Standard Deviation

[247sniper]

Standard Deviation...Can someone please explain what it means in a bit of detail please

Many thanks

Steve.

[Joe O]

I can only refer you to, the guide that comes with your chronograph,or this URL:

http://home.comcast.net/~jesse99/math.html

My simple explanation is ,"It's the average deviation from the average velocity.I like to have my SD under 20.Single didgets are great.

[dellaquila]

Technically, standard deviation is the square root of the variance in a data set. The variance is the sum of the differences between each data point and the mean or average of the points divided by n-1 where n is the number of data points. In shooting, to find the variance you would need to find the average velocity for all of the shots, and then subtract that from each individual velocity and square the result. Then if you add them all up and divide by n-1 where n is the number of shots, you have the variance. Take the square root of that and you have the standard deviation. The overall meaning of sd is that it's a measure of the variation or spread of the data points. You want low sd in almost every case it's used, that just means your process is tighter and there's little change from one shot to another.

A simple example using small numbers:
If your velocities were 1, 2, 3, 4, 5 then the avg would be (1+2+3+4+5)/5 or 3. Then you subtract 3 from each data point and get -2, -1, 0, 1, 2. Squaring each of them yields 4, 1, 0, 1, 4. The sum of those is 10. 10/(n-1) = 10/(4) = 2.5 which is the variance. The sd would then be sqrt(2.5) or 1.58 which is pretty good relatively.

Now say that data set was changed to be 1, 2, 3, 4, 10. The new avg is 4. The new variance is 12.5 and the new sd is 3.54, over 2 times bigger just from changing the 5 to 10 in the data set. So yeah, bottom line, you want the smallest sd you can get.

[GaCop]

Technically, standard deviation is the square root of the variance in a data set. The variance is the sum of the differences between each data point and the mean or average of the points divided by n-1 where n is the number of data points. In shooting, to find the variance you would need to find the average velocity for all of the shots, and then subtract that from each individual velocity and square the result. Then if you add them all up and divide by n-1 where n is the number of shots, you have the variance. Take the square root of that and you have the standard deviation. The overall meaning of sd is that it's a measure of the variation or spread of the data points. You want low sd in almost every case it's used, that just means your process is tighter and there's little change from one shot to another.

A simple example using small numbers:
If your velocities were 1, 2, 3, 4, 5 then the avg would be (1+2+3+4+5)/5 or 3. Then you subtract 3 from each data point and get -2, -1, 0, 1, 2. Squaring each of them yields 4, 1, 0, 1, 4. The sum of those is 10. 10/(n-1) = 10/(4) = 2.5 which is the variance. The sd would then be sqrt(2.5) or 1.58 which is pretty good relatively.

Now say that data set was changed to be 1, 2, 3, 4, 10. The new avg is 4. The new variance is 12.5 and the new sd is 3.54, over 2 times bigger just from changing the 5 to 10 in the data set. So yeah, bottom line, you want the smallest sd you can get.

Great explaination!

[Jim White]

Just a word to the wise...just because the SD is real low won't mean your groups are good. I've had loads with large SD put make bug holes on the target and vice versa.

[Fred_C_Dobbs]

In a nutshell, SD is a calculation of how close your typical load's MV tends to be to the average MV of all your loads. The lower the SD, the more tightly they're all clustered around that magical average MV number.

SD is macht nichts at short range but at longer ranges, it's King Schiznit. That's because the rate of change due to gravity is exponential with respect to time of flight.

At 100 yards, time of flight is too short for even a hefty MV difference of, say, 50 fps to make a very substantial difference in bullet drop. That is why, at such short ranges, barrel harmonics is the key determinant.

But if you run that out to, say, 500 yards, because bullet drop increases at the time of flight squared (ToF^2), even if fired in a vacuum, that 50 fps difference in velocity will cause 25x as much difference in POI @500 (5^2 = 25) as it did @100. Factor in de-acceleration due to aerodynamic drag and the difference becomes even more pronounced.

[GaCop]

In a nutshell, SD is a calculation of how close your typical load's MV tends to be to the average MV of all your loads. The lower the SD, the more tightly they're all clustered around that magical average MV number.

SD is macht nichts at short range but at longer ranges, it's King Schiznit. That's because the rate of change due to gravity is exponential with respect to time of flight.

At 100 yards, time of flight is too short for even a hefty MV difference of, say, 50 fps to make a very substantial difference in bullet drop. That is why, at such short ranges, barrel harmonics is the key determinant.

But if you run that out to, say, 500 yards, because bullet drop increases at the time of flight squared (ToF^2), even if fired in a vacuum, that 50 fps difference in velocity will cause 25x as much difference in POI @500 (5^2 = 25) as it did @100. Factor in de-acceleration due to aerodynamic drag and the difference becomes even more pronounced.

+1, lower SD means better groups at 1K, less verticle stringing.

[Hedge]

Well described, Fred.

Haven't seen a better practical description of the reason to strive for low SD.

[Wrangler John]

You guys are all wrong.

Standard deviation is where you can't pass a gun shop without entering and fondling the new rifles. It is treatable with daily injections of Hoppies #9.

[GaCop]

You guys are all wrong.

Standard deviation is where you can't pass a gun shop without entering and fondling the new rifles. It is treatable with daily injections of Hoppies #9.

Man, ya learn sumpthin every day!