Standard deviation is not the same as range of variation
Often research results are expressed in means and standard deviations. For example, in the study reviewed in this post , it is stated that the weight of participants in a 12-week weight loss study varied from: 87.9 plus or minus 15.4 kg (at baseline, or before the 12-week intervention) to 81.7 plus or minus 16.2 kg (after the 12-week intervention). The 87.9 and 81.7 are the average weights (a.k.a. “mean” weights), in kilograms, before and after the 12-week intervention. However, the 15.4 and 16.2 are NOT the range of variation in weights around the means before and after 12-week intervention. They are actually the ranges around the means encompassing approximately 68 percent of all of the values measured (see figure below, from www.electrical-res.com). In the figure above, the minus and plus 15.4 and 16.2 values would be the “mean(x) – s” and “mean(x) + s” points on the horizontal axis of histograms of weights plotted before and after the 12-week intervention. This assumes that the dis...