Question

what would a standard deviation of 0 indicate about a dataset?
a. the data contains no values
b. all data points are the same
c. the mean of the data is 0
d. the data points are spread widely apart

Explanation:

• Option a: A dataset with no values is an empty dataset, but standard deviation is calculated for datasets with values, so this is incorrect.
• Option b: Standard deviation measures the spread of data. If all data points are the same, the difference between each data point and the mean (which would also be that same value) is 0. So the standard deviation, which is based on these differences, would be 0. This is correct.
• Option c: The mean being 0 has no direct relation to the standard deviation being 0. For example, data like -1, 0, 1 has a mean of 0 but a non - zero standard deviation.
• Option d: If data points are spread widely apart, the standard deviation would be large, not 0.

Answer:

b. All data points are the same