What happens when your standard deviation is small?
The data is clustered around the mean
When the standard deviation (SD) is small, it indicates that the data points in a set are clustered around the mean and there is little variation in the data. This means that the values are close to each other, and the average is a good representation of the data.
For example, consider a set of exam scores for a class of students. If the SD is small, it means that the majority of students scored similarly on the exam. This suggests that the exam was neither too difficult nor too easy, and that the scores are reliable in measuring students’ knowledge of the subject matter.
A small SD can also indicate that a process is highly controlled and predictable. For instance, if a factory produces a batch of items and the SD of the weights is small, it means that the items are uniform in weight and the production process is consistent.
In summary, a small standard deviation means that the data points are close together and have little variation. This can be an indication of consistent results and reliability in the data.
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