Question 824725
The {{{highlight(mean)}}} would be the most useful of the listed measurements,
because {{{6*mean=sum}}}{{{of}}}{{{weights}}} .
If the mean is {{{mean<=200pounds}}} ,
then {{{total}}}{{{weight=6*mean<=6*200pounds=1200pounds}}} ,
and the 6 people can ride together.
 
If we knew that the median and mode were both {{{200pounds}}} we would still not know if the 6 people could ride together.
Maybe 4 of them weigh {{{200pounds}}} with their equipment, a fifth person is lighter and the sixth person is heavier.
That would make {{{median=mode=200pounds}}} , but it would all depend on the weights of the fifth and sixth people.
If their weights (including equipment) add up to {{{400pounds}}} or less the total weight would be
{{{total<=4*200pounds+400pounds=1200pounds}}} and they can ride together.
The range would not help either, unless we knew the range did not include {{{200pounds}}} .
If the range was fully below {{{200pounds}}} we would know each person weighs less than {{{200pounds}}} including equipment,
and the total would be less than {{{6*200pounds=1200pounds}}} .
If the range was fully above {{{200pounds}}} we would know each person weighs more than {{{200pounds}}} including equipment,
and the total would be more than {{{6*200pounds=1200pounds}}} .
If the range includes {{{200pounds}}} , we have no clue.
With a {{{160pounds}}} to {{{210pounds}}} range,
we could have five {{{210pound}}} people and one {{{160pound}}} person for a total weight of
{{{5*210pounds+160pounds=1050pounds+160pounds=1210pounds}}} , or
we could have five {{{160pound}}} people and one {{{210pound}}} person for a total weight of
{{{5*160pounds+210pounds=800pounds+210pounds=1010pounds}}} .