No, if the standard deviation is small the data is less dispersed.
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Standard deviation is a measure of the spread of data.
Standard deviation is the variance from the mean of the data.
The smaller the standard deviation, the closer together the data is. A standard deviation of 0 tells you that every number is the same.
You cannot. If you are told the standard deviation of a variable there is no way to tell whether that was derived from grouped or ungrouped data.
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.!