Q: I recently was questioned by client about the meaning of "standard deviation" and I had some difficulty explaining it in a way the group could really understand. Can you provide a simple explanation—in layman's terms—and give me some additional information I could use to explain why this is important for the client to have?
A: The standard deviation provides some idea about the distribution of scores around the mean (average). The smaller the standard deviation, the more narrow the range between the lowest and highest scores or, more generally, that the scores cluster closely to the average score.
You might think of it as a measure of "agreement" between raters. If everyone gave the same score, then the standard deviation would be zero and the agreement would be high (or perfect).
For an individual leader, you might notice that most Observers agree on their scores for that person when it comes to Model the Way, for example, as illustrated by a low standard deviation. But on the practice Inspire a Shared Vision, Observers don't agree about how that person behaves as would be illustrated by a high standard deviation. However, given the relatively small sample sizes at an individual level, the standard deviation, like the average score, can be heavily influenced by one or two outliers (scores much different from everyone else).
From a more empirical perspective, we assume a normal distribution of scores (which is very true as the sample size increases). In this case it can be said that approximately two-thirds of the scores will fall within the range of plus or minus one standard deviation around the mean (and 90% of the scores would fall between two standard deviations, plus and minus). For example, with a mean score of 50 and standard deviation of 10, we would expect that most scores would fall between 40 and 60 and that nearly all scores would fall between 30 and 70.
In a rough way, the standard deviation could be considered a measure of the extent to which one's observers agree or disagree with each another. The smaller the standard deviation suggests that people are in more agreement with one another than would be the case with a large standard deviation. Remember, however, that a single "outlying" response can distort the standard deviation and the sense of agreement between Observers. So taking this one important caveat into consideration, looking at the standard deviation can help leaders make a quick determination of whether others see them in the same fashion or not.
Barry Posner is the Accolti Professor of Leadership at SCU's Leavey School of Business, where he served as Dean for 12 years. Together with Jim Kouzes, he is author of The Leadership Challenge and over a thirty other books and workbooks on leadership and leadership development, including Credibility: How Leaders Gain and Lose It, Why People Demand It.