Which of the following comparisons is false regarding standard deviation and range?

The statement that range is always equal to standard deviation is false because these two measures of dispersion are fundamentally different and typically yield different values.

Range calculates the difference between the maximum and minimum values in a dataset, providing a straightforward measure of the total spread of the data. In contrast, standard deviation assesses how much the individual data points deviate from the mean of the dataset. Since the standard deviation takes into account the distribution of all data points, it reflects how close or far these points are from the average.

In most cases, unless all data points in a dataset are identical (or in a very specific arrangement) leading to a standard deviation of zero, the range and standard deviation will differ, making it incorrect to state that they are always equal. This illustrates that while both measures describe variability, they do so in different ways, resulting in distinct numerical values under typical conditions.