evenly spaced sets

[mohankumar_bd]

hi,

I came across set of rules for evenly spaced sets. found the two below

a. average of odd no. of terms in a set will yield an integer
b. average of even no. of terms in a set will yield not yield an integer

This seems to contradict the below evenly spaced set. Any pointers to the exact rule please

set = {5,7,9,11} . here average is 5+7+9+11/4 = 8

[LazyNK]

Hey Mohan,
I think you have misinterpreted/mis-worded the rule for evenly spaced sets. I do the necessary corrections in the rules you mention below :
a. average of odd no. of terms in a set will yield an integer (but only if each element is an integer i.e. the first term and the difference between consecutive terms are both integers)
b. average of even no. of terms in a set may but not necessarily will yield yield an integer (for example, when all the elements are even integers or all elements are odd integers, its average will be an integer)
Hope this clarifies,
NK

[mohankumar_bd]

Hey Mohan,
I think you have misinterpreted/mis-worded the rule for evenly spaced sets. I do the necessary corrections in the rules you mention below :
a. average of odd no. of terms in a set will yield an integer (but only if each element is an integer i.e. the first term and the difference between consecutive terms are both integers)
b. average of even no. of terms in a set may but not necessarily will yield yield an integer (for example, when all the elements are even integers or all elements are odd integers, its average will be an integer)
Hope this clarifies,
NK

Hi NK,

Thank you for your response. But the two rules that i mentioned should hold good in case of consecutive integers i suppose?

[LazyNK]

Hi Mohan,
Yes, the rules you mention hold good for consecutive integers, which is a specific type of evenly spaced set. But in your post, you mentioned that those rules are valid for all evenly spaced sets, so I corrected.
If you look at the corrected rules which I have mentioned, you'd see that the conditions I mention for the mean/median to be an integer are true for consecutive integers.
-NK

[jnelson0612]

Again, LazyNK, thanks for your excellent contributions to the forum! Nice work.

[hkparikh09]

Thank you. I had this same question. This explanation helps a lot.

[RonPurewal]

the most important thing to say here is that it's completely unnecessary to memorize any of this stuff.

first, it's really hard to memorize it with any accuracy. for evidence of that, just look at this thread.

second, if you ever have to use these facts, you can discover (or re-discover) them within a few seconds, just by looking at a few examples until you see the pattern(s) involved.

if you memorize unnecessarily specific or intricate facts, that will make the thinking process harder, not easier.