Quantitative Literacy Practice Exam

Which of the following statements about standard deviation is true?

1. It can never be zero.

2. It reflects how much the data varies from the mean.

3. It is only used for large data sets.

4. It indicates the central tendency of data.

The correct answer is: It reflects how much the data varies from the mean.

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. When the standard deviation is low, it indicates that the data points tend to be close to the mean (or expected value), while a high standard deviation indicates that the data values are spread out over a wider range. In this context, the statement that the standard deviation reflects how much the data varies from the mean accurately captures its role in statistics. It provides insight into the distribution of values within a dataset, enabling researchers and analysts to understand the degree of variability around the average value. This is fundamental in many fields such as quality control, risk assessment, and in the interpretation of data distributions. The other statements do not correctly convey the properties of standard deviation: it can be zero when all data points are identical, it is applicable to both small and large datasets, and it does not indicate central tendency but rather variability. Thus, the true nature of standard deviation is well represented by its ability to reflect how much the data varies from the mean.