A hard one about standard deviation

Statement I:

Set A: 1,10,11,12,13,14,15,16
Set B: 2,3,5,7,10,13,15,16

Now it's quite impossible to calculate the two standard deviations for the above sets in two minutes, but because the gaps in set B are bigger, it will also have a greater stdev than set A despite a smaller range.

INSUFFICIENT

Statement II:

I made a mistake her when thinking about it the first time. Evenly spaced doesn't mean that the distance between two terms is equal! It just means that the distance between any two adjacent terms in one set is equal.

Set A: 2,4,6
Set B: 2,10,18

Obviously set B has the bigger standard deviation here. If you switch the terms of the two sets, set A has the bigger standard deviation.

INSUFFICIENT

Both statements together:

When set A has a greater range than set B and both sets are evenly spaced and both sets have the same number of terms, then set A must have the bigger standard deviation.


for example:
Set A: 1,4,7
Set B: 1,3,5

SUFFICIENT

Hence, the answer is C.

Koala wrote:If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B?

1) The range of set A is greater than the range of set B

2) Sets A and B are both evenly spaced sets

From Veritas Prep Free Test ==> OA is C

Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:

Do the values in set A deviate more from the mean than the do values in set B?

Statement 1:
The distance between the biggest value and the smallest value in set A is greater than the distance between the biggest value and the smallest value in set B. But we don't know how all the other values in each set are deviating from the mean, so there is no way to determine the standard deviation. Insufficient.

Statement 2:
When values are evenly spaced, mean = median. Thus the median in each set -- the middle value -- is also the mean. But we can't determine the standard deviation without knowing the distance between each successive pair of terms.

A could be {1,2,3}, and B could be {1,2,3}. The standard deviations are equal.
A could be {100, 200, 300}, and B could be {1,2,3}. The standard deviation of set A is larger.
Insufficient.

Statements 1 and 2:
The values in each set are evenly spaced, so the mean in each set is the median (the middle value). If sets A and B had the same range, their standard deviations would be equal: the biggest value and the smallest value in each set would be the same distance from the mean. But since the range of set A is greater than the range of set B, the biggest value and the smallest value in set A are each further from the median than are the biggest value and the smallest value in set B. Thus, set A has a greater standard deviation. Sufficient.

The correct answer is C.