Which measure of central tendency is defined as the value for which half the observations are higher and half are lower?

The median is the measure of central tendency that represents the middle value in a dataset when it is ordered from least to greatest. This means that when you arrange all the observations, the median is the point that divides the dataset into two equal halves: one half has values greater than the median, and the other half has values lower.

This characteristic of the median makes it particularly useful in datasets that may contain outliers or skewed distributions, as it provides a better central location than the mean in such cases. When the data is not symmetrically distributed, the mean can be significantly affected by extreme values, whereas the median remains a more robust indicator of central tendency.

In contrast, the mean is the average of all observations and can be influenced heavily by outliers, while the mode represents the most frequently occurring value and does not provide information about the distribution of all values. Variance, on the other hand, measures the spread or dispersion of the dataset rather than a central tendency. Therefore, the median is correctly identified as the value for which half the observations are higher and half are lower.