What is a high and low standard deviation?
A low standard deviation indicates that the data points tend to be very close to the mean. A high standard deviation indicates that the data points are spread out over a large range of values. ... The standard deviation is simply the square root of the variance.
What would be considered a high standard deviation?
For an approximate answer, please estimate your coefficient of variation (CV=standard deviation / mean). As a rule of thumb, a CV >= 1 indicates a relatively high variation, while a CV < 1 can be considered low. ... A "good" SD depends if you expect your distribution to be centered or spread out around the mean.
Why is standard deviation The square root of variance?
Standard deviation (S) = square root of the variance Because of its close links with the mean, standard deviation can be greatly affected if the mean gives a poor measure of central tendency. Standard deviation is also influenced by outliers one value could contribute largely to the results of the standard deviation.
Why standard deviation is always positive?
The standard deviation is always positive precisely because of the agreed on convention you state - it measures a distance (either way) from the mean. But you're wrong about square roots. Every positive real number has two of them. but only the positive one is meant when you use the sign.
Is variance always greater than standard deviation?
The point is for numbers > 1, the variance will always be larger than the standard deviation. Standard deviation has a very specific interpretation on a bell curve. Variance is a better measure of the "spread" of the data. ... But for values less than 1, the relationship between variance and SD becomes inverted.
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