Does a set with just one element have a range? I'm just wondering if a DS question asks whether the range of a non-empty set is greater than its mean and does not explicitly specify anything about the number of elements in the set, should I consider a one-element set?
Hi Kris,
That's a good question. To be honest (and I was a math major), I'm not sure what the range of a one element set would be... if it would be 0 or the value. Anyone else?
We can actually solve the problem without this knowledge, though.
Ex 1: Mean is greater than range. Look at the set {4, 4}. The range is 0 and the mean is 4.
Ex 2: Range is greater than mean. Look at the set {1, 4}. The range is 3, and the mean is 2.5.
Since we can come up with two different answers, we do not have sufficient information to determine if the range is greater than the mean of a non-empty set.
Tatiana
