/sci/ - Science & Math

>>4700000
you should close your business if you can't afford a fucking micrometer to check these massive inaccuracies..

>>4700021
Agreed, this is simply unacceptable. Any self respecting business owner should not allow such inaccuracies.

Also if a customer said to me:
>the critical diameter d which separates ball-bearings
into 2 boxes ( all with diameters ≤ d go to the first box;
all with diameters > d go to the other box) should have
the property that the sum of absolute errors between the
diameters of all ball-bearings and d is minimized.

I would punch him in the face.

i've read the last paragraph several times and it just doesn't make sense to me.
wtf is it saying d is?

The question is stupid, but the problem is still a problem.

The question is, at which diameter do you decide 'this ball bearing goes in the small box' or 'this ball bearing goes in the big box', while keeping the sum of the differences between the ball bearings and that point at the minimum possible

>>4700042
if he ordered d=6.1 I think d is 6.1

>>4700000
define ball bearing..

>>4700000
your bearing machine might need some checkin' done
just sayan

What you want to do is minimize the function

f(d) = 10*|6.01-d| + 6*|6.02-d| + ... + 7*|6.18-d|

Since there are only 15 options for d and from looking at the problem it should be somewhere around 6.09, just put that shit into a calculator and try to find the d for which f(d) is lowest.

>>4700115
Would make sense to pick d as the average diameter.

>>4700000
What a pushover customer! Who pays for faulty goods?!

pick the mean you retard

some vile inequality proves the mean is best

d= 6.09725
it is not the mean (the mean is 6.097479)

>sum of absolute errors between the
diameters of all ball-bearings and d is minimized.
How to determine d?
I can do better, i can make it zero (or wrong in one part in a million).


check the attached picture. Using excel, list out the information. the question is equivalent to asking to find d where the sum of the errors is minimised.
for example: let a,b,c...f be the errors

|a+b+c|-|d+e+f| is the same as a+b+c-d-e-f if {a,b...f}>0

so in difference, put the number multiplied by d-X (where x is the diameter).

sum it up, and use solver. changing the d term to make the sum zer.

>>4700000
dem quints

>>4700248
I'm sure f(d) as defined earlier is constant on the interval 6.08 through 6.1. If you're getting near zero values, I'm pretty sure you forgot the absolute value.

>>4700248
you done derped

If you want to see why it's constant in ]6.08, 6.1[, notice the number of ball bearings with diam < 6.08 is 10+6+4+10+19+11 = 60, half of them. So for any of those diameters X, with d in that interval, |X-d| = d-X. For the others, |X-d| = X-d.
Summing that over the first half of the diameters you get (some constant) - 60d.
Summing that over the latter half of the diameters, you get (Some other constant) + 60d.
Adding them cancels out the d, and your function is constant.