If more people understood statistics (and how they can be manipulated to make you think one ting when the data shows another) the government would have a much harder time fooling the people some of the time...
Happily they have done so much lying people are starting not to believe the government any of the time...which is just as bad. You should be able to tell the difference...using the mathematics as a guide.
Anyhow, here is a quick explanation of The Empirical Rule since I am on a kick where I show people I don't just do math for little kids...
A FB friend was embarrassed to ask me for further explanation because apparently she wasn't getting from here community college. My response:
No need to be embarrassed at all. That's what I'm here for...in fact please let some MCC students who are in college algebra like Math 23 know I exist. I hear many are failing Math 23: that's sick and wrong.
The Empirical Rule says that if you go 1 standard deviation out from the mean that you will capture 68 % of your data. Go out one more standard deviation (thats 2 so far) and you will capture 95% of your data, go out one more standard deviation (thats 3 so far) and you will capture 99.7% of your data. That's it.
Ok, so what the heck does all of that mean?
Lets try a simple problem.
You ask a bunch of young children how many gifts they got for Xmas. Lets say that the average (mean) answer is 10 gifts. The standard deviation is 3. This means that you start at 10 and go one standard deviation in both directions (one out each way 1 "up" an 1 "down"). 1 standard deviation from the mean in both directions will give you 7 and 13. (10 + 3 and 10 - 3)
Why? Because the mean is 10 and the standard deviation is 3 and three above the mean is 13 and 3 below the mean is 7.
Thus, out of all the kids that we asked this question to, 68% of them answered that they received 7 to 13 gifts.
How do we know this? Because 1 standard deviation away (remember you have to go in BOTH directions) will capture 68% of the data.
1 standard deviation away captures 68% of the data.
Now, lets go 2 standard deviations away. If the mean is 10 and the standard deviation is 3, then 2 standard deviations away from the mean would be 4 and 16. (10 - 6 and 10 + 6 (and 6 = 3x2 the amount of the stan dev is 3 and the number of them is 2))
Since you went 2 standard deviations away from the mean you have captured 95% of your data.
That means that out of all those kids you asked, 95% of them said that they received between 4 and 16 gifts...statistically speaking.
Now lets go three standard deviations out. Remember this, the empirical rule is also called the 68-95-99.7 rule because it gives you that info every time.
Remember that: 68-95-99.7, a really fat pear shaped woman.
Go three standard deviations out from the mean and you get 1 and 19.
(10 - 9 and 10 + 9 which is just plus or minus 3 x 3).
3 standard deviations captures 99.7% of the data.
NOW, this means that out of all those kids you asked 99.7% of them said that they received from 1 to 19 gifts. The poor little kid who only got one present or maybe they were naughty and the fat rich spoiled little kid who got 19 presents are all in there. Now there may have been some kids who got ZERO and some who got 20 or more BUT The Empirical Rule says we get 99.7 which is almost all but not all but not all of them.
Can we go out another standard deviation, that is 4 standard deviations from the mean? In a world were we can have negative gifts we can...
Now what would happen if the standard deviation was only 2?
Get it? If not I am available at 6 or a little after and I charge 40 bucks an hour...if you would like FREE tutoring find me some parents who have kids and whom want math enrichment for them, every two classes they pay for you get a class FREE.
Also I'll give you a class for 30 bucks as an introductory offer...if you come here and if you promise to tell a few people who have young kids to come see me BEFORE they start having trouble with math...
A TI-83 calculator from Texas Instruments will do ALL of the work for you I am told but I don't know how to use one...
Copy a problem that's giving you a problem here for me to see...the video is dry and boring but the info is there...put "The Empirical Rule" into a Youtube search...