Find a sample size for which the median will always equal one of the values in the sample

Any odd sample size, larger than 1.

Step-by-step explanation:

We use the median to find the "middle" value of a sample, that is, the value separating the lower half from the upper half of the sample.

If the size of the sample is even

1,2,3,4

Both the upper half and the lower half should have the same size.

In this case, it is not possible to select only one value which respects this condition. So the mean between 2 and 3 = 2.5 is calculated. This value is not part of the sample.

If the size of the sample is odd

1,2,3,4,5

For a n-sized sample, with n odd, the median is the value at the position (n+1) / 2. So her, it is 3, the value at the third position. In this case, it is always going to be an element at a position in the sample, that is, an element of the sample.