Why is the average score not always in the middle of the range - theliberators/columinity.docs GitHub Wiki

Teams with a subscription can see their team's range of scores in addition to the average result. This is useful for getting a sense of the distribution of scores. If the average score is 70 and the range falls between 65 and 75, the team has a high level of consensus. But if the range goes from 30 to 90 with the same average, it means that some people gave very low scores and others gave very high ones.

An extreme example is shown below and is useful to explain why this happens.

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In the example, the stakeholders (yellow) score 70 on average for "Stakeholder Concern." Their scores (the yellow bar) range from 7 to about 9, so the average is clearly not in the middle of the yellow bar. Why does this happen?

This snapshot's (fictional) data shows that the three stakeholders gave an average score of 70, 70, and 100. This results in:

  • A median average of 70
  • The lowest end of the range is calculated with the 15% percentile and is 70
  • The highest end of the range is calculated with the 85% percentile and is 91

These results correspond with the screenshot. The fact that the average falls all the way on the left of its range indicates that the underlying distribution is strongly positively skewed. Or, more simply put, most scores cluster around the low end (or the high end) instead of somewhere in the middle. The range is helpful in this case because it helps us understand the distribution of scores and how to interpret it. If the average score falls in the middle of the range, this indicates a normal distribution. The scores in such distributions cluster around the middle with a few at the lower end and a similar number at the higher end. In our tool, distributions often become more normal as more people participate. So the more participants you have, the more normal the distribution tends to be. On the other hand, with relatively few participants you often end up with a positively or negatively skewed distribution. This doesn't impact the meaning of your scores.