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evenly spaced sets - question

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evenly spaced sets - question [#permalink] New post 27 Feb 2012, 22:00
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

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Re: evenly spaced sets - question [#permalink] New post 27 Feb 2012, 22:56
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mohankumarbd wrote:
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


b. is not correct.

In any evenly spaced set the arithmetic mean (average) is equal to the median and can be calculated by the formula (first+last)/2.

If an evenly spaced set contains odd number of integers then: {mean}={median}={middle term}={integer};
If an evenly spaced set contains even number of integers the: {mean}={median}={average of two middle terms}, which may or may not be an integer.

For more check Number Theory Chapter of Math Book: math-number-theory-88376.html

Hope it helps.

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Re: evenly spaced sets - question [#permalink] New post 29 Feb 2012, 04:39
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mohankumarbd wrote:
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


Wherever you read these rules, go back there again and check: You will probably find that they were talking about a set of consecutive integers. In that case, both the rules apply (assuming that there is at least 1 number in each set).

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Re: evenly spaced sets - question   [#permalink] 29 Feb 2012, 04:39
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