Dispersion is where the real information lives, and there are five measures with different failure modes.
The range, max minus min, is 36.70 points on the twenty-quarter series. It uses two observations and throws away eighteen. It also grows mechanically with sample size, so it tells you almost nothing.
Mean absolute deviation averages the absolute distances from the mean: Σ|rᵢ − r̄|/n = 6.956 points. It is the honest measure of typical distance, and it is unpopular only because absolute values are hard to differentiate, which mattered before computers and matters not at all now.
How are variance and standard deviation calculated?
Sample variance squares the deviations and divides by n − 1. On this series the deviations sum to zero, as they must, and their squares sum to 1650.762, so s² = 1650.762/19 = 86.882211 and s = 9.321063 points. Divide by n instead and the standard deviation falls to 9.085048, a difference of 0.236 points on a sample of twenty. That divisor is not a matter of taste. Dividing by n biases the estimate downward, because the deviations are taken from the sample's own mean, which is by construction the value that minimises them.
Two library defaults sit on opposite sides of this, and neither warns you. The standard array library's standard deviation defaults to the population form and the standard dataframe library's defaults to the sample form. On the Sharpe ratio computed in Worked example 5 that single default moves the answer from 0.1136 to 0.1166, which is a 2.6% relative change produced by a keyword nobody typed.
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What are downside deviation and the coefficient of variation?
Downside deviation asks how far below a target the series goes. Take the shortfall min(rᵢ − target, 0), square it, sum, divide, take the root. Against a zero target the twenty-quarter series gives 6.252368 with six breaching quarters; against a +2% target, 7.145112 with eight. Both the target and the denominator are choices you must disclose, since some conventions divide by the count of breaches rather than of observations. Two funds ranked under different conventions are not ranked at all.
The coefficient of variation, s/r̄, is the unit-free comparison a raw standard deviation cannot make. A fund with an 11.2% mean and a 14.6% standard deviation has a CV of 1.3036; one with a 6.8% mean and a 7.4% standard deviation has 1.0882. The second delivers less volatility per unit of return, and staring at the two standard deviations never reveals that.
It has a sharp limit, and the twenty-quarter series shows it: 9.321063/2.67 = 3.4910. As the mean approaches zero the ratio explodes, and a negative mean flips the sign while draining the meaning. Use it on quantities that are reliably positive, and treat it with suspicion on a return series whose mean is small relative to its noise.