What does it mean to have a standard deviation of 0?
Standard deviation indicates the quantity by which the data points in a set of data differ from each other.
Answer: If we have a standard deviation of 0, then this implies that all the elements of the set are equal. Elements of the group are no different from the mean.
Let us see how we will use the concept of standard deviation in order to find the required answer.
The definition of standard deviation states that standard deviation is a quantity expressing by how much the elements of the group differ from the mean of the group.
Hence, if we have a 0 standard deviation then it is clear that elements of the group are no different from the mean and hence, the list of elements doesn't differ from each other also. This implies every element is equal.