What statistical measure divides a data set such that half of the values lie above and half lie below?

The median is the statistical measure that effectively divides a data set into two equal parts, where half of the data values are below it and half are above it. This characteristic makes the median a valuable measure of central tendency, particularly in skewed distributions where the mean can be influenced by extreme values.

In a sorted list of numbers, finding the median involves locating the middle value. If the data set has an odd number of observations, the median is simply the middle number. If there is an even number of observations, the median is the average of the two middle numbers. This ensures that the median is always representative of the central location of the data set, regardless of its distribution.

Other statistical measures, such as mean, standard deviation, and variance, do not serve this purpose of dividing the dataset into halves in the same way. The mean is affected by all data points and can be skewed by outliers, while the standard deviation and variance measure the spread of the data rather than its central tendency. Thus, the median remains the correct choice for identifying the middle point of a data set.