In an ordered set of data, which value separates the bottom 50% from the top 50%?

The value that separates the bottom 50% of a data set from the top 50% is known as the median. The median is calculated by arranging the data points in ascending order and identifying the middle value. If there is an even number of observations, the median is the average of the two middle values. This characteristic makes the median a robust measure of central tendency, as it is not affected by extreme values or outliers in the data.

In contrast, the mean, while also a measure of central tendency, is calculated as the sum of all data points divided by the number of points, and it can be skewed by very high or very low values. The mode indicates the most frequently occurring value in a data set, which does not provide information about the overall distribution of the data. The range is simply the difference between the maximum and minimum values in the data set and does not imply any central dividing point. Therefore, the median is the correct choice for identifying the point that divides the data into two equal halves.