The variable diameter refers to the shortest distance from side to side at the candy's widest height when it is placed flat on the table with the "m" facing up.
Put otherwise, when the candy is placed in that position, imagine taking horizontal cross-sections of the candy.
They will be roughly elliptical.
The diameter of the candy is the length of the minor axis of the largest such cross-sectional ellipse (which will generally be the cross-section at half the total height).
As you might expect, this axis can be somewhat difficult to determine and was no doubt a source of measurement error, but this definition of diameter does correspond fairly well to the way that an M & M fits into a caliper.
Diameters were measured with a General Tools Ultratech Fraction+ Digital Fractional Caliper (claimed accurate up to plus or minus 0.02mm),
and masses were measured with a MyWeigh Durascale 50 (claimed accurate up to plus or minus 0.01 g).
The candies were measured in the order given in the data set, which although not entirely random was not intentionally systematic in any way (other than by type).