10/2001 Steve Sailer on Bell Curve Calculations:
How to do Bell Curve calculations in Excel:
Say you want to find number of people with IQ of 145 or higher out of 200
million.
First, type "200000000" into a cell (without the quotes).
Then, in the cell next to it, type an "=" (without the quotes).
In the leftmost box in the first row above the column letters, click on the
down arrow. This gives you a list of recently used "functions."
Click on "More Functions" at the bottom of that list that pops up.
Then click on "Statistical" in the left hand list that pops up.
Then, you'll find NORMDIST in the right hand list of Statistical functions.
Highlight that and click on "OK"
This brings up a handly little fill-in-the-blanks table:
Here's the variable's you plug in to Normdist for this problem.
X = 145
Mean = 100
Standard_dev = 15
Cumulative = True
(The last 3 variables are always the same if you are looking at a general
population. For subgroups, the mean and S.D. can change, of course.)
Hit Enter. That gives 99.87% - the proportion of the population with IQs
below 145. 100%-99.87% = 0.13%, which is the proportion at 145 or above. Then
multiply 200,000,000 times 0.13% to get roughly 270,000.
Just plug a different X and a different population size to use for any bell
curve related question. Sure, there are wrinkles that Charles Murray would
worry about, but this method is good enough for quick calculations.
Steve Sailer
To do the same calculation I start, after opening Excel, by clicking
on the Function button/icon [f x] in the top row and choosing amongst
Statistical functions the NORMDIST.
That gives the opportunity to type a figure in the space with a z on
the left. The explanatory "z is the value for which you want the
distribution" may not help much but what you get below if you type in
a figure, positive or negative, is the "standard normal cumulative
distribution (for mean 0 and standard deviation 1). So if you type
in 3 because you know that 145 is three SDs above the average you
immediately get the figure .998650033 (99.87% as Steve puts it).
For even greater efficiency you put in -3 (minus 3) and go straight
to the figure you need,viz. .001349967. You then multiply it by 200
million or whatever the relevant population figure is.
For maximum ease and speed consider having Microsoft Windows
calculator [calc.exe] open at the same time as Excel so you can, eg.
most quickly and reliably determine how many SDs above average an IQ
of 135 is if the average is 115 and the SD 16.5
Too bad if the curve isn't much like a Bell Curve at the interesting
parts.
James Guest
Ken Hirsh adds:
Also, if you want to use Griffe's method of thresholds to calculate
the standard differences of proportions, in Excel that would be:
=normsinv(PCTA)-normsinv(PCTB)
For example, the difference between a pass rate of 68% and a pass
rate of 30% =normsinv(.68) - normsinv(.3)