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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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The standard deviation must be greater than or equal to zero.

A standard deviation of zero means that all the data points are the same value.

The standard deviation is a measure of how much variation there is in a data set. It can be zero only if all the values are exactly the same - no variation.

A standard deviation of 0 implies all of the observations are equal. That is, there is no variation in the data.

No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.

Yes

Because the average deviation will always be zero.

no

Its zero dummy

Variance is standard deviation squared. If standard deviation can be zero then the variance can obviously be zero because zero squared is still zero. The standard deviation is equal to the sum of the squares of each data point in your data set minus the mean, all that over n. The idea is that if all of your data points are the same then the mean will be the same as every data point. If the mean is the equal to every data point then the square of each point minus the mean would be zero. All of the squared values added up would still be zero. And zero divided by n is still zero. In this case the standard deviation would be zero. Short story short: if all of the points in a data set are equal than the variance will be zero. Yes the variance can be zero.

If the standard deviation of 10 scores is zero, then all scores are the same.

A negative Z-Score corresponds to a negative standard deviation, i.e. an observation that is less than the mean, when the standard deviation is normalized so that the standard deviation is zero when the mean is zero.

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