# Language Lessons: Standard Deviation (SD)

We hearken back to high school mathematics for this one. However, before your eyes glaze over and roll back out of boredom, remember that standard deviation helps you shoot things at long ranges. Mad Duo [This article was made possible by JTF Awesome team member PROOF Research. If you don’t know who they are, first knifehand yourself and then check in here]

Language Lessons: Standard Deviation (SD)

Term: Standard Deviation

Category: Shooting Terminology

Relates To: Velocity, Group Size

Applications of Use: Any type of shooting (even with bows)

Definition: A mathematical method of measuring variations or dispersions from average

Why it matters: Calculating the SD for velocity or group size can help you predict accuracy and precision of your ammunition. Large deviations in velocity can manifest itself in poor groups (for example, large group sizes). Measuring the SD of your group sizes can give you realistic expectations of how your ammunition performs.

Into the Weeds: If you’re measuring the velocity, most chronographs will give you the SD without you having to take additional steps in calculating it. But if you’re measuring group size, you’ll have to do the math. We’ll show you both equations. Example of how to get the SD for velocity:

For the following five shots, the velocities were:

3030 fps, 3028 fps, 3015 fps, 3035 fps, 3022 fps

First, add those velocities together and then divide the sum by the number of velocities to get your mean:

3030 + 3028 + 3015 +3035 + 3022 / 5 = 3026

Now, subtract your mean from each velocity to get your deviation from the mean:

3030 – 3026 = 4

3028 – 3026 = 2

3015 – 3026 = -11

3035 – 3026 = 9

3022 – 3026 = -4

Next, square the deviations:

4×4 = 16

2×2 = 4

-11x-11 = 121

9×9 = 81

-4x-4 = 16

Add those values together and divide by the number of values:

16 + 4 + 121 + 81 + 16 /5 = 47.6

Finally, calculate the square root of 47.6 and you’ll have the SD of 6.90 fps for this five-shot group. This means there is a variance of +-6.90 fps from the mean velocity. Meaning, you can expect velocities from 3032.9 fps to 3019.1 fps for the lot of ammunition you’re using.

Keep in mind, theses numbers will vary from lot-to-lot, so if precision is important for the style shooting you’re doing, get the SD for every new lot of ammo.

The same formula can be used to measure the SD of group sizes. All you do is replace the numbers used for velocities with the extreme spread of each group. So, if you measure the extreme spread of three five-shot groups at a given distance, it would start like this: Extreme spread of three 5-shot groups at 100 yards:

1.5” + 0.9 “ + 1.3” / 3 = 1.23 (mean)

Subtract the mean from each group:

1.5 – 1.23 = 0.27

0.9 – 1.23 = -0.33

1.3 – 1.23 = 0.07

Square each deviation:

0.27×0.27 = 0.073

-0.33x-0.33 = 0.109

0.07×0.07 = .005

Add the squared values and divide by the number of values:

0.073 + 0.109 + 0.05 /3 = .08

The square root of .08 is 0.28 (.3 rounded up). This means there is a deviation of +-0.3 from the mean group size. Using this data, you can predict grouping and extreme spread even out at farther distances. The results will change according to how many groups you shoot and use in the equation. In summary, being able to more effectively predict how your weapon system will perform will increase the likelihood of your success. Test and test again to get gain the most information on variables that affect your hits.

Question to the crowd: Have you ever experienced sub-MOA groups at close distances and then notice the groups open up to 2-3-or 4 MOA at further distances? If so, how did you remedy that?

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Find them on Facebook here and on Instagram here (@proof_research). ### 2 thoughts on “Language Lessons: Standard Deviation (SD)”

• October 7, 2016 at 7:32 pm
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