the most frequent value per group) you could try imputation algorithms like MICE which are in a way predicting the missing value based on other variables. This is possible for nominal as well as ordinal categorical factors.
Please be aware that imputation is highly depended on the question of why a value is missing. You have to make sure that the value is not MNAR before you try imputation at all.