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Empirical Rule Basic

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Ok in this video I am going to show you how we apply the mean and the standard deviation In our last video we had the data values of 60, 70, 80, 80, 90, and 100 and in our computations we found that the sample mean was 80 we found that the median was also 80, which indicates we have a normal distribution. and then we went further to find out that the sample standard deviation was about, now it's rounded, but it was about 14. Now if we know we have a Normal Distribution we can apply the empirical rule The Empirical Rule says that in a normal distribution 68% of the data will fall within 1 standard deviation within 1 standard deviation 95% - this writing is atrocious! will fall within 2 standard deviations hopefully I get better at this (writing!) and 99.7% of the time data will fall within 3 standard deviations so basically we can make predictions on FUTURE data values based on the data values we have here so we have 6 test grades we can make predictions on what that 7th, 8th, or 9th test grade might be based on the mean and standard deviation again the Empirical Rule ONLY applies to Normal Distributions and again a Normal Distribution is when the mean and the median are equal as a side note if the mean is less than the median then you have a distribution that's skewed which means there must be an outlier to skew the data that's skewed LEFT we skew in the direction of the TAIL of the data, so this would be skewed LEFT obviously our mode, our highest point is here here we have our mode and what would happen is the median would still be in about the center of the data but the mean would be drawn closer to the outlier that's skewing the data so in this case you'd have the mean which is less than the median and the mode the mode is our largest value. Alternatively, if the mean is GREATER than the median, this is a situation where we are skewed RIGHT and again in order to be skewed there are outliers that draw the mean to either smaller or in this case bigger so here we are skewed RIGHT our highest point is our mode the middle of our range here, is about here, for the median, but due to a large outlier the mean is increased so now that was our commercial break, back to our situation at hand.... we have a normal distribution and in a normal distribution the mean so the mean is in the center of the distribution and the mean is the best predictor of central tendancy unlike when we are skewed and the median is in the center so you have the mean in the center and then the Empirical Rule tells us to go out 3 standard deviations from the mean our mean was 80 and the empirical rule says that we add 3 standard deviations and subtract 3 standard deviations well our standard deviation is 14 so if we continually add 14 1 standard deviation above the mean would be 94 add another 14, we have 108 and lastly add one more 14, and we have 122. if we conintually subtract the standard deviations in this case 14 we find that we have 1 standard deviation below the mean at 66 2 standard deviations below the mean at 52, and 3 standard deviations below the mean at 38. which tells us then that, 68% of the time, or we have a 68% chance a probability of having test scores that fall between a 66 and a 94 there is a 95% chance that test scores will fall between a 52 and a 108 and there is almost 100%, but not quite.... a 99.7% chance and these numbers are static, they're always 68, 95 and 99.7 so 99.7% chance that the test scores will be between a 38 and a 122! Very rare it would be for a test score to be greater than 122 or less than 38 it is possible. But it is very rare - highly unusual. and actually statistically speaking it is unusual to be greater than 2 standard deviations above or below the mean. so it would be unusual to have a test score greater than 108 or less than 52 because 95% of the time we fall within this region which means we only have a 5% chance or a 2.5% chance of being greater than 108 and also a 2.5% chance of scoring less than a 52

Video Details

Duration: 7 minutes and 38 seconds
Country: United States
Language: English
Producer: D. Cichocki
Director: D. Cichocki
Views: 283
Posted by: cichocki on Sep 16, 2010

Basic concept of Empirical Rule

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