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Understanding Standard Deviation

Understanding Standard Deviation. At a shooting range, targets are placed 200 yards away with a paper for every 25 shots to track the shooters accuracy. Two people are in line to shoot their round of 25 shots. The first is David, a retired sharp shooter for the marines.

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Understanding Standard Deviation

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  1. Understanding Standard Deviation

  2. At a shooting range, targets are placed 200 yards away with a paper for every 25 shots to track the shooters accuracy.

  3. Two people are in line to shoot their round of 25 shots. The first is David, a retired sharp shooter for the marines. The second is Adam, worker at a local construction site after a long day at work.

  4. What do you think the accuracy sheets will look like after the two guys each shoot one round? How do you think the two sheets will compare?

  5. Consider making bulls eye targets made specifically for each of the two shooters. -If you wanted 15 of their shots to be in the first circle, 20 in either of the first two circles, and all shots within the largest (third) circle, what would the two bulls eyes designed specifically for the shooter look like?

  6. What do you think the accuracy sheets will look like after the two guys each shoot one round? How do you think the two sheets will compare?

  7. The very center of the target (bulls eye) is like the mean. All of the shots should be spread around that center. The width of each part of the bulls eyes that you would have to make is like the standard deviation. It explains the amount of shots within that distance from the bulls eye (or mean).

  8. If someone does not shoot very accurately, each part of the target needs to be thicker. If someone is a good shooter and shoots accurately most of the time, each part of the target will be thinner. This means there is less variation in their shooting. The same applies to standard deviation. The more consistent the data, the smaller the standard deviation.

  9. Coefficient of Variation The standard deviation divided by the mean *Shows variation relative to the mean For samples: CVar = s ___ _ X *100% *If necessary, round to one decimal place

  10. Comparing Coefficientof Variation Stock A: Average price last year = $50 Standard deviation = $2 Stock B: Average price last year = $100 Standard deviation = $5 Coefficient of Variation: Stock A: Stock B:

  11. The mean of the number of sales of cars over a 3-month period is 87, and the standard deviation is 5. The mean of the commissions is $5225, and the standard deviation is $773. Which is more variable?

  12. Number of Sales: _ 87 X = s = 5 _s_ _5_ Cvar = _ 5.7% = (100) = (100) X 87 Commissions: _ $5225 X = s = $773 _s_ 773 Cvar = _ 14.8% = (100) = (100) X 5225 Commissions are more variable.

  13. P128 # 28, 29, 30

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