I'm on the lookout now for a definition of SD and MAD.
What can make this confusing is the use of two terms that are synonymous: Mean and Average. So recognize they're just being used interchangeably to make things a bit easier to follow.
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MAD: Mean Absolute Deviation. This is the mean of the deviations from the average of all data points. In other words, what is the average deviation from the overall mean.
Example (small number of data points):
12 14 16 18
Sum of the items is 60. Mean of the items is 15 (60/4).
How far, on the average is each data point from the overall mean?
12-15= -3
14-15= -1
16-15= 1
18-15= 3
The mean "absolute" deviation is the absolute value of the difference, so the negatives become positives. Thus the four absolute deviations from the mean are
3, 1, 1, and 3.
The sum of those absolute deviations is 8. The mean absolute deviation, then, is 8/4, or 2.
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SD: Standard Deviation. It's a little trickier. SD is the square root of the average *squared* deviation from the overall mean, as opposed to the average *absolute* deviation from the overall mean.
It has value in statistics as it describes a distribution that is normally distributed (meaning a bell-shaped curve of specific characteristics). It's simply a different measure of dispersion, except for this: If you can assume your dispersion of velocities is "normal," meaning approximating a bell-shaped distribution, the standard deviation means this:
In a normal distribution:
--About 68 percent (specifically 68.26 percent) of all data points will be within 1 standard deviation of the mean (that's both above and below).
--About 95 percent of all data points (specifically 95.44 percent) will be within two standard deviations of the mean. (both above and below the mean).
For this reason, the standard deviation has more value (to those versed in statistics) because it gives an indication of how closely the distribution centers around the mean.
It gives more weight to the values further from the mean (that's what the squaring does). So, if most values are close, they're accounted for that way; if further, more weight is given to them.
In our example from above:
The average *squared* deviation from the mean:
12-15= -3 9
14-15= -1 1
16-15= 1 1
18-15= 3 9
The sum of those squared deviations is 20. The average is 20/4 or 5. The square root of 5 is about 2.24.
You'll note it's higher than the MAD, but that's to be expected, as it's assuming a bell-shaped distribution.
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Conceptually, the Mean Absolute Deviation is a little easier to understand; however, the Standard Deviation has more value as it can be used to forecast just how good the overall distribution of velocities would be.
For all intents and purposes, Extreme Spread is worthless unless it's very tight. You can't know if a wide ES is due to the data points being all spread out more-or-less evenly, or if there's just one wild one making the range much wider.
While the Standard Deviation will take into account extreme values, it will not overweight them so much as to make the statistic valueless as is the case with Extreme Spread.
Two more things about this:
First, there's always the question of how many data points you need for these statistics to be valuable (meaning, stable). I generally shoot 10 at a load that's close to my "working" or potentially max load. But usually I'll start low, shoot I'll shoot 5 at the low level and look at the Chrono readings to get a sense of where I am. Then the next level up, and maybe 5 more.
These are what I consider my "safety" loads, i.e., starting at the bottom, at what should be a safe pressure. I'll shoot them through the Chrono and see where I am. I'm not quantifying a load (as this is a low load to begin with), but rather ensuring I'm starting safe.
When I get to a higher powder charges, I load 10, and that's my basic test number. IMO, anything much less than 10 is going to be relatively unreliable.
I should note I've been doing statistics for 30+ years, teaching and using them, so I can look at numbers and get a sense of how stable they are. Less experienced stat users might want to shoot 15 at one load. But 10 usually lets me see where I am.
Second, in the final analysis, all measures of dispersion only have value in comparison to some standard. That standard might be what you typically get as data, or some threshold or what others may indicate as "good enough."
You'll find that being able to see how fast your loads are will really help you in reloading. Try chronographing some commercial ammo first, then compare yours. I think you'll be surprised.
), but the end result is where and how consistent the round is on target...
