/sci/ - Science & Math

A customer ordered 120 ball-bearings of
diameter 6.1mm. 120 ball-bearings were
supplied but accurate measurements showed
that the diameter did not met the required
specifications. Namely, they were:


10 ball bearings with diameter 6.01 mm
6 ball bearings with diameter 6.02 mm
4 ball bearings with diameter 6.03 mm
10 ball bearings with diameter 6.05 mm
19 ball bearings with diameter 6.07 mm
11 ball bearings with diameter 6.08 mm
6 ball bearings with diameter 6.10 mm
6 ball bearings with diameter 6.11 mm
8 ball bearings with diameter 6.12 mm
10 ball bearings with diameter 6.14 mm
17 ball bearings with diameter 6.16 mm
6 ball bearings with diameter 6.17 mm
7 ball bearings with diameter 6.18 mm


Fortunately, another customer agreed to accept
the ball-bearings under the following conditions:
• the ball-bearings are to be supplied in 2 boxes, one
containing the larger ones, and the other containing
smaller ones,
• 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.
How to determine d?