What is the role of the median in a data set?

The median serves the specific function of dividing a data set into two equal halves. When a data set is ordered from smallest to largest, the median is the middle value. If there is an odd number of observations, the median is simply the middle number. In cases where there is an even number of observations, the median is calculated by taking the average of the two middle numbers. This characteristic makes the median particularly useful in assessing the central tendency of a data set, especially when the data contains outliers or is skewed, as it is not affected by extreme values.

In contrast, the other options describe different statistical concepts. The first option refers to the mode, which identifies the most frequently occurring score in a data set. The arithmetic average, mentioned in the third option, relates to the mean, which sums all values and divides by the number of observations. The fourth option pertains to the concept of variability, often measured by the range, variance, or standard deviation, rather than a measure of central tendency like the median. Understanding the distinct roles of these statistical measures is crucial for interpreting data sets appropriately.