ABCTE Professional Teaching Knowledge Practice Exam

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What does a low standard deviation indicate about a data set?

The data is widely spread around the mean.
The data set has extreme values.
The data points are clustered closely around the mean.
The data points are randomly distributed.

The correct answer is: The data points are clustered closely around the mean.

A low standard deviation signifies that the data points in the data set are clustered closely around the mean. This means that most of the values tend to be near the average, indicating little variability or dispersion within the data. When standard deviation is low, it reflects that the values do not differ significantly from each other, resulting in a tighter grouping around the central measure of the data. In contrast, a high standard deviation would indicate that the data points are spread out over a wider range of values, which is not the case here. Additionally, extreme values or outliers would increase the standard deviation, highlighting that the data is not tightly grouped. Randomly distributed data would also not suggest a low standard deviation, as this implies variability rather than close clustering. Thus, a low standard deviation directly correlates with data points being closely clustered around the mean, providing insight into the consistency and reliability of the dataset.