if the value for the median of a set is not found in the data set what must be true about the data set?

Question

It's statistics question  pls help me 

Answer 1

How many elements are in the set if the median IS in the set?

 

The median is the value for which there are an equal number of values greater than it and less than it.  So let's suppose the number of values less then the median is x.  Then the number greater than the median is also x.  So the number of elements in the set is x + x, plus 1 for the median itself, or 2x + 1.  This is always an odd number.

 

If the median in NOT in the set, then you don't add in the extra value for the median, so the number of elements is 2x.  This is always an even number.

 

So the answer is that the data set has an even number of values.