Approach to detect unused column in a table based on low variance

Question

I have a table which is used a people to fill some information, some 30 fields.

Sample Data:

ID Name Gender ZIP  Phone   Income Expense Family_size ......
1  A1   M      2321 5325222 45000  3553    5

Now most of the fields are mandatory, I have an intuition that some column are just being filled with random values or 0.

My guess is that the column/fields that little variance/randomess are the once that people are not bothering to fill well (some fields will have little variance, example: gender)

Question1:

Does my approach makes sense? How can variance of categorical variable be calculated?

Question2:

Is there a better way to do this? If yes how?

P.S: There is no data that reveals us the amount of time spend that could be used as a proxy to asses this.

I am using R for my analysis!

Answer 1

In general it does not make any sense to do these calculation on categorical data. One can find out what percent of categorical data belong to which category and their predict their probability of belonging to certain category and make confusion matrix (Logistic Regression) .

for simpler version you can use table command in R to check what percent of a particular quantity belongs to .

for further reading please go to What summary statistics to use with categorical or qualitative variables?

Hope this will answer your query more precisely and elaborated manner.