consecutive numbers

[kuleen]

hello

this is regarding consecutive numbers. I always get confused say if asked, find average between positive integers 50 and 700 inclusive or without inclusive..how will it affect the solution and way to solve it.

thanks

[Guest]

in consecutive series of numbers including odd and even series...the mean(average) = median = sum of end points/2
hence if u include the no's between 50 & 700 its (50+700)/2 or else (49+699)/2

[RonPurewal]

hello

this is regarding consecutive numbers. I always get confused say if asked, find average between positive integers 50 and 700 inclusive or without inclusive..how will it affect the solution and way to solve it.

thanks

interestingly enough, the average of those integers is completely unaffected by whether the collection is inclusive of the endpoints 50 and 700.

here's why:

in any symmetric set - a description that includes all sets of consecutive integers - the average of the set, as has been pointed out by the poster above me, is just the average of the first and last terms. in fact, because of symmetry, the average is equal to the average of any two terms that are symmetric about the middle number, but the first and last are usually the easiest to figure out and think about.

so:
if the set includes 50 and 700 ('inclusive'), then the average of the set is the average of 50 and 700, which is 375.
if the set excludes 50 and 700, then the average of the set is the average of 51 and 700, which is still 375.

visually, the average doesn't change because you're pinching off the top and bottom numbers, which themselves are symmetrically distributed about the mean. therefore, the overall symmetry is undisturbed.

--

there is one mistake in the post above: if 50 is excluded, then the new lowest number is 51, not 49.

[kuleen]

Thanks a million