You are doing your calculations with the wrong figures. The category is what you want to find the mean of. For your first set of data where the categories are 1,2,3... 7 and the frequency of the i^{th}category is f_{i}the mean is

The median is the value of i where 50% of the samples are less than or equal to i.

The mode is the value of i which is most common.

The variance can be calculated as