Garmin Xero C1 gets the SD wrong

legi0n

legi0n

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my Garmin Xero C1 with the latest updates computes the SD wrong

the formula for a "sample of shots" should be
1728442047884.png

instead they use the formula for the "population of shots" as if there are no more of those shots to be ever fired.
1728442090264.png
note: x̄ and μ are the same value, the average (aka mean) of the velocities
 
It's been documented on various forums and YouTube since the Garmin was released.

The Garmin uses Population SD not Sample SD as you have discovered.

As long as you are comparing SD from the Garmin to the SD from the Garmin there should be no 'issues' as long as you are aware how the SD is calculated.

Here's one example
 
legi0n said:
my Garmin Xero C1 with the latest updates computes the SD wrong

the formula for a "sample of shots" should be
View attachment 832493

instead they use the formula for the "population of shots" as if there are no more of those shots to be ever fired.
View attachment 832495
note: x̄ and μ are the same value, the average (aka mean) of the velocities
Click to expand...
My question…How wrong?

If you had a 100 shot sample size, how different would both equations look?
 
Paul_T said:
It's been documented on various forums and YouTube since the Garmin was released.

The Garmin uses Population SD not Sample SD as you have discovered.

As long as you are comparing SD from the Garmin to the SD from the Garmin there should be no 'issues' as long as you are aware how the SD is calculated.

Here's one example
Click to expand...
I for one am not comparing SDs, I am looking at shot to shot consistency and that's what the SD shows.

my Statistics 101 professor said that population statistics should not be used unless one is certain that's the whole population. As in no more shots ever fired from that rifle with that ammo.

His fable was about a biologist who spent half a year on a small, isolated pacific island studying a species of foxes that evolved in a divergent way. He tagged, weighted and measured each of them. In the last 2 months he didn't see any tag-free foxes so he assumed he's got the whole population and wrote his 500 page PHD thesis.
When the boat arrived to take him home, he had a final look at the island through his binoculars. Then he noticed two un-tagged foxes that evaded him the whole 6 months. He had to re-write the thesis.
 
6MT said:
My question…How wrong?

If you had a 100 shot sample size, how different would both equations look?
Click to expand...
if you look at the video of that clueless guy who thinks the population SD is correct (but removed all comments after being schooled on it), for the 3 shot group he looked at, the values were very different (as in 7 vs 1.8 or so).
the sample SD is always greater than the population SD
on a sample of 10 shots, the diff would be about 5%
on a sample of 100 shots, the diff would be about 0.5%
you get the idea
 
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legi0n said:
if you look at the video of that clueless guy who thinks the population SD is correct (but removed all comments after being schooled on it), for the 3 shot group he looked at, the values were very different (as in 7 vs 1.8 or so).
Click to expand...

What are we calculating? The SD of that string, or the SD of your gun/ammo?

If its the SD of that particular string, than I think population is correct? Lets say its 10 shots. You're using all 10 of those datapoints to calculate the SD, you're not using a sample of those datapoints to calculate it.

If you want to extrapolate from that data and apply it to your gun as a whole, then yes, those 10 shots would become a sample rather than a population. For example if you loaded up 100 rounds with the same recipe and shot 10 of them, then you'd want to use sample SD not population.
 
Last edited:
legi0n said:
if you look at the video of that clueless guy who thinks the population SD is correct (but removed all comments after being schooled on it), for the 3 shot group he looked at, the values were very different (as in 7 vs 1.8 or so).
the sample SD is always greater than the population SD
on a sample of 10 shots, the diff would be about 5%
on a sample of 100 shots, the diff would be about 0.5%
you get the idea
Click to expand...
Ok cool. I wouldn’t worry then.
 
legi0n said:
my Garmin Xero C1 with the latest updates computes the SD wrong

the formula for a "sample of shots" should be
View attachment 832493

instead they use the formula for the "population of shots" as if there are no more of those shots to be ever fired.
View attachment 832495
note: x̄ and μ are the same value, the average (aka mean) of the velocities
Click to expand...
What on earth is that language? lol
Can you translate the top equation.
 
Suther said:
What are we calculating? The SD of that string, or the SD of your gun/ammo?

If its the SD of that particular string, than I think population is correct? Lets say its 10 shots. You're using all 10 of those datapoints to calculate the SD, you're not using a sample of those datapoints to calculate it.

If you want to extrapolate from that data and apply it to your gun as a whole, then yes, those 10 shots would become a sample rather than a population. For example if you loaded up 100 rounds with the same recipe and shot 10 of them, then you'd want to use sample SD not population.
Click to expand...
fair enough, but what would be the practical reason to compute the SD of just a string of ammo ?
shooters obsessing about small SDs want that for their competition ammo. Or maybe for long range hunting.
 
legi0n said:
fair enough, but what would be the practical reason to compute the SD of just a string of ammo ?
Click to expand...
Exactly, just a string of ammo. When testing a load, once it is dialed in I am not going to carry around a chronograph wherever I go so I can keep qualifing data. In long range shooting there are so many other exterior eviromental factors that have a much more significant impact.
 
legi0n said:
my Garmin Xero C1 with the latest updates computes the SD wrong

the formula for a "sample of shots" should be
View attachment 832493

instead they use the formula for the "population of shots" as if there are no more of those shots to be ever fired.
View attachment 832495
I taught statistics at university. The formula for a series of observation, as is the case when we shoot 10 shots at the range includes 1/N. The formula for a sample, chosen randomly form a defined population includes 1/N-1. Since there is no sampling here the formula with the 1/N should be the good one.
Click to expand...
 
The whole point of wanting the SD of your ammo/rifle is to predict it's behaviour when shooting in the future. To do this you must treat the shots you have measured as a sample of the entire population. To do this you must use the sample SD.

There is little point in using statistics incorrectly.

An even bigger issue is people comparing two sets of data after making a change and thinking they have made a big improvement when what they have done is statistically insignificant.

Another factor people ignore is that the chronograph is a measuring device. All measuring devices have errors that can behave in a couple of different ways which affects the data you collect. Those errors can be significant too.

This stuff is significant enough that there are entire courses and books written about how to design experiments and interpret the results correctly. It's a deep rabbit hole.

Chris.
 
legi0n said:
fair enough, but what would be the practical reason to compute the SD of just a string of ammo ?
shooters obsessing about small SDs want that for their competition ammo. Or maybe for long range hunting.
Click to expand...
Assuming the goal is to compare one load to another I don't think it really matters which SD you're using, as long as you're consistently using the same SD formula and the same number of shots to calculate it?

The way I see it, the absolute number you get isn't the really important part, the relation between two or more SD calculations is the real thing to be concerned about? And that relationship doesn't change as long as both SDs are calculated with the same formula.
 
Suther said:
Assuming the goal is to compare one load to another I don't think it really matters which SD you're using, as long as you're consistently using the same SD formula and the same number of shots to calculate it?

The way I see it, the absolute number you get isn't the really important part, the relation between two or more SD calculations is the real thing to be concerned about? And that relationship doesn't change as long as both SDs are calculated with the same formula.
Click to expand...
The absolute number is important to have a better ability to predict the range of speeds each of your shots might launch at. So yes, relative numbers are useful. But absolute numbers are more useful.
 
adamg said:
The absolute number is important to have a better ability to predict the range of speeds each of your shots might launch at. So yes, relative numbers are useful. But absolute numbers are more useful.
Click to expand...
Wouldn't extreme spread be a better indication of the range of speeds your shots might launch at? Using SD for that sounds like a good way to under-estimate that IMO.
 
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