How to calculate an average, skipping blanks

I have a spreadsheet, where I keep the times I come in and leave at and from work. In the next column, I summarise those values in order to see the amount of time I spent at work, which gives me the amount of time I spent at work during a week.

Now I'd like to know what is the average time I spent at work during a week.

I'd thought I could achieve this using the AVERAGEIF function, using ">0" in order to skip blank entries, but this seems not to work:

E.g.

        A          B           C     D      E     F
1       Day        Date        In    Out    Diff  Cumul
2       Monday     13/10/2014  8:15  16:30  7:30  
3       Tuesday    14/10/2014  8:15  17:10  8:10  
4       Wednesday  15/10/2014  8:05  17:10  8:20  
5       Thursday   16/10/2014  8:25  17:10  8:00  
6       Friday     17/10/2014  8:25  17:00  7:50  
7       Saturday   18/10/2014                     39:50

As you see, column E contains the difference between "In" and "Out" (taking into account the lunch break), column F contains the sum of the values of column E.

For calculating the average of the entries in column F, I've tried to use the function "AVERAGEIF", as follows:

=AVERAGEIF(F1:F7;">0") // I thought of ">0" for skipping blanks,
                       //  and so only use cells which are filled in.

The result of this function however is 15:50 (no idea how to interpret this), afterwards I'd like to replace "F1:F7" by "F:F" for calculating the average of the whole sheet.

There are two solutions to my problem:

either tell the AVERAGEIF formula only to use the cells F7, F14, F21, ... (is this even possible?)
either keep on using the "F:F" range but use another condition than ">0" for skipping blanks, I think this is the easiest solution.

Does anybody know how to skip blanks in formulas?

Thanks

Solution

The answer has correctly been given by Fabian F, thanks a lot for that. The situation is the following:

I had forgotten that the cells in Column F had a special formatting [u]:mm, causing 39:50 to be correctly shown as 39:50, in normal cases this gets translated into 15:50 (you can't fit 39:50 hours in a day, hence 39:50-24:00=15:50).

It seems that blanks are skipped automatically by the AVERAGE function, so my request to skip blanks has no sense.

However, I'll keep using the formula as you can see in following template of next week:

        A           B  C  D  E      F
Monday     07/11/2016               
Tuesday    08/11/2016               
Wednesday  09/11/2016               
Thursday   10/11/2016               
Friday     11/11/2016               
Saturday   12/11/2016           0:00

As you see, column F contains sums (of empty values), hence this contains a zero value. By using the AVERAGEIF function with condition ">0", I can skip the templates of the weeks which are not filled in yet.