Formula for calculating SD?
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Re: Formula for calculating SD?
Here is how to figure ES and SD.
EXAMPLE:
Shot 1) <span style="color: #FF0000">3,642fps</span> Shot 2) <span style="color: #FF0000">3,667fps</span> Shot 3) <span style="color: #FF0000">3,674fps</span>
Average Velocity=<span style="color: #3366FF">3,661fps</span>
Now you can calculate the following: (use the average fps to find the difference)
(<span style="color: #3366FF">3,661</span>-<span style="color: #FF0000">3,642</span>) Squared=<span style="font-weight: bold">361</span>
(<span style="color: #FF0000">3,667</span>-<span style="color: #3366FF">3,661</span>) Squared=<span style="font-weight: bold">36</span>
(<span style="color: #FF0000">3,674</span>-<span style="color: #3366FF">3,661</span>) Squared=<span style="font-weight: bold">169</span>
Now you would add the results:
<span style="font-weight: bold">361</span>
<span style="font-weight: bold">36</span>
<span style="text-decoration: underline"><span style="font-weight: bold">169</span>+</span>
<span style="font-weight: bold">566</span> divided by 3 (number of shots) Equals <span style="color: #33CC00">188.6</span>
<span style="color: #33CC00">188.6</span> the square root of this will give you the SD of <span style="color: #006600">13.73fps</span>
And the ES is the difference from the lowest velocity measured to the highest. In this case the ES is <span style="color: #660000">34fps</span>
<span style="font-weight: bold">ES of 34fps
SD of 13.73fps</span>
Here is how to figure ES and SD.
EXAMPLE:
Shot 1) <span style="color: #FF0000">3,642fps</span> Shot 2) <span style="color: #FF0000">3,667fps</span> Shot 3) <span style="color: #FF0000">3,674fps</span>
Average Velocity=<span style="color: #3366FF">3,661fps</span>
Now you can calculate the following: (use the average fps to find the difference)
(<span style="color: #3366FF">3,661</span>-<span style="color: #FF0000">3,642</span>) Squared=<span style="font-weight: bold">361</span>
(<span style="color: #FF0000">3,667</span>-<span style="color: #3366FF">3,661</span>) Squared=<span style="font-weight: bold">36</span>
(<span style="color: #FF0000">3,674</span>-<span style="color: #3366FF">3,661</span>) Squared=<span style="font-weight: bold">169</span>
Now you would add the results:
<span style="font-weight: bold">361</span>
<span style="font-weight: bold">36</span>
<span style="text-decoration: underline"><span style="font-weight: bold">169</span>+</span>
<span style="font-weight: bold">566</span> divided by 3 (number of shots) Equals <span style="color: #33CC00">188.6</span>
<span style="color: #33CC00">188.6</span> the square root of this will give you the SD of <span style="color: #006600">13.73fps</span>
And the ES is the difference from the lowest velocity measured to the highest. In this case the ES is <span style="color: #660000">34fps</span>
<span style="font-weight: bold">ES of 34fps
SD of 13.73fps</span>
Re: Formula for calculating SD?
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: MuleHunter</div><div class="ubbcode-body">
<span style="color: #33CC00">188.6</span> Squared will give you the SD of <span style="color: #006600">13.73fps</span>
</div></div>
You need to find the square root of 188.6 to get 13.73. Don't square it.
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: MuleHunter</div><div class="ubbcode-body">
<span style="color: #33CC00">188.6</span> Squared will give you the SD of <span style="color: #006600">13.73fps</span>
</div></div>
You need to find the square root of 188.6 to get 13.73. Don't square it.
Re: Formula for calculating SD?
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: DBohn</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: MuleHunter</div><div class="ubbcode-body">
<span style="color: #33CC00">188.6</span> Squared will give you the SD of <span style="color: #006600">13.73fps</span>
</div></div>
You need to find the square root of 188.6 to get 13.73. Don't square it. </div></div>
Minor technicality.
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: DBohn</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: MuleHunter</div><div class="ubbcode-body">
<span style="color: #33CC00">188.6</span> Squared will give you the SD of <span style="color: #006600">13.73fps</span>
</div></div>
You need to find the square root of 188.6 to get 13.73. Don't square it. </div></div>
Minor technicality.
Re: Formula for calculating SD?
Your right, square root. I just punch in the 188.6 on the calculator and hit the square root button.
Your right, square root. I just punch in the 188.6 on the calculator and hit the square root button.
Re: Formula for calculating SD?
Easiest just to plug it into an Excel spreadsheet (and I believe there is also a free OpenOffice equivalent). I like to keep track of my shots this way anyways.
Easiest just to plug it into an Excel spreadsheet (and I believe there is also a free OpenOffice equivalent). I like to keep track of my shots this way anyways.
Re: Formula for calculating SD?
Understand that SD is a measure of AVERAGE DEVIATIONS from the MEAN of a set of numbers. Some of these numbers are NEGATIVE and some are POSITIVE. I like to call this "spread-out-ness". Think of it as irregularity, noise, or variation in a system. Spreadoutness.
The mean is subtracted from each of the individual data. Each deviation is then squared so that negative and positive deviations don't cancel each other out.
These SQUARED deviations are summed. This gives the SUM OF THE SQUARED DEVIATION (i.e. "SUM OF SQUARES"). The SQUARE ROOT of the sum of the squared deviations is then found to return to sensible numbers, like the ones you started with.
Finally, the square root of the sum of squared deviations is DIVIDED BY THE NUMBER OF OBSERVATIONS MINUS ONE, to get the Standard Deviation. (the AVERAGE DEVIATION FROM THE MEAN).
Extreme spread has always seemed to me to be a much more graphic, useful, and sensitive metric for representing ballistic consistency than S.D., however.
Understand that SD is a measure of AVERAGE DEVIATIONS from the MEAN of a set of numbers. Some of these numbers are NEGATIVE and some are POSITIVE. I like to call this "spread-out-ness". Think of it as irregularity, noise, or variation in a system. Spreadoutness.
The mean is subtracted from each of the individual data. Each deviation is then squared so that negative and positive deviations don't cancel each other out.
These SQUARED deviations are summed. This gives the SUM OF THE SQUARED DEVIATION (i.e. "SUM OF SQUARES"). The SQUARE ROOT of the sum of the squared deviations is then found to return to sensible numbers, like the ones you started with.
Finally, the square root of the sum of squared deviations is DIVIDED BY THE NUMBER OF OBSERVATIONS MINUS ONE, to get the Standard Deviation. (the AVERAGE DEVIATION FROM THE MEAN).
Extreme spread has always seemed to me to be a much more graphic, useful, and sensitive metric for representing ballistic consistency than S.D., however.
Re: Formula for calculating SD?
Using Excel 97-2003, listing the velocities in cells B1 thru B10:
Average velocity =Average(B1:B10)
SD = STDEV(B1:B10)
ES = MAX(B1:B10)-MIN(B1:B10)
Using Excel 97-2003, listing the velocities in cells B1 thru B10:
Average velocity =Average(B1:B10)
SD = STDEV(B1:B10)
ES = MAX(B1:B10)-MIN(B1:B10)
Re: Formula for calculating SD?
and one more SD variation in Excel
I have 10 shot velocities in cells O4 thru X4
=SQRT(DEVSQ(O4:X4)/(COUNT(O4:X4)-1))
and my ES formula right next to it
=IF(O4>0,MAX(O4:X4)-MIN(O4:X4)," ")
and one more SD variation in Excel
I have 10 shot velocities in cells O4 thru X4
=SQRT(DEVSQ(O4:X4)/(COUNT(O4:X4)-1))
and my ES formula right next to it
=IF(O4>0,MAX(O4:X4)-MIN(O4:X4)," ")
