In statistics, what does the $\mathrm{median}$ represent in a set of numbers?

• A. The difference between the largest $x$_max and smallest $x$_min values in the data set
• B. The most frequently occurring value $\mathrm{mode}$ in the data set
• C. The arithmetic average $\frac{\sum x}{n}$ of all values in the data set
• D. The value $m$ that separates the higher half from the lower half of the data set

Answer: (D)

Verified step by step guidance

1. Understand that the median is a measure of central tendency, which helps to identify the middle point of a data set.
2. Arrange the data set in ascending order, from the smallest value to the largest value.
3. If the number of observations (n) is odd, the median is the value at position \( \frac{n+1}{2} \) in the ordered list.
4. If the number of observations (n) is even, the median is the average of the values at positions \( \frac{n}{2} \) and \( \frac{n}{2} + 1 \) in the ordered list.
5. Recognize that the median divides the data set into two equal halves: half of the values are less than or equal to the median, and half are greater than or equal to the median.