Prompt: What is the standard deviation of 5 numbers?
Normally, the only way you would have the information to know the standard deviation of a list is to know every single entry on the list. One exception is the special case in which all the numbers on a list are identical. Then, standard deviation would equal zero.
Statement #1: Mean=the greatest number
So, no number on the list is greater than the mean. In order for it to be the mean, that must also mean: no number on the list is less than the mean. In other words, the only way the greatest number on a list equal the mean is if all numbers on the list are identical. If that's the case, standard deviation = 0. Statement #1 is sufficient.
Statement #2: Range=0
If range = (max) - (min) = 0, that means (max) = (min) --- the highest and lowest numbers are equal, which means all five numbers on the list are equal, which means the standard deviation = 0. Statement #2 is sufficient.
Answer = D
Does that make sense? Let me know if you have any questions on this.
Mike
