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Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.

A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.

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Q: Can standard deviation equal zero
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