ha15 wrote:
Is it true that when the number of terms in a set is even, then it can’t be concluded that 50% of terms are greater/less than or equal to the median?
But then, the I found the following statement in an official answer: The average of a set of consecutive integers is also the middle of the set, with an equal number of terms greater and smaller than it.
Is that statement only ALWAYS true for when the number of consecutive terms are NOT even?
Say there are 4 numbers in a set:
2, 5, 6, 8
Median will be the average of 5 and 6. 50% elements are smaller than the median and 50% elements are greater than the median.
2, 5, 5, 9
Median will be 5. 1 element is smaller, 2 are equal and 1 is greater.
This statement talks about the average: "The average of a set of consecutive integers is also the middle of the set, with an equal number of terms greater and smaller than it. "
Median is not discussed here at all. This is regarding arithmetic mean. Generally, there are no such constraints for arithmetic mean (also called average).
e.g 2, 5, 6, 9 - Avg is 5.5
1, 2, 3, 14 - Avg is 5
If there is at least one element smaller than the average, there has to be at least one which is greater. But how many will be smaller and how many greater, we cannot say.
Consecutive integers are different. Their median = arithmetic mean = Middle value
If you have odd number of consecutive integers, middle value will be the middle integer. 3,
5, 7
If you have an even number of consecutive integers, middle value will be the average of two middle integers. 3,
5, 7, 9
In fact, this is true for all arithmetic progressions.
Check these posts for details:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/categor ... om/page/6/Go down the page. The first post you should look at is "The Meaning of Arithmetic Mean" of April 24. Then one - by - one check out the 4-5 posts above it.