FTCE General Knowledge Math Practice Test 2025 – 400 Free Practice Questions to Pass the Exam

The correct answer is indeed the statement that the standard deviation will always equal the range of the data set. This is not a characteristic of standard deviation.

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It indicates the average distance of each data point from the mean, making it a valuable tool for understanding the spread of the data. Unlike the range, which is simply the difference between the highest and lowest values in the dataset, standard deviation takes into account how each data point varies from the mean.

While standard deviation can only take positive values (since it involves squaring the differences from the mean), its relationship with the range is not fixed; they can be very different depending on the distribution of the data. For example, a dataset can have a large range but a small standard deviation if most of the values are clustered together. This further illustrates that standard deviation and range are distinct measures with different interpretations in the context of statistics.