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Monday, November 4, 2013

Standard deviation is not the same as range of variation

Typically research results are expressed in signifies and normal deviations. For instance, in the research reviewed in this post, it is stated that the excess weight of individuals in a 12-7 days fat decline review diverse from: 87.nine additionally or minus 15.4 kg (at baseline, or prior to the 12-7 days intervention) to 81.seven in addition or minus sixteen.2 kg (following the 12-7 days intervention).

The 87.nine and 81.seven are the common weights (a.k.a. “mean” weights), in kilograms, just before and after the 12-week intervention. However, the fifteen.4 and sixteen.2 are NOT the selection of variation in weights about the indicates just before and right after 12-week intervention. They are truly the ranges all around the indicates encompassing about sixty eight p.c of all of the values measured (see determine underneath, from www.electrical-res.com).


In the determine previously mentioned, the minus and plus fifteen.4 and 16.two values would be the “mean(x) – s” and “mean(x) + s” details on the horizontal axis of histograms of weights plotted prior to and soon after the twelve-7 days intervention. This assumes that the distributions of weights are standard, or quasi-standard (i.e., comparable to a bell-shaped, or regular, curve) a widespread assumption in this variety of investigation.

The bigger the common deviation, the wider is the variation in the steps, and the flatter is the connected histogram (the bell-shaped curve). This residence has a quantity of fascinating implications, some of which will be reviewed in other posts.

Occasionally one more measure of dispersion, the variance, is reported alternatively of the regular deviation. The variance is the normal deviation squared.

The cause why normal deviations are reported as an alternative of ranges of variation is that outliers (unusually high or lower values) can significantly widen the ranges. The common deviation coefficient is much significantly less delicate to outliers.
Title: Standard deviation is not the same as range of variation
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