range

[kris610]

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?

[VP_Tatiana]

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

[Ian Stewart]

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?

The range of a one-element set is zero. This follows from any definition of the range (range = largest - smallest; range = largest distance between any elements in the set; range = distance of the smallest interval in which all data points can be found). Note that the range certainly will not be equal to the value of the single element in the set, because then you could easily violate one of the fundamental properties of the range: if you add an element to a set, the range can never decrease.

You will, however, never be tested on this type of technicality on the GMAT.

[VP_Tatiana]

Thanks Ian! That's what my gut told me, but a weird range function in a mathematical program I found online returned the value. That's why math people and CS people are rivals!

; )

Tatiana