What central value is used in a data set arranged in order of increasing size?

The median is the central value in a data set that has been arranged in order of increasing size. To find the median, you organize the data from the smallest to the largest value and then identify the middle number. If the data set has an odd number of observations, the median is the value at the center. If there is an even number of observations, the median is calculated as the average of the two middle numbers.

This characteristic of the median makes it particularly useful for understanding the central tendency of a data set, especially when the data contains outliers or is skewed. Unlike the mean, which can be heavily influenced by extreme values, the median provides a clearer perspective of the typical value in the data set.

In contrast, the mean signifies the arithmetic average of all values, the mode refers to the most frequently occurring value, and the term "average" is often used interchangeably with the mean in everyday language, but it does not specifically point to the central value in ordered data. Therefore, the median is the correct choice for identifying the central value in an ordered data set.