Because this subject relates to shooting, hunting and common knowledge, I figured I would put it here.
As we know, uniformity or consistency is very important as we work up loads and this subject deals with that subject, so at the risk of being tarred and feathered here it comes:
STANDARD DEVIATION
Almost all of the people who are interested in shooting sooner or later will come across the words “Standard Deviation”. A few of them will know what it is but, most folks just see some numbers and don’t know what to do with them or what they mean.
At the risk of boring many, I thought I would try to give these people an idea of what Standard Deviation really means. To do this, we have to understand why we even need or want to have such a thing.
First I’ll just say Standard Deviation has to do with situations where we are measuring several examples of something. For instance maybe we want to find out what sort of velocity a certain ball/powder/patch load will have so we set up our chronograph and fire 5 shots thru it. Not surprisingly, it will give us 5 different velocities. These velocities may be real close to each other or they may be quite different.
If we add up the 5 velocities and then divide by 5 we can come up with some “average velocity”.
While this gives us a useful value if all of the shots have a velocity that is fairly close to each other it doesn’t tell the whole story if the velocities of each shot is quite a bit different.
Saying this with a few numbers may show what I mean.
Lets say a given load gives the following velocity for 5 shots: 1500, 1510, 1495, 1505, 1490. Adding these up and dividing by 5 gives us the average 1500. The maximum and minimum variation from the average is 10.
Now lets say we are using a poor powder and run the same test and we come up with the following velocity for 5 shots: 1250, 1495, 1600, 1627, 1527. If we add these up and divide by 5 we come up with an average of 1499.8 which is pretty close to the first groups average. We notice that the maximum variation from the average is about -250 but this only happened once so it is not representative of what we can typically expect from the load.
This leaves us wondering what are the chances of this error happening again? What is a reasonable number to think about for a high and a low velocity?
While folks could come up with a probability number for any velocity error you might want to think about, the Mathematicians decided it would be easier and more useful just to come up with a value that if it is added to or subtracted from the average would cover 98 percent of all of the cases. In other words, a number that would represent the maximum and minimum variation from the average 98 percent of the time. This, they decided would be called Standard Deviation. It shows how uniform or varied the data is.
If the Standard Deviation is a small number it means there will be very little change from the average. You can expect little change from the average.
If the Standard Deviation is a large number it means you will see a lot of change and can expected a lot of variation from the average.
OK, so how do you use it?
When you see some data for anything where a number of pieces of data were collected whether it is the velocity of a load or the percentage of return of a Stock or Bond there may (should) be the average and the Standard Deviation. If you add the value of the Standard Deviation to the average you will know what the maximum should be 98 percent of the time. If you subtract the Standard Deviation from the average you will know what the minimum should be 98 percent of the time.
Using numbers again, if the Average interest return for a bond is 7 percent and the Standard Deviation for that bonds performance over the last 5 years is 3 then you can figure that there is a 98 percent chance that the bond will produce something between 4 and 10 percent.
If the Standard Deviation is large expect the rate of return to be all over the place. If it is small you can expect the rate of return to be fairly constant.
If the velocity of a load averages 1740 FPS with a standard deviation of 35 there is a 98 percent chance that the loads will have a 1705 to 1775 FPS velocity.
If the velocity of a load averages 1740 FPS with a Standard Deviation of 5 there is a 98 percent chance that the loads will have a 1735 to 1745 FPS velocity.
When I say there is a 98 percent chance the variation will fall within the high and low values you should keep in mind that MOST of the velocities will be close to the average and very few of them will be out at the high or low value.
I won't try to explain that in detail but just remember, for consistency in shooting, we want the smallest Standard Deviation we can have.
Hopefully this wasn't too boring and you won't heat the tar very hot. :grin:
zonie
As we know, uniformity or consistency is very important as we work up loads and this subject deals with that subject, so at the risk of being tarred and feathered here it comes:
STANDARD DEVIATION
Almost all of the people who are interested in shooting sooner or later will come across the words “Standard Deviation”. A few of them will know what it is but, most folks just see some numbers and don’t know what to do with them or what they mean.
At the risk of boring many, I thought I would try to give these people an idea of what Standard Deviation really means. To do this, we have to understand why we even need or want to have such a thing.
First I’ll just say Standard Deviation has to do with situations where we are measuring several examples of something. For instance maybe we want to find out what sort of velocity a certain ball/powder/patch load will have so we set up our chronograph and fire 5 shots thru it. Not surprisingly, it will give us 5 different velocities. These velocities may be real close to each other or they may be quite different.
If we add up the 5 velocities and then divide by 5 we can come up with some “average velocity”.
While this gives us a useful value if all of the shots have a velocity that is fairly close to each other it doesn’t tell the whole story if the velocities of each shot is quite a bit different.
Saying this with a few numbers may show what I mean.
Lets say a given load gives the following velocity for 5 shots: 1500, 1510, 1495, 1505, 1490. Adding these up and dividing by 5 gives us the average 1500. The maximum and minimum variation from the average is 10.
Now lets say we are using a poor powder and run the same test and we come up with the following velocity for 5 shots: 1250, 1495, 1600, 1627, 1527. If we add these up and divide by 5 we come up with an average of 1499.8 which is pretty close to the first groups average. We notice that the maximum variation from the average is about -250 but this only happened once so it is not representative of what we can typically expect from the load.
This leaves us wondering what are the chances of this error happening again? What is a reasonable number to think about for a high and a low velocity?
While folks could come up with a probability number for any velocity error you might want to think about, the Mathematicians decided it would be easier and more useful just to come up with a value that if it is added to or subtracted from the average would cover 98 percent of all of the cases. In other words, a number that would represent the maximum and minimum variation from the average 98 percent of the time. This, they decided would be called Standard Deviation. It shows how uniform or varied the data is.
If the Standard Deviation is a small number it means there will be very little change from the average. You can expect little change from the average.
If the Standard Deviation is a large number it means you will see a lot of change and can expected a lot of variation from the average.
OK, so how do you use it?
When you see some data for anything where a number of pieces of data were collected whether it is the velocity of a load or the percentage of return of a Stock or Bond there may (should) be the average and the Standard Deviation. If you add the value of the Standard Deviation to the average you will know what the maximum should be 98 percent of the time. If you subtract the Standard Deviation from the average you will know what the minimum should be 98 percent of the time.
Using numbers again, if the Average interest return for a bond is 7 percent and the Standard Deviation for that bonds performance over the last 5 years is 3 then you can figure that there is a 98 percent chance that the bond will produce something between 4 and 10 percent.
If the Standard Deviation is large expect the rate of return to be all over the place. If it is small you can expect the rate of return to be fairly constant.
If the velocity of a load averages 1740 FPS with a standard deviation of 35 there is a 98 percent chance that the loads will have a 1705 to 1775 FPS velocity.
If the velocity of a load averages 1740 FPS with a Standard Deviation of 5 there is a 98 percent chance that the loads will have a 1735 to 1745 FPS velocity.
When I say there is a 98 percent chance the variation will fall within the high and low values you should keep in mind that MOST of the velocities will be close to the average and very few of them will be out at the high or low value.
I won't try to explain that in detail but just remember, for consistency in shooting, we want the smallest Standard Deviation we can have.
Hopefully this wasn't too boring and you won't heat the tar very hot. :grin:
zonie
