How to calculate mean with blank items

Question

I have 20 items that people asked to pick their top 10 and rate them from 1-10 with 1 being the best.  We want to calculate which item ended up being #1 for the group, then #2, etc.  However, since some items were left blank, they look like they are a score of zero which throws the averages.  How do I actually calculate the correct result?

example of simpler version would be--Review these 5 items and rank your top 3 with 1-3 and 1 being best:

               Person 1            Person 2             Person 3

Item1:          1                       3          

 

Item2:          2                       2                        1

 

Item 3:                                                           3                                            

 

Item 4:         3                    

 

Item 5:                                  1                         2

Answer 1

Typically the way to rank votes like this is to assign points to each vote, where higher rankings = more points. The simplest way for this example would be to give 3, 2, 1 points for ranking 1st, 2nd, 3rd, and 0 points for no ranking. Your point values for the example you gave would look like:

 

              Person 1 Person 2 Person 3
Item1:   3              1
Item2:   2              2                3
Item 3:                                    1
Item 4:  1
Item 5:                   3                2

 

Here, Item 2 is overall the favorite, with 7 points total, and so on

Item 2: 7 pts

Item 5: 5 pts

Item 1: 4 pts

Items 3,4: 1 pt

 

If you wanted to count a #1 ranking as worth extra over a #2 ranking, you could give an uneven scale of points, perhaps 4, 2, 1 for 1st, 2nd, 3rd place.