Re: Standard Deviation & the 68-95-99.7 rule
- From: "FredJeffries@xxxxxxxxx" <FredJeffries@xxxxxxxxx>
- Date: Fri, 21 Dec 2007 13:02:41 -0800 (PST)
On Dec 21, 11:39 am, Maya <maya_s...@xxxxxxxxxxx> wrote:
At the bottom of the intro to the Wikipedia entry on the 68-95-99.7
rule, it states:
"This rule is often used to quickly get a rough estimate of
something's probability, given its standard deviation."
What an awful sentence.
What " thing's " probability could I estimate, given the thing's
standard deviation? Let's say I have this data set: {6, 6, 8, 8} .
It's standard deviation is 1. So, given its "1", I can estiate the
probability of ..... what?
http://en.wikipedia.org/wiki/68-95-99.7_rule
You also need the mean, in the case of your data set 7. So the
68-95-99.7 rule says that about 68% of observations will be within 1
of 7 (between 6 and 8), 95% within 2 of 7 (between 5 and 9) and 99.7%
within 3 of 7 (between 4 and 10) IF your data set were distributed
normally.
Say you have a normally distributed data set with mean 7 and standard
deviation 1. Pick an element at random from your set. The probability
of that element's being between 6 and 8 is 68%, the probability of its
being between 5 and 9 is 95%, etc.
There is a better example at the bottom of this page:
http://www-stat.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html
.
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