Quote:
Originally Posted by DanielleSisk
This is simple to do by reducing to number of bins instead of increasing them. Put all responses below the Neutral choice, the 55%, in one bin and call it say bin 4 (to keep our median at 5), then put the 12% which are Neutral into bin 5, and those above neutral, the 33%, into bin 6. Finding the average this way, (55*4+12*5+33*6)/100 = 4.78. Interesting... this shows that giving more options for a positive response gave their average, 4.45 (which should have been 4.47) a skew in the negative response direction. Now the same calculation cannot done for a '1 vote per team' because that data is unavailable.
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I'm not sure I understand: your representative bin values are entirely arbitrary, as is the average they produce. I could repeat this same calculation calling "negative" 3 and "positive" 7: I get 4.56. 2 and 8 yields 4.34; 1 and 9 is 4.12; 0 and 10 is 3.9. The problem is that the logical value to assign to each bin is the average of the values in it--1 through 4 as 2.5 and 6 to 10 as 8--but these averages are not centered about the neutral. Shrinking the bin count does not remove this problem.