# 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