Question

fill in the blank so that the resulting statement is true.
if n data items are arranged in order, from smallest to largest, the data item in the middle is the value in position.

Explanation:

Step1: Consider the formula for the position of the median

When \(n\) data items are arranged in order (from smallest to largest), if \(n\) is odd, the median is the \(\frac{n + 1}{2}\) -th data item. For example, if \(n=5\), then \(\frac{5+1}{2}=3\), and the median is the 3rd data item. If \(n\) is even, the median is the average of the \(\frac{n}{2}\) -th and \((\frac{n}{2}+1)\) -th data items. But the formula for the position of the middle - like value (in the sense of the formula for the index in the ordered list) when considering the single - value representation (even though for even \(n\) we take an average) is still based on the formula \(\frac{n + 1}{2}\) (it gives the non - fractional part of the index for even \(n\) when we consider the two middle values).

Answer:

\(\frac{n + 1}{2}\)