Definition Standard Deviation - Working vs. Thinking

I

imceepee

#1
A student of business statistics asked me, based on a homework assignment, what the difference is between the "working" formula and the "thinking" formula in calculating a standard deviation.

:frust: I am at a lost.

:confused: Anybody have a clue?
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#2
imceepee said:
A student of business statistics asked me, based on a homework assignment, what the difference is between the "working" formula and the "thinking" formula in calculating a standard deviation.

:frust: I am at a lost.

:confused: Anybody have a clue?
It's possible the reference is to calculating the standard deviation using the range values on a moving range or xbar - R set of charts versus using the statistical formula (like "stdev" in excel) to calculate the standard deviation.
 

Tim Folkerts

Super Moderator
#3
Perhaps if has to do with the fact that there are two equivalent ways to calculate the stdev.

The familiar way is find the differences, square them, and then sum the results:
s = [ sum( x(i) - x-bar)^2 / n-1 ] ^ (1/2)

It turns out you can also square first and then sum
s = [ sum( x(i) )^2 - n*(x-bar)^2 / n-1] ^ (1/2)

It is often less work to do the calculations the second way, but it takes a bit of thinking to get to that equations. So perhaps the first equation is the "working" way and the second equation is the "thinking" way.

Just a guess; I haven't heard this terminology before.


Tim F
 
R

ralphsulser

#4
How about:
Working-using calculations to define and quantify
Thinking-How the variation affects you process and /or product, and do you need to do anything.
Just a couple quick thoughts on the subject
 
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