Which descriptive statistic identifies how 'spread out' the data is?

The correct choice is variance because it is a measure that quantifies the extent to which data points in a dataset differ from the mean of that dataset. By calculating the variance, you can assess the dispersion or spread of the data from the average value. A higher variance indicates that the data points are more spread out from the mean, while a lower variance suggests they are closer to the mean. This is particularly useful in statistics for understanding the variability within the data, allowing researchers to perceive trends, identify outliers, and make predictions.

In contrast, the mode, mean, and percentile are all measures of central tendency or position rather than measures of spread. The mode refers to the most frequently occurring value in the dataset, the mean is the arithmetic average of all values, and the percentile indicates the value below which a certain percentage of observations fall. These statistics provide insights into the location of the data points rather than their distribution or variability within the range.