Nutty Professors Mindlessly enthuse over standard deviation method of measuring variance from mean
Microsoft's Excel spreadsheet (stats tables) program allows you to calculate the standard deviation of values in specified table cells ( http://www.angelfire.com/ma/vincemoon/excel_functions.htm ).
The standard deviation method of measuring the average variation from the mean, exaggerates the effect of relatively extreme variations from the mean, compared to the simple taking the average value of variations from the mean without squares and square roots being involved. This because 2 squared plus 3 squared is 13 whereas 5 squared is 25 even though 2 and 3 add up to 5, and etc.
Thus with the standard deviation an arrow is considered as deviating from the center of the target more when it misses by zero feet 2 times, by a foot once, and by two feet twice, compared to missing by 1 foot 5 times.
The simple average of the variations from the mean without squaring and square roots being involved by way of contrast, measures being off by a foot 5 times as the same level of variance as being off by 2 feet twice off by a foot once and hitting the center, being off by zero, 2 times.
So which is the better measure? It all depends on the level of acceptable error. If you are going to be shooting after practice at a real life target that is smaller than a circle with a radius of 1 foot, then you would be realistically speaking more accurate (manifest less variance) if you missed by zero 2 times compared to missing by a foot 5 times, because missing by 1 foot would entail a complete miss.
Thus in such a case, the standard deviation would not be as good a measure of "variance" in hitting your target as the simple unsquared average of the distance from the mean.
The standard deviation would count you as showing more variance if you hit the exact center 2 times missed by a foot once and by 2 feet twice, this despite the fact that in such a case shooting at a target with a radius of less than a foot you would hit it 2 times whereas missing the center by 1 foot 5 times you would completely miss the target 5 times.
Thus I find it unacceptable that the mathematics academics, manifest this knee-jerk reaction that avers that squaring variations from the mean and then taking the square root as in the formula for the standard deviation, is of course superior to the simple unsquared average of variations from the mean, simply because the standard deviation formula exaggerates the effect of relatively larger variations.
@2006 David Virgil Hobbs
The standard deviation method of measuring the average variation from the mean, exaggerates the effect of relatively extreme variations from the mean, compared to the simple taking the average value of variations from the mean without squares and square roots being involved. This because 2 squared plus 3 squared is 13 whereas 5 squared is 25 even though 2 and 3 add up to 5, and etc.
Thus with the standard deviation an arrow is considered as deviating from the center of the target more when it misses by zero feet 2 times, by a foot once, and by two feet twice, compared to missing by 1 foot 5 times.
The simple average of the variations from the mean without squaring and square roots being involved by way of contrast, measures being off by a foot 5 times as the same level of variance as being off by 2 feet twice off by a foot once and hitting the center, being off by zero, 2 times.
So which is the better measure? It all depends on the level of acceptable error. If you are going to be shooting after practice at a real life target that is smaller than a circle with a radius of 1 foot, then you would be realistically speaking more accurate (manifest less variance) if you missed by zero 2 times compared to missing by a foot 5 times, because missing by 1 foot would entail a complete miss.
Thus in such a case, the standard deviation would not be as good a measure of "variance" in hitting your target as the simple unsquared average of the distance from the mean.
The standard deviation would count you as showing more variance if you hit the exact center 2 times missed by a foot once and by 2 feet twice, this despite the fact that in such a case shooting at a target with a radius of less than a foot you would hit it 2 times whereas missing the center by 1 foot 5 times you would completely miss the target 5 times.
Thus I find it unacceptable that the mathematics academics, manifest this knee-jerk reaction that avers that squaring variations from the mean and then taking the square root as in the formula for the standard deviation, is of course superior to the simple unsquared average of variations from the mean, simply because the standard deviation formula exaggerates the effect of relatively larger variations.
@2006 David Virgil Hobbs
posted by David Virgil at 3:14 AM
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