Standard Deviation Overview

Standard Deviation and Music Tests

My question relates to music tests.  A while ago, you mentioned that in addition to the average score and a few other things, that it’s also important to check the standard deviation for each song to see how much the respondents agreed in their evaluation of the songs.  Can you explain that in more detail? 

I’ll be happy to explain it.

If you simply look at a song’s mean (average) score, you don’t know how that scored was achieved.  That is, let’s say that on a 10-point rating scale, a song receives a score of 5.5—right in the middle of the scale.

The first reaction to such a score is probably something like, “That’s an average testing song; not a hit; and not a piece of trash.  But is that true?  The standard deviation tells you the amount of agreement among the respondents in reference to their song scores.  (I know you could look at the raw scores to see how they are distributed, but if you have 100 respondents and test 400+ songs, that’s a lot of data to review.  You’d go nuts looking at all those numbers.  The standard deviation speeds up the process.)

To make this easier to see, I developed a sample spreadsheet for three songs—each with an average (mean) score of 5.5.  While each song’s average is 5.5, the average was arrived at in three unique ways.  Look at the bottom of the table to see the standard deviations.

Respondent	Song 1	Song 2	Song 3
1	1	1	5
2	1	3	5
3	1	3	5
4	1	3	5
5	1	4	5
6	1	4	5
7	1	4	5
8	1	5	5
9	1	5	5
10	1	6	5
11	10	6	6
12	10	6	6
13	10	6	6
14	10	7	6
15	10	7	6
16	10	7	6
17	10	8	6
18	10	8	6
19	10	8	6
20	10	9	6
Mean	5.5	5.5	5.5
Standard Deviation	4.6	2.1	0.5

Song 1 has a standard deviation of 4.6, which is high for a 10-point scale and shows that there isn’t a lot of agreement among the respondents—the song is highly polarized—respondents either hate it or love it.  Song 2 has a standard deviation of 2.1—more agreement than Song 1, but still shows that the song is not universally liked or disliked (there is some polarization).  Song 3 has a standard deviation of 0.5, indicating that there is a lot of agreement among the respondents.

Get the idea here?  In addition to the average score, you need to look at the standard deviation (standard/average difference from the mean) of the songs to determine how much the respondents agree in their ratings.  A song that receives a standard deviation of 0.0 indicates that everyone rated the song the same way.  The higher the standard deviation, the more disagreement there is among the respondents.  (The standard deviation can’t be higher than the highest number in the rating scale.)